\u5206\u7c7b\u8bc4\u4f30\u6307\u6807\u5b8c\u6574\u6307\u5357 \u00b7 Classification Metrics Guide<\/title>\n<style>\n*,*::before,*::after{box-sizing:border-box;margin:0;padding:0}\nhtml{scroll-behavior:smooth}\n:root{\n --bg:#f8f9fa;--bg2:#fff;--ink:#1a1a2e;--muted:#6c7086;--rule:#e2e4eb;\n --accent:#2563eb;--accent2:#16a34a;--accent3:#dc2626;--accent4:#d97706;--accent5:#7c3aed;\n --card-bg:#fff;--code-bg:#f1f3f5;--nav-bg:rgba(255,255,255,0.85);\n --cm-tp:#dbeafe;--cm-tp-t:#1e40af;--cm-fp:#fef9c3;--cm-fp-t:#713f12;\n --cm-fn:#fee2e2;--cm-fn-t:#991b1b;--cm-tn:#dcfce7;--cm-tn-t:#166534;\n --tag-g:#dcfce7;--tag-g-t:#166534;--tag-b:#dbeafe;--tag-b-t:#1e40af;\n --tag-r:#fee2e2;--tag-r-t:#991b1b;--tag-y:#fef9c3;--tag-y-t:#713f12;--tag-p:#f3e8ff;--tag-p-t:#581c87;\n --shadow:0 1px 3px rgba(0,0,.08);--radius:8px;--max-w:940px\n}\n[data-theme=\"dark\"]{\n --bg:#0b0b1a;--bg2:#16162a;--ink:#e2e4f0;--muted:#7f8396;--rule:#26263e;\n 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Mono\",Consolas,\"Courier New\",monospace;font-size:1rem;color:var(--ink);font-weight:600}\n.formula-box .formula-name{font-size:.82rem;color:var(--muted);margin-bottom:.5rem}\n\/* Metric bar *\/\n.metric-bar-container{background:var(--card-bg);border:1px solid var(--rule);border-radius:var(--radius);padding:1.25rem;margin:1rem 0;box-shadow:var(--shadow)}\n.metric-bar{display:flex;align-items:center;gap:.75rem;margin-bottom:.6rem}\n.metric-bar:last-child{margin-bottom:0}\n.metric-bar .label{font-size:.82rem;font-weight:600;width:90px;flex-shrink:0}\n.metric-bar .bar-bg{flex:1;height:24px;background:var(--bg);border-radius:4px;overflow:hidden;border:1px solid var(--rule)}\n.metric-bar .bar-fill{height:100%;border-radius:4px;display:flex;align-items:center;justify-content:flex-end;padding-right:.5rem;color:#fff;font-size:.75rem;font-weight:700;transition:width .5s ease}\n.metric-bar .value{font-size:.82rem;font-weight:700;width:50px;text-align:right;flex-shrink:0}\n\/* Scenario cards *\/\n.scenario-grid{display:grid;grid-template-columns:repeat(auto-fill,minmax(260px,1fr));gap:1rem;margin:1rem 0}\n.scenario-card{background:var(--card-bg);border:1px solid var(--rule);border-radius:var(--radius);padding:1.1rem;box-shadow:var(--shadow);border-top:4px solid var(--accent)}\n.scenario-card.spam{border-top-color:var(--accent4)}\n.scenario-card.medical{border-top-color:var(--accent3)}\n.scenario-card.search{border-top-color:var(--accent)}\n.scenario-card.fraud{border-top-color:var(--accent5)}\n.scenario-card h4{margin:0 0 .4rem;font-size:.9rem}\n.scenario-card .priority{font-size:.78rem;color:var(--muted);margin-bottom:.3rem}\n.scenario-card .reason{font-size:.8rem;color:var(--muted)}\n\/* Python terminal *\/\n.terminal{background:#1a1a2e;color:#a8e6cf;border-radius:var(--radius);padding:.9rem 1rem;font-family:\"SF Mono\",Consolas,\"Courier New\",monospace;font-size:.82rem;line-height:1.6;margin:.6rem 0;overflow-x:auto;border:1px solid #333}\n.terminal 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a{word-break:break-all}\n.back-top{position:fixed;bottom:2rem;right:2rem;width:42px;height:42px;border-radius:50%;background:var(--accent);color:#fff;border:none;cursor:pointer;font-size:1.2rem;display:flex;align-items:center;justify-content:center;opacity:0;transition:opacity .3s,transform .3s;z-index:99;box-shadow:var(--shadow)}\n.back-top.visible{opacity:1;transform:translateY(0)}\n.back-top:hover{transform:translateY(-3px)}\n@media(max-width:640px){\n h1{font-size:1.4rem}.toc ol{columns:1}.header-inner{padding:0 1rem}main{padding:72px 1rem 2rem}\n .steps li{padding-left:2.4rem}.steps li::before{left:-11px;width:22px;height:22px;font-size:.7rem}\n .two-col{grid-template-columns:1fr}.cmd-grid{grid-template-columns:1fr}.compare-box{grid-template-columns:1fr}\n .scenario-grid{grid-template-columns:1fr}\n .cm-table{max-width:100%}\n}\n<\/style>\n<\/head>\n<body>\n<div class=\"progress-bar\" id=\"progressBar\"><\/div>\n<header>\n <div class=\"header-inner\">\n <div class=\"logo\"><span>\ud83d\udcca<\/span> \u5206\u7c7b\u8bc4\u4f30\u6307\u6807<\/div>\n <div class=\"controls\">\n <div class=\"lang-switch\">\n <button class=\"active\" onclick=\"setLang('zh')\" id=\"btn-zh\">\u4e2d\u6587<\/button>\n <button onclick=\"setLang('en')\" id=\"btn-en\">English<\/button>\n <\/div>\n <button class=\"theme-toggle\" onclick=\"toggleTheme()\" title=\"\u5207\u6362\u660e\u6697\u4e3b\u9898\">☼<\/button>\n <\/div>\n <\/div>\n<\/header>\n<main>\n\n\n<div class=\"lang-section active\" id=\"lang-zh\">\n<div class=\"hero\">\n <h1>\u5206\u7c7b\u8bc4\u4f30\u6307\u6807\u5b8c\u6574\u6307\u5357<span class=\"sub\">\u4ece\u6df7\u6dc6\u77e9\u9635\u5230 Accuracy\u3001Precision\u3001Recall\u3001F1-score \u7684\u5168\u9762\u89e3\u6790<\/span><\/h1>\n <p>\u7406\u89e3\u673a\u5668\u5b66\u4e60\u5206\u7c7b\u4efb\u52a1\u4e2d\u56db\u5927\u6838\u5fc3\u8bc4\u4f30\u6307\u6807\u7684\u539f\u7406\u3001\u516c\u5f0f\u3001\u9002\u7528\u573a\u666f\u4e0e\u6743\u8861\u5173\u7cfb<\/p>\n<\/div>\n\n<div class=\"toc\">\n <h3>\u76ee\u5f55<\/h3>\n <ol>\n <li><a href=\"#zh-1\">\u4e00\u3001\u6982\u8ff0\uff1a\u4e3a\u4ec0\u4e48\u9700\u8981\u8bc4\u4f30\u6307\u6807<\/a><\/li>\n <li><a href=\"#zh-2\">\u4e8c\u3001\u6df7\u6dc6\u77e9\u9635\uff1a\u4e00\u5207\u7684\u57fa\u7840<\/a><\/li>\n <li><a href=\"#zh-3\">\u4e09\u3001Accuracy\uff08\u51c6\u786e\u7387\uff09<\/a><\/li>\n <li><a href=\"#zh-4\">\u56db\u3001Precision\uff08\u7cbe\u786e\u7387\uff09<\/a><\/li>\n <li><a href=\"#zh-5\">\u4e94\u3001Recall\uff08\u53ec\u56de\u7387\uff09<\/a><\/li>\n <li><a href=\"#zh-6\">\u516d\u3001F1-score\uff08F1 \u5206\u6570\uff09<\/a><\/li>\n <li><a href=\"#zh-7\">\u4e03\u3001\u6307\u6807\u95f4\u7684\u5173\u7cfb\u4e0e\u6743\u8861<\/a><\/li>\n <li><a href=\"#zh-8\">\u516b\u3001\u4e0d\u5747\u8861\u6570\u636e\u96c6\u7684\u6311\u6218<\/a><\/li>\n <li><a href=\"#zh-9\">\u4e5d\u3001\u591a\u5206\u7c7b\u573a\u666f\u6269\u5c55<\/a><\/li>\n <li><a href=\"#zh-10\">\u5341\u3001\u5b9e\u9645\u5e94\u7528\u6307\u5357\u4e0e\u4ee3\u7801\u793a\u4f8b<\/a><\/li>\n <\/ol>\n<\/div>\n\n\n<h2 id=\"zh-1\">\u4e00\u3001\u6982\u8ff0\uff1a\u4e3a\u4ec0\u4e48\u9700\u8981\u8bc4\u4f30\u6307\u6807<\/h2>\n\n<p>\u5728\u673a\u5668\u5b66\u4e60\u7684\u5206\u7c7b\u4efb\u52a1\u4e2d\uff0c\u6a21\u578b\u9884\u6d4b\u7684\u7ed3\u679c\u9700\u8981\u7528\u5ba2\u89c2\u3001\u91cf\u5316\u7684\u6307\u6807\u6765\u8bc4\u4f30\u597d\u574f\u3002\u4ec5\u4ec5\u77e5\u9053”\u6a21\u578b\u9884\u6d4b\u4e86 95 \u4e2a\u6b63\u786e”\u662f\u4e0d\u591f\u7684\u2014\u2014\u6211\u4eec\u9700\u8981\u77e5\u9053\u5b83\u5728<strong>\u6b63\u7c7b<\/strong>\u548c<strong>\u8d1f\u7c7b<\/strong>\u4e0a\u5206\u522b\u8868\u73b0\u5982\u4f55\uff0c\u662f\u5426\u504f\u5411\u67d0\u4e00\u7c7b\uff0c\u4ee5\u53ca\u5728\u7279\u5b9a\u4e1a\u52a1\u573a\u666f\u4e0b\u662f\u5426\u6ee1\u8db3\u8981\u6c42<sup><a href=\"#cite-1\">[1]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"info-box\">\n <strong>\u6838\u5fc3\u95ee\u9898\uff1a<\/strong>\u4e0d\u540c\u6307\u6807\u8861\u91cf\u7684\u662f\u6a21\u578b\u6027\u80fd\u7684\u4e0d\u540c\u7ef4\u5ea6\u3002\u6ca1\u6709”\u4e07\u80fd\u6307\u6807”\u2014\u2014\u9009\u62e9\u54ea\u4e2a\u6307\u6807\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u4e1a\u52a1\u573a\u666f\u3001\u6570\u636e\u5206\u5e03\u548c\u4ee3\u4ef7\u6743\u8861\u3002\u7406\u89e3\u6bcf\u4e2a\u6307\u6807\u7684<strong>\u5b9a\u4e49\u3001\u9002\u7528\u6761\u4ef6\u548c\u5c40\u9650\u6027<\/strong>\u662f\u6b63\u786e\u8bc4\u4f30\u6a21\u578b\u7684\u524d\u63d0\u3002\n<\/div>\n\n<h3>1.1 \u56db\u5927\u6838\u5fc3\u6307\u6807\u901f\u89c8<\/h3>\n\n<div class=\"cmd-grid\">\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge acc\">Accuracy<\/span><\/h4>\n <span class=\"desc\">\u6574\u4f53\u9884\u6d4b\u6b63\u786e\u7387\u3002\u6240\u6709\u9884\u6d4b\u4e2d\u6b63\u786e\u7684\u6bd4\u4f8b\u3002\u76f4\u89c2\u4f46\u60e7\u6015\u6570\u636e\u4e0d\u5747\u8861\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge pre\">Precision<\/span><\/h4>\n <span class=\"desc\">\u67e5\u51c6\u7387\u3002\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u771f\u6b63\u4e3a\u6b63\u7684\u6bd4\u4f8b\u3002\u5173\u6ce8”\u9884\u6d4b\u7684\u7eaf\u5ea6”\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge rec\">Recall<\/span><\/h4>\n <span class=\"desc\">\u67e5\u5168\u7387\u3002\u5b9e\u9645\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u88ab\u6b63\u786e\u9884\u6d4b\u7684\u6bd4\u4f8b\u3002\u5173\u6ce8”\u662f\u5426\u6f0f\u6389”\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge f1\">F1-score<\/span><\/h4>\n <span class=\"desc\">\u7cbe\u786e\u7387\u4e0e\u53ec\u56de\u7387\u7684\u8c03\u548c\u5e73\u5747\u3002\u7efc\u5408\u5e73\u8861\u4e24\u8005\u7684\u5355\u4e00\u6307\u6807\u3002<\/span>\n <\/div>\n<\/div>\n\n<figure id=\"fig-1\">\n <div class=\"flow-diagram\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">\u6df7\u6dc6\u77e9\u9635<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item\">TP \/ TN \/ FP \/ FN<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.5rem\">\n <span class=\"flow-arrow\">\u2193<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">Accuracy<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item green\">Precision<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item yellow\">Recall<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item purple\">F1<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 1<\/strong> \u56db\u5927\u8bc4\u4f30\u6307\u6807\u5747\u7531\u6df7\u6dc6\u77e9\u9635\u4e2d\u7684\u56db\u4e2a\u57fa\u672c\u91cf\u63a8\u5bfc\u800c\u6765<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"zh-2\">\u4e8c\u3001\u6df7\u6dc6\u77e9\u9635\uff1a\u4e00\u5207\u7684\u57fa\u7840<\/h2>\n\n<p><strong>\u6df7\u6dc6\u77e9\u9635<\/strong>\uff08Confusion Matrix\uff09\u662f\u4e00\u4e2a 2\u00d72 \u7684\u8868\u683c\uff0c\u5c06\u6a21\u578b\u9884\u6d4b\u7ed3\u679c\u4e0e\u771f\u5b9e\u6807\u7b7e\u4ea4\u53c9\u5bf9\u6bd4\uff0c\u4ea7\u751f\u56db\u4e2a\u57fa\u672c\u91cf\u3002\u6240\u6709\u8bc4\u4f30\u6307\u6807\u90fd\u4ece\u8fd9\u56db\u4e2a\u91cf\u63a8\u5bfc\u800c\u6765<sup><a href=\"#cite-2\">[2]<\/a><\/sup>\u3002<\/p>\n\n<h3>2.1 \u56db\u4e2a\u57fa\u672c\u91cf<\/h3>\n\n<div class=\"cm-table\">\n <div class=\"cm-cell cm-corner\"><\/div>\n <div class=\"cm-cell cm-axis\">\u9884\u6d4b\u4e3a\u6b63<\/div>\n <div class=\"cm-cell cm-axis\">\u9884\u6d4b\u4e3a\u8d1f<\/div>\n\n <div class=\"cm-cell cm-axis\">\u5b9e\u9645\u4e3a\u6b63<\/div>\n <div class=\"cm-cell cm-tp\">TP<span class=\"cm-label\">True Positive<\/span><\/div>\n <div class=\"cm-cell cm-fn\">FN<span class=\"cm-label\">False Negative<\/span><\/div>\n\n <div class=\"cm-cell cm-axis\">\u5b9e\u9645\u4e3a\u8d1f<\/div>\n <div class=\"cm-cell cm-fp\">FP<span class=\"cm-label\">False Positive<\/span><\/div>\n <div class=\"cm-cell cm-tn\">TN<span class=\"cm-label\">True Negative<\/span><\/div>\n<\/div>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 1<\/strong> \u6df7\u6dc6\u77e9\u9635\u56db\u4e2a\u57fa\u672c\u91cf\u7684\u542b\u4e49<\/caption>\n <thead>\n <tr><th>\u7b26\u53f7<\/th><th>\u540d\u79f0<\/th><th>\u542b\u4e49<\/th><th>\u901a\u4fd7\u7406\u89e3<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>TP<\/strong><\/td><td>True Positive<\/td><td>\u5b9e\u9645\u4e3a\u6b63\uff0c\u9884\u6d4b\u4e3a\u6b63<\/td><td>\u6b63\u786e\u53d1\u73b0\uff08\u547d\u4e2d\uff09<\/td><\/tr>\n <tr><td><strong>TN<\/strong><\/td><td>True Negative<\/td><td>\u5b9e\u9645\u4e3a\u8d1f\uff0c\u9884\u6d4b\u4e3a\u8d1f<\/td><td>\u6b63\u786e\u6392\u9664\uff08\u6b63\u786e\u62d2\u7edd\uff09<\/td><\/tr>\n <tr><td><strong>FP<\/strong><\/td><td>False Positive<\/td><td>\u5b9e\u9645\u4e3a\u8d1f\uff0c\u9884\u6d4b\u4e3a\u6b63<\/td><td>\u8bef\u62a5\uff08\u5047\u9633\u6027 \/ Type I \u9519\u8bef\uff09<\/td><\/tr>\n <tr><td><strong>FN<\/strong><\/td><td>False Negative<\/td><td>\u5b9e\u9645\u4e3a\u6b63\uff0c\u9884\u6d4b\u4e3a\u8d1f<\/td><td>\u6f0f\u62a5\uff08\u5047\u9634\u6027 \/ Type II \u9519\u8bef\uff09<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<h3>2.2 \u8bb0\u5fc6\u53e3\u8bc0<\/h3>\n\n<div class=\"card\">\n <h4>\u901f\u8bb0\u89c4\u5219<\/h4>\n <p><strong>T \/ F<\/strong> = \u9884\u6d4b\u662f\u5426<strong>\u6b63\u786e<\/strong>\uff08True = \u5bf9\u4e86\uff0cFalse = \u9519\u4e86\uff09<\/p>\n <p><strong>P \/ N<\/strong> = \u6a21\u578b\u7684<strong>\u9884\u6d4b\u7c7b\u522b<\/strong>\uff08Positive = \u9884\u6d4b\u4e3a\u6b63\uff0cNegative = \u9884\u6d4b\u4e3a\u8d1f\uff09<\/p>\n <p>\u7ec4\u5408\u8d77\u6765\uff1a<strong>TP<\/strong> = \u9884\u6d4b\u6b63\u786e\u4e14\u9884\u6d4b\u4e3a\u6b63\uff1b<strong>FP<\/strong> = \u9884\u6d4b\u9519\u8bef\u4e14\u9884\u6d4b\u4e3a\u6b63\uff08\u5b9e\u9645\u4e0a\u662f\u8d1f\uff09\u3002<\/p>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>\u5173\u952e\u5173\u7cfb\uff1a<\/strong>\u6837\u672c\u603b\u6570 = TP + TN + FP + FN\u3002\u5176\u4e2d <strong>TP + FN<\/strong> = \u5b9e\u9645\u6b63\u7c7b\u603b\u6570\uff0c<strong>TP + FP<\/strong> = \u9884\u6d4b\u6b63\u7c7b\u603b\u6570\u3002\u8fd9\u4e24\u4e2a\u5173\u7cfb\u662f\u63a8\u5bfc\u6240\u6709\u6307\u6807\u7684\u57fa\u77f3\u3002\n<\/div>\n\n\n<h2 id=\"zh-3\">\u4e09\u3001Accuracy\uff08\u51c6\u786e\u7387\uff09<\/h2>\n\n<p><strong>Accuracy<\/strong>\uff08\u51c6\u786e\u7387\uff09\u662f\u6700\u76f4\u89c2\u7684\u8bc4\u4f30\u6307\u6807\uff0c\u8868\u793a\u6240\u6709\u6837\u672c\u4e2d\u6a21\u578b\u9884\u6d4b\u6b63\u786e\u7684\u6bd4\u4f8b<sup><a href=\"#cite-3\">[3]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Accuracy \u516c\u5f0f<\/div>\n <div class=\"formula\">Accuracy = (TP + TN) \/ (TP + TN + FP + FN)<\/div>\n<\/div>\n\n<h3>3.1 \u76f4\u89c2\u7406\u89e3<\/h3>\n\n<p>Accuracy \u56de\u7b54\u7684\u95ee\u9898\u662f\uff1a<strong>“\u6a21\u578b\u6574\u4f53\u8868\u73b0\u5982\u4f55\uff1f”<\/strong> \u5b83\u5c06\u6b63\u7c7b\u548c\u8d1f\u7c7b\u7684\u6b63\u786e\u9884\u6d4b\u4e00\u89c6\u540c\u4ec1\u5730\u8ba1\u5165\u5206\u5b50\uff0c\u662f\u552f\u4e00\u540c\u65f6\u8003\u8651 TN \u7684\u6307\u6807\u3002<\/p>\n\n<figure id=\"fig-2\">\n <div class=\"metric-bar-container\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"metric-bar\">\n <span class=\"label\">TP (60)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:60%;background:var(--accent)\">\u547d\u4e2d<\/div><\/div>\n <span class=\"value\">60<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">TN (30)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:30%;background:var(--accent2)\">\u6b63\u786e\u6392\u9664<\/div><\/div>\n <span class=\"value\">30<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">FP (5)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:5%;background:var(--accent4)\">\u8bef\u62a5<\/div><\/div>\n <span class=\"value\">5<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">FN (5)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:5%;background:var(--accent3)\">\u6f0f\u62a5<\/div><\/div>\n <span class=\"value\">5<\/span>\n <\/div>\n <div class=\"metric-bar\" style=\"margin-top:.8rem;border-top:1px solid var(--rule);padding-top:.6rem\">\n <span class=\"label\" style=\"color:var(--accent)\">Accuracy<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:90%;background:var(--accent)\">90 \/ 100<\/div><\/div>\n <span class=\"value\" style=\"color:var(--accent)\">90%<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 2<\/strong> Accuracy \u793a\u4f8b\uff1a100 \u4e2a\u6837\u672c\u4e2d 90 \u4e2a\u9884\u6d4b\u6b63\u786e\uff08TP=60 + TN=30\uff09\uff0c\u51c6\u786e\u7387 = 90%<\/figcaption>\n<\/figure>\n\n<h3>3.2 Accuracy \u7684\u81f4\u547d\u9677\u9631<\/h3>\n\n<div class=\"info-box danger\">\n <strong>\u4e0d\u5747\u8861\u6570\u636e\u7684\u9677\u9631\uff1a<\/strong>\u5f53\u6570\u636e\u4e25\u91cd\u4e0d\u5747\u8861\u65f6\uff0cAccuracy \u4f1a\u4ea7\u751f\u8bef\u5bfc\u3002\u4f8b\u5982\uff0c1000 \u5c01\u90ae\u4ef6\u4e2d 950 \u5c01\u662f\u6b63\u5e38\u90ae\u4ef6\u300150 \u5c01\u662f\u5783\u573e\u90ae\u4ef6\u3002\u4e00\u4e2a<strong>\u4ec0\u4e48\u90fd\u4e0d\u505a<\/strong>\u7684\u5206\u7c7b\u5668\uff08\u5168\u90e8\u5224\u4e3a”\u6b63\u5e38”\uff09\u7684 Accuracy = 950\/1000 = <strong>95%<\/strong>\uff0c\u4f46\u5b83\u5b8c\u5168\u6ca1\u6709\u8bc6\u522b\u51fa\u4efb\u4f55\u5783\u573e\u90ae\u4ef6<sup><a href=\"#cite-3\">[3]<\/a><\/sup>\u3002\n<\/div>\n\n<div class=\"compare-box\">\n <div class=\"compare-col good\">\n <h4>\u2705 \u9002\u7528\u573a\u666f<\/h4>\n <p>\u5404\u7c7b\u522b\u6837\u672c\u6570\u91cf\u5927\u81f4\u5747\u8861<\/p>\n <p>\u6b63\u7c7b\u548c\u8d1f\u7c7b\u7684\u9519\u8bef\u4ee3\u4ef7\u76f8\u8fd1<\/p>\n <p>\u9700\u8981\u5feb\u901f\u4e86\u89e3\u6574\u4f53\u8868\u73b0<\/p>\n <p>\u591a\u5206\u7c7b\u4efb\u52a1\u7684\u521d\u59cb\u53c2\u8003<\/p>\n <\/div>\n <div class=\"compare-col bad\">\n <h4>\u274c \u4e0d\u9002\u7528\u573a\u666f<\/h4>\n <p>\u6570\u636e\u4e25\u91cd\u4e0d\u5747\u8861\uff08\u5982\u6b3a\u8bc8\u68c0\u6d4b\u3001\u7f55\u89c1\u75c5\u8bca\u65ad\uff09<\/p>\n <p>\u6b63\u7c7b\u6781\u5c11\u4f46\u6781\u91cd\u8981\uff08\u6f0f\u62a5\u4ee3\u4ef7\u9ad8\uff09<\/p>\n <p>\u5355\u72ec\u4f7f\u7528 Accuracy \u4f5c\u4e3a\u552f\u4e00\u6307\u6807<\/p>\n <p>\u9700\u8981\u533a\u5206\u4e0d\u540c\u7c7b\u578b\u9519\u8bef\u7684\u573a\u666f<\/p>\n <\/div>\n<\/div>\n\n\n<h2 id=\"zh-4\">\u56db\u3001Precision\uff08\u7cbe\u786e\u7387 \/ \u67e5\u51c6\u7387\uff09<\/h2>\n\n<p><strong>Precision<\/strong>\uff08\u7cbe\u786e\u7387\uff0c\u53c8\u79f0\u67e5\u51c6\u7387\uff09\u8861\u91cf\u7684\u662f\uff1a<strong>\u5728\u6240\u6709\u88ab\u6a21\u578b\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u5b9e\u9645\u4e3a\u6b63\u7684\u6bd4\u4f8b<\/strong><sup><a href=\"#cite-1\">[1]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Precision \u516c\u5f0f<\/div>\n <div class=\"formula\">Precision = TP \/ (TP + FP)<\/div>\n<\/div>\n\n<h3>4.1 \u76f4\u89c2\u7406\u89e3<\/h3>\n\n<p>Precision \u56de\u7b54\u7684\u95ee\u9898\u662f\uff1a<strong>“\u6a21\u578b\u8bf4’\u662f’\u7684\u65f6\u5019\uff0c\u6709\u591a\u53ef\u4fe1\uff1f”<\/strong> \u5b83\u5173\u6ce8\u7684\u662f\u9884\u6d4b\u7684<strong>\u7eaf\u5ea6<\/strong>\u2014\u2014\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u6709\u591a\u5c11\u662f\u771f\u6b63\u7684\u6b63\u6837\u672c\u3002<\/p>\n\n<div class=\"card\">\n <h4>\u5783\u573e\u90ae\u4ef6\u8fc7\u6ee4\u7684\u4f8b\u5b50<\/h4>\n <p>\u6a21\u578b\u6807\u8bb0\u4e86 20 \u5c01\u90ae\u4ef6\u4e3a”\u5783\u573e\u90ae\u4ef6”\uff0c\u5176\u4e2d 16 \u5c01\u786e\u5b9e\u662f\u5783\u573e\u90ae\u4ef6\uff0c4 \u5c01\u662f\u6b63\u5e38\u90ae\u4ef6\u88ab\u8bef\u5224\u3002\u5219 Precision = 16 \/ 20 = <strong>80%<\/strong>\u3002<\/p>\n <p>Precision \u8d8a\u9ad8\uff0c\u610f\u5473\u7740\u6b63\u5e38\u90ae\u4ef6\u88ab\u8bef\u5224\u4e3a\u5783\u573e\u90ae\u4ef6\u7684\u53ef\u80fd\u6027\u8d8a\u4f4e\u2014\u2014\u7528\u6237\u4e0d\u4f1a\u56e0\u4e3a\u91cd\u8981\u90ae\u4ef6\u88ab\u8bef\u5220\u800c\u53d7\u635f\u5931\u3002<\/p>\n<\/div>\n\n<h3>4.2 Precision \u7684\u7279\u6027<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 2<\/strong> Precision \u6307\u6807\u7279\u6027\u5206\u6790<\/caption>\n <thead>\n <tr><th>\u7ef4\u5ea6<\/th><th>\u8bf4\u660e<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>\u5173\u6ce8\u7126\u70b9<\/td><td>\u9884\u6d4b\u4e3a\u6b63\u7684\u7eaf\u5ea6\uff08\u51cf\u5c11 FP\uff09<\/td><\/tr>\n <tr><td>\u5206\u5b50<\/td><td>TP\uff08\u6b63\u786e\u9884\u6d4b\u7684\u6b63\u6837\u672c\uff09<\/td><\/tr>\n <tr><td>\u5206\u6bcd<\/td><td>TP + FP\uff08\u6240\u6709\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\uff09<\/td><\/tr>\n <tr><td>\u4e0d\u542b TN<\/td><td>\u4e0d\u5173\u5fc3\u6b63\u786e\u6392\u9664\u7684\u8d1f\u6837\u672c<\/td><\/tr>\n <tr><td>\u6781\u7aef\u503c<\/td><td>FP=0 \u65f6 Precision=1\uff08\u5b81\u53ef\u5c11\u62a5\u4e5f\u4e0d\u9519\u62a5\uff09<\/td><\/tr>\n <tr><td>\u63d0\u9ad8\u65b9\u5f0f<\/td><td>\u63d0\u9ad8\u5224\u65ad\u95e8\u69db\uff0c\u53ea\u5bf9\u6700\u6709\u628a\u63e1\u7684\u6837\u672c\u9884\u6d4b\u4e3a\u6b63<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box warn\">\n <strong>Precision \u7684\u5c40\u9650\uff1a<\/strong>\u9ad8 Precision \u4e0d\u4e00\u5b9a\u4ee3\u8868\u597d\u6a21\u578b\u3002\u5982\u679c\u6a21\u578b\u6781\u5ea6\u4fdd\u5b88\uff0c\u53ea\u5bf9 1 \u4e2a\u6700\u786e\u4fe1\u7684\u6837\u672c\u9884\u6d4b\u4e3a\u6b63\uff08\u4e14\u786e\u5b9e\u4e3a\u6b63\uff09\uff0cPrecision = 1\/1 = 100%\uff0c\u4f46\u5b83\u53ef\u80fd\u6f0f\u6389\u4e86 999 \u4e2a\u6b63\u6837\u672c\u3002\u9ad8 Precision \u53ef\u80fd\u4ee5\u727a\u7272 Recall \u4e3a\u4ee3\u4ef7\u3002\n<\/div>\n\n\n<h2 id=\"zh-5\">\u4e94\u3001Recall\uff08\u53ec\u56de\u7387 \/ \u67e5\u5168\u7387\uff09<\/h2>\n\n<p><strong>Recall<\/strong>\uff08\u53ec\u56de\u7387\uff0c\u53c8\u79f0\u67e5\u5168\u7387\u3001\u7075\u654f\u5ea6 Sensitivity\u3001\u771f\u9633\u6027\u7387 TPR\uff09\u8861\u91cf\u7684\u662f\uff1a<strong>\u5728\u6240\u6709\u5b9e\u9645\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u88ab\u6a21\u578b\u6b63\u786e\u9884\u6d4b\u4e3a\u6b63\u7684\u6bd4\u4f8b<\/strong><sup><a href=\"#cite-4\">[4]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Recall \u516c\u5f0f<\/div>\n <div class=\"formula\">Recall = TP \/ (TP + FN)<\/div>\n<\/div>\n\n<h3>5.1 \u76f4\u89c2\u7406\u89e3<\/h3>\n\n<p>Recall \u56de\u7b54\u7684\u95ee\u9898\u662f\uff1a<strong>“\u6240\u6709\u771f\u6b63\u7684\u6b63\u6837\u672c\uff0c\u6a21\u578b\u627e\u5230\u4e86\u591a\u5c11\uff1f”<\/strong> \u5b83\u5173\u6ce8\u7684\u662f<strong>\u67e5\u5168\u7387<\/strong>\u2014\u2014\u6709\u6ca1\u6709\u6f0f\u6389\u5e94\u8be5\u88ab\u53d1\u73b0\u7684\u6b63\u6837\u672c\u3002<\/p>\n\n<div class=\"card\">\n <h4>\u764c\u75c7\u68c0\u6d4b\u7684\u4f8b\u5b50<\/h4>\n <p>100 \u4e2a\u60a3\u764c\u75c5\u4eba\u4e2d\uff0c\u6a21\u578b\u6b63\u786e\u8bc6\u522b\u4e86 85 \u4e2a\uff0c\u6f0f\u6389\u4e86 15 \u4e2a\u3002\u5219 Recall = 85 \/ 100 = <strong>85%<\/strong>\u3002<\/p>\n <p>Recall \u8d8a\u9ad8\uff0c\u610f\u5473\u7740\u8d8a\u5c11\u7684\u75c5\u4eba\u88ab\u6f0f\u8bca\u3002\u5728\u533b\u7597\u573a\u666f\u4e2d\uff0c\u6f0f\u8bca\uff08FN\uff09\u7684\u4ee3\u4ef7\u8fdc\u9ad8\u4e8e\u8bef\u8bca\uff08FP\uff09\u2014\u2014\u5b81\u53ef\u591a\u505a\u4e00\u6b21\u68c0\u67e5\uff0c\u4e5f\u4e0d\u80fd\u653e\u8fc7\u4e00\u4e2a\u75c5\u4eba\u3002<\/p>\n<\/div>\n\n<h3>5.2 Recall \u7684\u7279\u6027<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 3<\/strong> Recall \u6307\u6807\u7279\u6027\u5206\u6790<\/caption>\n <thead>\n <tr><th>\u7ef4\u5ea6<\/th><th>\u8bf4\u660e<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>\u5173\u6ce8\u7126\u70b9<\/td><td>\u6b63\u6837\u672c\u7684\u8986\u76d6\u7387\uff08\u51cf\u5c11 FN\uff09<\/td><\/tr>\n <tr><td>\u5206\u5b50<\/td><td>TP\uff08\u88ab\u627e\u5230\u7684\u6b63\u6837\u672c\uff09<\/td><\/tr>\n <tr><td>\u5206\u6bcd<\/td><td>TP + FN\uff08\u6240\u6709\u5b9e\u9645\u4e3a\u6b63\u7684\u6837\u672c\uff09<\/td><\/tr>\n <tr><td>\u4e0d\u542b TN<\/td><td>\u4e0d\u5173\u5fc3\u6b63\u786e\u6392\u9664\u7684\u8d1f\u6837\u672c<\/td><\/tr>\n <tr><td>\u6781\u7aef\u503c<\/td><td>FN=0 \u65f6 Recall=1\uff08\u5168\u90e8\u627e\u5230\uff0c\u5b81\u53ef\u9519\u62a5\uff09<\/td><\/tr>\n <tr><td>\u63d0\u9ad8\u65b9\u5f0f<\/td><td>\u964d\u4f4e\u5224\u65ad\u95e8\u69db\uff0c\u5bf9\u6240\u6709\u53ef\u80fd\u4e3a\u6b63\u7684\u6837\u672c\u90fd\u9884\u6d4b\u4e3a\u6b63<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box warn\">\n <strong>Recall \u7684\u5c40\u9650\uff1a<\/strong>\u9ad8 Recall \u4e0d\u4e00\u5b9a\u4ee3\u8868\u597d\u6a21\u578b\u3002\u5982\u679c\u6a21\u578b\u5bf9\u6240\u6709\u6837\u672c\u90fd\u9884\u6d4b\u4e3a\u6b63\uff0c\u5219 FN=0\uff0cRecall=100%\uff0c\u4f46\u5b83\u4ea7\u751f\u4e86\u5927\u91cf FP\u3002\u9ad8 Recall \u53ef\u80fd\u4ee5\u727a\u7272 Precision \u4e3a\u4ee3\u4ef7\u3002\n<\/div>\n\n\n<h2 id=\"zh-6\">\u516d\u3001F1-score\uff08F1 \u5206\u6570\uff09<\/h2>\n\n<p><strong>F1-score<\/strong> \u662f Precision \u548c Recall \u7684<strong>\u8c03\u548c\u5e73\u5747<\/strong>\uff08Harmonic Mean\uff09\uff0c\u7528\u4e8e\u5728\u4e24\u8005\u4e4b\u95f4\u53d6\u5f97\u5e73\u8861<sup><a href=\"#cite-5\">[5]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">F1-score \u516c\u5f0f<\/div>\n <div class=\"formula\">F1 = 2 \u00d7 (Precision \u00d7 Recall) \/ (Precision + Recall)<\/div>\n<\/div>\n\n<p>\u7b49\u4ef7\u5f62\u5f0f\uff1a<\/p>\n\n<pre class=\"code-block\">F1 = 2 \u00d7 TP \/ (2 \u00d7 TP + FP + FN)<\/pre>\n\n<h3>6.1 \u4e3a\u4ec0\u4e48\u7528\u8c03\u548c\u5e73\u5747\uff1f<\/h3>\n\n<p>\u8c03\u548c\u5e73\u5747\u4e0e\u7b97\u672f\u5e73\u5747\u7684\u5173\u952e\u533a\u522b\u5728\u4e8e\uff1a<strong>\u5b83\u5bf9\u6781\u7aef\u503c\u66f4\u654f\u611f<\/strong>\u3002\u5982\u679c Precision=0.01 \u800c Recall=1.0\uff0c\u7b97\u672f\u5e73\u5747 = 0.505\uff08\u770b\u8d77\u6765\u8fd8\u884c\uff09\uff0c\u4f46\u8c03\u548c\u5e73\u5747 F1 = 0.0198\uff08\u66b4\u9732\u4e86 Precision \u6781\u4f4e\u7684\u95ee\u9898\uff09<sup><a href=\"#cite-5\">[5]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 4<\/strong> \u4e0d\u540c\u5e73\u5747\u65b9\u5f0f\u5bf9\u6bd4<\/caption>\n <thead>\n <tr><th>Precision<\/th><th>Recall<\/th><th>\u7b97\u672f\u5e73\u5747<\/th><th>F1\uff08\u8c03\u548c\u5e73\u5747\uff09<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>0.80<\/td><td>0.80<\/td><td>0.80<\/td><td><strong>0.80<\/strong><\/td><\/tr>\n <tr><td>0.90<\/td><td>0.50<\/td><td>0.70<\/td><td><strong>0.643<\/strong><\/td><\/tr>\n <tr><td>1.00<\/td><td>0.50<\/td><td>0.75<\/td><td><strong>0.667<\/strong><\/td><\/tr>\n <tr><td>0.01<\/td><td>1.00<\/td><td>0.505<\/td><td><strong>0.0198<\/strong><\/td><\/tr>\n <tr><td>0.00<\/td><td>1.00<\/td><td>0.50<\/td><td><strong>0.00<\/strong><\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box\">\n <strong>\u8c03\u548c\u5e73\u5747\u7684\u60e9\u7f5a\u6027\uff1a<\/strong>\u5f53 Precision \u6216 Recall \u4efb\u4e00\u4e3a 0 \u65f6\uff0cF1 \u4e00\u5b9a\u4e3a 0\u3002\u8fd9\u610f\u5473\u7740 F1 \u8981\u6c42\u6a21\u578b\u5728\u4e24\u4e2a\u7ef4\u5ea6\u4e0a\u90fd\u8868\u73b0\u4e0d\u9519\uff0c\u4e0d\u5141\u8bb8”\u4e00\u6761\u817f\u8d70\u8def”\u3002\u800c\u7b97\u672f\u5e73\u5747\u4f1a\u63a9\u76d6\u4e00\u4e2a\u6781\u7aef\u4f4e\u503c\u7684\u95ee\u9898\u3002\n<\/div>\n\n<h3>6.2 F-beta \u63a8\u5e7f<\/h3>\n\n<p>F1 \u662f\u66f4\u4e00\u822c\u7684 <strong>F-\u03b2<\/strong> \u6307\u6807\u7684\u7279\u4f8b\uff08\u03b2=1\uff09\u3002\u03b2 \u63a7\u5236\u4e86 Recall \u76f8\u5bf9\u4e8e Precision \u7684\u6743\u91cd\uff1a<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">F-\u03b2 \u516c\u5f0f<\/div>\n <div class=\"formula\">F\u03b2 = (1 + \u03b2\u00b2) \u00d7 (Precision \u00d7 Recall) \/ (\u03b2\u00b2 \u00d7 Precision + Recall)<\/div>\n<\/div>\n\n<div class=\"cmd-grid\">\n <div class=\"cmd-card\">\n <h4>F1 (\u03b2=1)<\/h4>\n <span class=\"desc\">Precision \u548c Recall \u7b49\u6743\u3002\u6700\u5e38\u7528\u7684\u7efc\u5408\u6307\u6807\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4>F2 (\u03b2=2)<\/h4>\n <span class=\"desc\">Recall \u6743\u91cd\u66f4\u9ad8\u3002\u9002\u7528\u4e8e\u6f0f\u62a5\u4ee3\u4ef7\u9ad8\u7684\u573a\u666f\uff08\u5982\u533b\u7597\uff09\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4>F0.5 (\u03b2=0.5)<\/h4>\n <span class=\"desc\">Precision \u6743\u91cd\u66f4\u9ad8\u3002\u9002\u7528\u4e8e\u8bef\u62a5\u4ee3\u4ef7\u9ad8\u7684\u573a\u666f\uff08\u5982\u5783\u573e\u90ae\u4ef6\uff09\u3002<\/span>\n <\/div>\n<\/div>\n\n\n<h2 id=\"zh-7\">\u4e03\u3001\u6307\u6807\u95f4\u7684\u5173\u7cfb\u4e0e\u6743\u8861<\/h2>\n\n<h3>7.1 Precision-Recall \u7684\u8df7\u8df7\u677f\u6548\u5e94<\/h3>\n\n<p>Precision \u548c Recall \u4e4b\u95f4\u5b58\u5728\u5929\u7136\u7684<strong>\u6743\u8861\u5173\u7cfb<\/strong>\uff08Trade-off\uff09\u3002\u901a\u8fc7\u8c03\u6574\u5206\u7c7b\u9608\u503c\uff0c\u53ef\u4ee5\u63d0\u9ad8\u4e00\u4e2a\u6307\u6807\u4f46\u901a\u5e38\u4f1a\u964d\u4f4e\u53e6\u4e00\u4e2a<sup><a href=\"#cite-4\">[4]<\/a><\/sup>\u3002<\/p>\n\n<figure id=\"fig-3\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item yellow\">\u964d\u4f4e\u9608\u503c<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">\u9884\u6d4b\u66f4\u591a\u6b63\u6837\u672c<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">Recall \u2191<\/span>\n <span class=\"flow-arrow\">+<\/span>\n <span class=\"flow-item red\">FP \u2191<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item red\">Precision \u2193<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.6rem\">\n <span class=\"flow-item yellow\">\u63d0\u9ad8\u9608\u503c<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item\">\u9884\u6d4b\u66f4\u5c11\u6b63\u6837\u672c<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">Precision \u2191<\/span>\n <span class=\"flow-arrow\">+<\/span>\n <span class=\"flow-item red\">FN \u2191<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item red\">Recall \u2193<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 3<\/strong> Precision-Recall \u6743\u8861\uff1a\u8c03\u6574\u9608\u503c\u5982\u8e29\u8df7\u8df7\u677f\uff0c\u4e00\u7aef\u4e0a\u5347\u5219\u53e6\u4e00\u7aef\u4e0b\u964d<\/figcaption>\n<\/figure>\n\n<h3>7.2 \u56db\u6307\u6807\u5173\u7cfb\u56fe<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 5<\/strong> \u56db\u5927\u6307\u6807\u7684\u6838\u5fc3\u5bf9\u6bd4<\/caption>\n <thead>\n <tr><th>\u6307\u6807<\/th><th>\u516c\u5f0f<\/th><th>\u5173\u6ce8<\/th><th>\u4e0d\u5305\u542b<\/th><th>\u6700\u6015<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>Accuracy<\/strong><\/td><td>(TP+TN)\/All<\/td><td>\u6574\u4f53\u6b63\u786e\u7387<\/td><td>\u2014<\/td><td>\u6570\u636e\u4e0d\u5747\u8861<\/td><\/tr>\n <tr><td><strong>Precision<\/strong><\/td><td>TP\/(TP+FP)<\/td><td>\u9884\u6d4b\u7eaf\u5ea6<\/td><td>TN<\/td><td>FP \u8fc7\u591a<\/td><\/tr>\n <tr><td><strong>Recall<\/strong><\/td><td>TP\/(TP+FN)<\/td><td>\u6b63\u7c7b\u8986\u76d6<\/td><td>TN<\/td><td>FN \u8fc7\u591a<\/td><\/tr>\n <tr><td><strong>F1<\/strong><\/td><td>2PR\/(P+R)<\/td><td>P\/R \u5e73\u8861<\/td><td>TN<\/td><td>P \u6216 R \u6781\u7aef<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>\u5173\u952e\u6d1e\u5bdf\uff1a<\/strong>Precision\u3001Recall\u3001F1 \u4e09\u4e2a\u6307\u6807\u90fd<strong>\u4e0d\u5305\u542b TN<\/strong>\u3002\u8fd9\u610f\u5473\u7740\u5728\u8d1f\u6837\u672c\u6781\u591a\u7684\u573a\u666f\u4e0b\uff08\u5982\u6b3a\u8bc8\u68c0\u6d4b\uff0c99.9% \u662f\u6b63\u5e38\u4ea4\u6613\uff09\uff0cTN \u867d\u7136\u5de8\u5927\u4f46\u4e0d\u53c2\u4e0e\u8fd9\u4e09\u4e2a\u6307\u6807\u7684\u8ba1\u7b97\uff0c\u56e0\u6b64\u5b83\u4eec\u4e0d\u53d7\u6570\u636e\u4e0d\u5747\u8861\u7684\u76f4\u63a5\u5f71\u54cd\u2014\u2014\u8fd9\u662f\u5b83\u4eec\u6bd4 Accuracy \u66f4\u9002\u5408\u4e0d\u5747\u8861\u6570\u636e\u7684\u539f\u56e0\u3002\n<\/div>\n\n<h3>7.3 \u6570\u503c\u793a\u4f8b\uff1a\u540c\u4e00\u6a21\u578b\u7684\u591a\u7ef4\u8bc4\u4f30<\/h3>\n\n<div class=\"card\">\n <h4>\u573a\u666f\uff1a\u75be\u75c5\u7b5b\u67e5<\/h4>\n <p>1000 \u4eba\u4e2d\u5b9e\u9645 100 \u4eba\u60a3\u75c5\u3002\u6a21\u578b\u9884\u6d4b 120 \u4eba\u4e3a”\u60a3\u75c5”\uff08\u5176\u4e2d 80 \u4eba\u786e\u5b9e\u60a3\u75c5\uff0c40 \u4eba\u8bef\u62a5\uff09\uff0c\u5176\u4f59 880 \u4eba\u4e3a”\u5065\u5eb7”\uff08\u5176\u4e2d 20 \u4eba\u6f0f\u8bca\uff0c860 \u4eba\u6b63\u786e\u6392\u9664\uff09\u3002<\/p>\n <ul style=\"margin-left:1.5rem;margin-bottom:.5rem\">\n <li>TP=80, FP=40, FN=20, TN=860<\/li>\n <li><strong>Accuracy<\/strong> = (80+860)\/1000 = <strong>94%<\/strong>\uff08\u770b\u4f3c\u4e0d\u9519\uff09<\/li>\n <li><strong>Precision<\/strong> = 80\/(80+40) = <strong>66.7%<\/strong>\uff08\u6bcf 3 \u4e2a\u8bca\u65ad\u4e2d 1 \u4e2a\u8bef\u62a5\uff09<\/li>\n <li><strong>Recall<\/strong> = 80\/(80+20) = <strong>80%<\/strong>\uff08100 \u4e2a\u60a3\u8005\u627e\u5230 80 \u4e2a\uff09<\/li>\n <li><strong>F1<\/strong> = 2\u00d7(0.667\u00d70.80)\/(0.667+0.80) = <strong>72.7%<\/strong><\/li>\n <\/ul>\n<\/div>\n\n<figure id=\"fig-4\">\n <div class=\"metric-bar-container\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent)\">Accuracy<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:94%;background:var(--accent)\">94%<\/div><\/div>\n <span class=\"value\">94%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent2)\">Precision<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:66.7%;background:var(--accent2)\">66.7%<\/div><\/div>\n <span class=\"value\">66.7%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent4);color:#1a1a2e\">Recall<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:80%;background:var(--accent4)\">80%<\/div><\/div>\n <span class=\"value\">80%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent5)\">F1<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:72.7%;background:var(--accent5)\">72.7%<\/div><\/div>\n <span class=\"value\">72.7%<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 4<\/strong> \u540c\u4e00\u6a21\u578b\u5728\u56db\u4e2a\u6307\u6807\u4e0a\u7684\u8868\u73b0\u5dee\u5f02\uff1aAccuracy \u865a\u9ad8\uff0cF1 \u53cd\u6620\u771f\u5b9e\u7efc\u5408\u6c34\u5e73<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"zh-8\">\u516b\u3001\u4e0d\u5747\u8861\u6570\u636e\u96c6\u7684\u6311\u6218<\/h2>\n\n<p>\u5f53\u6b63\u8d1f\u6837\u672c\u6bd4\u4f8b\u60ac\u6b8a\u65f6\uff08\u5982\u6b3a\u8bc8\u68c0\u6d4b 1:1000\u3001\u7f55\u89c1\u75c5 1:10000\uff09\uff0cAccuracy \u4f1a\u5931\u6548\uff0c\u9700\u8981\u4f9d\u8d56 Precision\u3001Recall \u548c F1<sup><a href=\"#cite-6\">[6]<\/a><\/sup>\u3002<\/p>\n\n<h3>8.1 Accuracy \u5931\u6548\u6f14\u793a<\/h3>\n\n<div class=\"compare-box\">\n <div class=\"compare-col bad\">\n <h4>\u274c \u4ec5\u770b Accuracy<\/h4>\n <p>10000 \u7b14\u4ea4\u6613\u4e2d 10 \u7b14\u662f\u6b3a\u8bc8\u3002\u6a21\u578b\u5168\u90e8\u9884\u6d4b\u4e3a”\u6b63\u5e38”\u3002<\/p>\n <p>TP=0, FP=0, FN=10, TN=9990<\/p>\n <p><strong>Accuracy = 9990\/10000 = 99.9%<\/strong><\/p>\n <p>\u770b\u8d77\u6765\u975e\u5e38\u597d\u2014\u2014\u4f46\u4e00\u4e2a\u6b3a\u8bc8\u90fd\u6ca1\u6293\u5230\u3002<\/p>\n <\/div>\n <div class=\"compare-col good\">\n <h4>\u2705 \u770b Precision\/Recall\/F1<\/h4>\n <p>\u540c\u4e00\u6a21\u578b\uff1a<\/p>\n <p><strong>Precision<\/strong> = 0\/(0+0) = <strong>\u672a\u5b9a\u4e49<\/strong>\uff08\u65e0\u9884\u6d4b\u6b63\u6837\u672c\uff09<\/p>\n <p><strong>Recall<\/strong> = 0\/(0+10) = <strong>0%<\/strong><\/p>\n <p><strong>F1<\/strong> = <strong>0%<\/strong>\uff08\u6216\u672a\u5b9a\u4e49\uff09<\/p>\n <p>\u7acb\u523b\u66b4\u9732\u4e86\u6a21\u578b\u5b8c\u5168\u65e0\u6548\u3002<\/p>\n <\/div>\n<\/div>\n\n<h3>8.2 \u4e0d\u5747\u8861\u6570\u636e\u7684\u5e94\u5bf9\u7b56\u7565<\/h3>\n\n<ol class=\"steps\">\n <li>\n <strong>\u9009\u62e9\u6b63\u786e\u7684\u6307\u6807<\/strong>\n <span class=\"note\">\u4f7f\u7528 Precision\u3001Recall\u3001F1 \u66ff\u4ee3 Accuracy\u3002\u8003\u8651 PR-AUC\uff08Precision-Recall \u66f2\u7ebf\u4e0b\u9762\u79ef\uff09\u3002<\/span>\n <\/li>\n <li>\n <strong>\u91cd\u91c7\u6837\uff08Resampling\uff09<\/strong>\n <span class=\"note\">\u8fc7\u91c7\u6837\u5c11\u6570\u7c7b\uff08SMOTE\uff09\u6216\u6b20\u91c7\u6837\u591a\u6570\u7c7b\uff0c\u4f7f\u8bad\u7ec3\u96c6\u66f4\u5747\u8861\u3002<\/span>\n <\/li>\n <li>\n <strong>\u7c7b\u522b\u6743\u91cd\uff08Class Weight\uff09<\/strong>\n <span class=\"note\">\u5728\u635f\u5931\u51fd\u6570\u4e2d\u7ed9\u5c11\u6570\u7c7b\u66f4\u9ad8\u6743\u91cd\uff0c\u8ba9\u6a21\u578b\u66f4\u91cd\u89c6\u5c11\u6570\u7c7b\u7684\u9519\u8bef\u3002<\/span>\n <\/li>\n <li>\n <strong>\u8c03\u6574\u51b3\u7b56\u9608\u503c<\/strong>\n <span class=\"note\">\u9ed8\u8ba4\u9608\u503c 0.5 \u4e0d\u4e00\u5b9a\u6700\u4f18\uff0c\u53ef\u6839\u636e\u4e1a\u52a1\u9700\u6c42\u8c03\u6574\u4ee5\u5e73\u8861 P\/R\u3002<\/span>\n <\/li>\n <li>\n <strong>\u4f7f\u7528\u9002\u5408\u7684\u7b97\u6cd5<\/strong>\n <span class=\"note\">\u96c6\u6210\u65b9\u6cd5\uff08\u5982 XGBoost\uff09\u3001\u5f02\u5e38\u68c0\u6d4b\u65b9\u6cd5\u5bf9\u4e0d\u5747\u8861\u6570\u636e\u66f4\u9c81\u68d2\u3002<\/span>\n <\/li>\n<\/ol>\n\n\n<h2 id=\"zh-9\">\u4e5d\u3001\u591a\u5206\u7c7b\u573a\u666f\u6269\u5c55<\/h2>\n\n<p>\u5728\u591a\u5206\u7c7b\u4efb\u52a1\u4e2d\uff08\u5982\u624b\u5199\u6570\u5b57\u8bc6\u522b 0-9\uff09\uff0c\u6df7\u6dc6\u77e9\u9635\u6269\u5c55\u4e3a N\u00d7N\u3002\u5982\u4f55\u5c06\u4e8c\u5206\u7c7b\u6307\u6807\u6269\u5c55\u5230\u591a\u5206\u7c7b\uff1f\u6709\u4e09\u79cd\u5e38\u89c1\u5e73\u5747\u65b9\u5f0f<sup><a href=\"#cite-7\">[7]<\/a><\/sup>\uff1a<\/p>\n\n<h3>9.1 \u4e09\u79cd\u5e73\u5747\u7b56\u7565<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 6<\/strong> \u591a\u5206\u7c7b\u5e73\u5747\u7b56\u7565\u5bf9\u6bd4<\/caption>\n <thead>\n <tr><th>\u7b56\u7565<\/th><th>\u8ba1\u7b97\u65b9\u5f0f<\/th><th>\u7279\u70b9<\/th><th>\u9002\u7528\u573a\u666f<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>Macro<\/strong><\/td><td>\u5404\u7c7b\u522b\u6307\u6807\u5206\u522b\u8ba1\u7b97\u540e\u53d6\u7b97\u672f\u5e73\u5747<\/td><td>\u5404\u7c7b\u522b\u7b49\u6743\uff0c\u91cd\u89c6\u5c11\u6570\u7c7b<\/td><td>\u5404\u7c7b\u522b\u540c\u7b49\u91cd\u8981<\/td><\/tr>\n <tr><td><strong>Micro<\/strong><\/td><td>\u6240\u6709\u7c7b\u522b TP\/FP\/FN \u6c47\u603b\u540e\u8ba1\u7b97\u5168\u5c40\u6307\u6807<\/td><td>\u6837\u672c\u591a\u7684\u7c7b\u6743\u91cd\u66f4\u5927<\/td><td>\u6574\u4f53\u6027\u80fd\u8bc4\u4f30<\/td><\/tr>\n <tr><td><strong>Weighted<\/strong><\/td><td>\u5404\u7c7b\u522b\u6307\u6807\u6309\u6837\u672c\u91cf\u52a0\u6743\u5e73\u5747<\/td><td>\u517c\u987e\u7c7b\u522b\u6bd4\u4f8b<\/td><td>\u4e0d\u5747\u8861\u591a\u5206\u7c7b<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<h3>9.2 Macro vs Micro \u793a\u4f8b<\/h3>\n\n<div class=\"card\">\n <h4>\u4e09\u5206\u7c7b\u793a\u4f8b<\/h4>\n <p>3 \u4e2a\u7c7b\u522b A\u3001B\u3001C\uff0c\u6837\u672c\u6570\u5206\u522b\u4e3a 100\u300150\u300110\u3002<\/p>\n <pre class=\"code-block\">\u5404\u7c7b\u522b\u7684 Recall:\n \u7c7b\u522b A (100\u6837\u672c): Recall = 90\/100 = 0.90\n \u7c7b\u522b B ( 50\u6837\u672c): Recall = 40\/50 = 0.80\n \u7c7b\u522b C ( 10\u6837\u672c): Recall = 5\/10 = 0.50\n\nMacro-Recall = (0.90 + 0.80 + 0.50) \/ 3 = 0.733\n \u2192 \u6bcf\u4e2a\u7c7b\u522b\u540c\u7b49\u91cd\u8981\uff0cC \u7684\u4f4e Recall \u62c9\u4f4e\u4e86\u5747\u503c\n\nMicro-Recall = (90+40+5) \/ (100+50+10) = 135\/160 = 0.844\n \u2192 \u6309\u6837\u672c\u52a0\u6743\uff0cA \u7684\u9ad8\u5360\u6bd4\u63a8\u9ad8\u4e86\u5747\u503c\n\nWeighted-Recall = (0.90\u00d7100 + 0.80\u00d750 + 0.50\u00d710) \/ 160 = 0.844\n \u2192 \u4e0e Micro \u76f8\u540c\uff08\u56e0\u4e3a Recall \u7684\u52a0\u6743\u672c\u8d28\uff09<\/pre>\n<\/div>\n\n<div class=\"info-box\">\n <strong>\u9009\u62e9\u5efa\u8bae\uff1a<\/strong>\u5982\u679c\u5c11\u6570\u7c7b\u7684\u8868\u73b0\u540c\u6837\u91cd\u8981\uff08\u5982\u5404\u75be\u75c5\u8bca\u65ad\uff09\uff0c\u7528 <strong>Macro-F1<\/strong>\uff1b\u5982\u679c\u5173\u6ce8\u6574\u4f53\u9884\u6d4b\u51c6\u786e\u5ea6\uff0c\u7528 <strong>Micro-F1<\/strong>\uff1b\u5982\u679c\u7c7b\u522b\u95f4\u4e0d\u5747\u8861\u4e14\u9700\u517c\u987e\u6bd4\u4f8b\uff0c\u7528 <strong>Weighted-F1<\/strong>\u3002\n<\/div>\n\n<h3>9.3 One-vs-Rest \u601d\u8def<\/h3>\n\n<p>\u591a\u5206\u7c7b\u6307\u6807\u7684\u5e95\u5c42\u8ba1\u7b97\u901a\u5e38\u91c7\u7528 <strong>One-vs-Rest<\/strong>\uff08OvR\uff09\u7b56\u7565\uff1a\u5c06\u6bcf\u4e2a\u7c7b\u522b\u4f9d\u6b21\u89c6\u4e3a”\u6b63\u7c7b”\uff0c\u5176\u4f59\u6240\u6709\u7c7b\u522b\u89c6\u4e3a”\u8d1f\u7c7b”\uff0c\u8ba1\u7b97\u8be5\u7c7b\u7684 Precision\/Recall\/F1\uff0c\u518d\u6309\u4e0a\u8ff0\u5e73\u5747\u65b9\u5f0f\u6c47\u603b\u3002<\/p>\n\n<figure id=\"fig-5\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item\">\u7c7b\u522b A \u4e3a\u6b63<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (A)<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">\u7c7b\u522b B \u4e3a\u6b63<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (B)<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item purple\">Macro\/Micro\/Weighted \u5e73\u5747<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">\u7c7b\u522b C \u4e3a\u6b63<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (C)<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 5<\/strong> One-vs-Rest \u7b56\u7565\uff1a\u5c06 N \u5206\u7c7b\u8f6c\u5316\u4e3a N \u4e2a\u4e8c\u5206\u7c7b\u95ee\u9898<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"zh-10\">\u5341\u3001\u5b9e\u9645\u5e94\u7528\u6307\u5357\u4e0e\u4ee3\u7801\u793a\u4f8b<\/h2>\n\n<h3>10.1 \u573a\u666f-\u6307\u6807\u5339\u914d\u6307\u5357<\/h3>\n\n<div class=\"scenario-grid\">\n <div class=\"scenario-card medical\">\n <h4>\ud83c\udfe5 \u533b\u7597\u8bca\u65ad<\/h4>\n <p class=\"priority\"><strong>\u4f18\u5148\u6307\u6807\uff1a<\/strong>Recall \/ F2-score<\/p>\n <p class=\"reason\">\u6f0f\u8bca\uff08FN\uff09\u4ee3\u4ef7\u8fdc\u9ad8\u4e8e\u8bef\u8bca\uff08FP\uff09\u3002\u5b81\u53ef\u591a\u505a\u68c0\u67e5\uff0c\u4e0d\u53ef\u653e\u8fc7\u4e00\u4e2a\u75c5\u4eba\u3002<\/p>\n <\/div>\n <div class=\"scenario-card spam\">\n <h4>\ud83d\udce7 \u5783\u573e\u90ae\u4ef6\u8fc7\u6ee4<\/h4>\n <p class=\"priority\"><strong>\u4f18\u5148\u6307\u6807\uff1a<\/strong>Precision \/ F0.5<\/p>\n <p class=\"reason\">\u8bef\u5220\u6b63\u5e38\u90ae\u4ef6\uff08FP\uff09\u4ee3\u4ef7\u8fdc\u9ad8\u4e8e\u653e\u8fc7\u4e00\u5c01\u5783\u573e\u90ae\u4ef6\uff08FN\uff09\u3002<\/p>\n <\/div>\n <div class=\"scenario-card fraud\">\n <h4>\ud83d\udcb3 \u6b3a\u8bc8\u68c0\u6d4b<\/h4>\n <p class=\"priority\"><strong>\u4f18\u5148\u6307\u6807\uff1a<\/strong>Recall \/ PR-AUC<\/p>\n <p class=\"reason\">\u6f0f\u6389\u4e00\u7b14\u6b3a\u8bc8\u635f\u5931\u5de8\u5927\uff0c\u5b81\u53ef\u591a\u5ba1\u6838\u3002\u6570\u636e\u6781\u5ea6\u4e0d\u5747\u8861\u3002<\/p>\n <\/div>\n <div class=\"scenario-card search\">\n <h4>\ud83d\udd0d \u641c\u7d22\u5f15\u64ce<\/h4>\n <p class=\"priority\"><strong>\u4f18\u5148\u6307\u6807\uff1a<\/strong>Precision@K<\/p>\n <p class=\"reason\">\u7528\u6237\u53ea\u770b\u524d\u51e0\u6761\u7ed3\u679c\uff0c\u8fd4\u56de\u7684\u7cbe\u786e\u5ea6\u6bd4\u8986\u76d6\u7387\u66f4\u91cd\u8981\u3002<\/p>\n <\/div>\n<\/div>\n\n<h3>10.2 \u51b3\u7b56\u6d41\u7a0b\u56fe<\/h3>\n\n<figure id=\"fig-6\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">\u6570\u636e\u662f\u5426\u5747\u8861\uff1f<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item green\">\u662f \u2192 Accuracy<\/span>\n <span class=\"flow-arrow\" style=\"margin:0 1rem\">|<\/span>\n <span class=\"flow-item yellow\">\u5426 \u2192 \u7ee7\u7eed<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.3rem\">\n <span class=\"flow-arrow\">\u2193<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">FP \u548c FN \u54ea\u4e2a\u4ee3\u4ef7\u9ad8\uff1f<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">FP \u9ad8 \u2192 Precision<\/span>\n <span class=\"flow-arrow\">|<\/span>\n <span class=\"flow-item green\">FN \u9ad8 \u2192 Recall<\/span>\n <span class=\"flow-arrow\">|<\/span>\n <span class=\"flow-item purple\">\u76f8\u5f53 \u2192 F1<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 6<\/strong> \u6307\u6807\u9009\u62e9\u51b3\u7b56\u6d41\u7a0b<\/figcaption>\n<\/figure>\n\n<h3>10.3 Python \u4ee3\u7801\u793a\u4f8b<\/h3>\n\n<pre class=\"terminal\"><span class=\"comment\"># \u4f7f\u7528 scikit-learn \u8ba1\u7b97\u5206\u7c7b\u8bc4\u4f30\u6307\u6807<\/span>\n<span class=\"keyword\">from<\/span> sklearn.metrics <span class=\"keyword\">import<\/span> (\n accuracy_score,\n precision_score,\n recall_score,\n f1_score,\n classification_report,\n confusion_matrix\n)\n<span class=\"keyword\">from<\/span> sklearn.datasets <span class=\"keyword\">import<\/span> make_classification\n<span class=\"keyword\">from<\/span> sklearn.model_selection <span class=\"keyword\">import<\/span> train_test_split\n<span class=\"keyword\">from<\/span> sklearn.ensemble <span class=\"keyword\">import<\/span> RandomForestClassifier\n\n<span class=\"comment\"># 1. \u751f\u6210\u4e0d\u5747\u8861\u6570\u636e\uff08\u6b63\u8d1f\u6bd4 1:9\uff09<\/span>\nX, y = make_classification(\n n_samples=<span class=\"string\">1000<\/span>,\n weights=[<span class=\"string\">0.1<\/span>],\n random_state=<span class=\"string\">42<\/span>\n)\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=<span class=\"string\">0.3<\/span>)\n\n<span class=\"comment\"># 2. \u8bad\u7ec3\u6a21\u578b<\/span>\nmodel = RandomForestClassifier(random_state=<span class=\"string\">42<\/span>)\nmodel.fit(X_train, y_train)\ny_pred = model.predict(X_test)\n\n<span class=\"comment\"># 3. \u6df7\u6dc6\u77e9\u9635<\/span>\ncm = confusion_matrix(y_test, y_pred)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Confusion Matrix:\\n{cm}\"<\/span>)\n<span class=\"output\"># [[256 11]\n# [ 13 20]]<\/span>\n\ntn, fp, fn, tp = cm.ravel()\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"TP={tp}, TN={tn}, FP={fp}, FN={fn}\"<\/span>)\n<span class=\"output\"># TP=20, TN=256, FP=11, FN=13<\/span>\n\n<span class=\"comment\"># 4. \u56db\u5927\u6307\u6807<\/span>\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Accuracy: {accuracy_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Accuracy: 0.9200<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Precision: {precision_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Precision: 0.6452<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Recall: {recall_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Recall: 0.6061<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"F1-score: {f1_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># F1-score: 0.6250<\/span>\n\n<span class=\"comment\"># 5. \u591a\u5206\u7c7b\u62a5\u544a\uff08\u542b Macro\/Micro\/Weighted\uff09<\/span>\n<span class=\"keyword\">print<\/span>(classification_report(y_test, y_pred, target_names=[<span class=\"string\">\"Negative\"<\/span>, <span class=\"string\">\"Positive\"<\/span>]))\n<span class=\"output\"># precision recall f1-score support\n# Negative 0.95 0.96 0.95 267\n# Positive 0.65 0.61 0.63 33\n# accuracy 0.92 300\n# macro avg 0.80 0.78 0.79 300\n# weighted avg 0.92 0.92 0.92 300<\/span>\n\n<span class=\"comment\"># 6. \u4ea4\u53c9\u9a8c\u8bc1\u4e2d\u6307\u5b9a average \u7b56\u7565<\/span>\n<span class=\"keyword\">from<\/span> sklearn.model_selection <span class=\"keyword\">import<\/span> cross_val_score\n\nmacro_f1 = cross_val_score(model, X, y, cv=<span class=\"string\">5<\/span>, scoring=<span class=\"string\">\"f1_macro\"<\/span>)\nweighted_f1 = cross_val_score(model, X, y, cv=<span class=\"string\">5<\/span>, scoring=<span class=\"string\">\"f1_weighted\"<\/span>)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Macro F1 CV: {macro_f1.mean():.4f}\"<\/span>)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Weighted F1 CV:{weighted_f1.mean():.4f}\"<\/span>)<\/pre>\n\n<h3>10.4 \u5e38\u89c1\u8bef\u533a<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 7<\/strong> \u5e38\u89c1\u8bef\u533a\u4e0e\u7ea0\u6b63<\/caption>\n <thead>\n <tr><th>\u8bef\u533a<\/th><th>\u95ee\u9898<\/th><th>\u7ea0\u6b63<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>\u53ea\u7528 Accuracy<\/td><td>\u4e0d\u5747\u8861\u6570\u636e\u4e0b\u865a\u9ad8<\/td><td>\u642d\u914d Precision\/Recall\/F1 \u4f7f\u7528<\/td><\/tr>\n <tr><td>\u8ffd\u6c42 F1 \u6700\u9ad8<\/td><td>\u53ef\u80fd\u4e0d\u7b26\u5408\u4e1a\u52a1\u9700\u6c42<\/td><td>\u6839\u636e FP\/FN \u4ee3\u4ef7\u9009\u62e9 F\u03b2<\/td><\/tr>\n <tr><td>\u5ffd\u7565\u9608\u503c\u8c03\u4f18<\/td><td>\u9ed8\u8ba4 0.5 \u9608\u503c\u672a\u5fc5\u6700\u4f18<\/td><td>\u7528 PR \u66f2\u7ebf\u9009\u62e9\u4e1a\u52a1\u6700\u4f18\u9608\u503c<\/td><\/tr>\n <tr><td>\u6d4b\u8bd5\u96c6\u4e0d\u5747\u8861<\/td><td>\u6307\u6807\u6709\u504f<\/td><td>\u5206\u5c42\u62bd\u6837\u4fdd\u6301\u6bd4\u4f8b\uff0c\u6216\u4f7f\u7528\u5206\u5c42\u4ea4\u53c9\u9a8c\u8bc1<\/td><\/tr>\n <tr><td>\u5ffd\u89c6 TN \u5f71\u54cd<\/td><td>F1 \u4e0d\u542b TN\uff0c\u53ef\u80fd\u9ad8\u4f30<\/td><td>\u6781\u7aef\u4e0d\u5747\u8861\u65f6\u8865\u5145 MCC \u6307\u6807<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>\u603b\u7ed3\uff1a<\/strong>Accuracy\u3001Precision\u3001Recall\u3001F1-score \u662f\u5206\u7c7b\u8bc4\u4f30\u7684\u57fa\u77f3\u3002\u5b83\u4eec\u5404\u6709\u9002\u7528\u573a\u666f\uff0c\u4e0d\u5b58\u5728”\u6700\u597d\u7684\u6307\u6807”\u2014\u2014\u53ea\u6709”\u6700\u9002\u5408\u5f53\u524d\u4e1a\u52a1\u573a\u666f\u7684\u6307\u6807”\u3002\u7406\u89e3\u6df7\u6dc6\u77e9\u9635\u662f\u638c\u63e1\u4e00\u5207\u7684\u524d\u63d0\uff0c\u800c\u6839\u636e\u6570\u636e\u5747\u8861\u6027\u3001FP\/FN \u4ee3\u4ef7\u6743\u8861\u9009\u62e9\u5408\u9002\u7684\u6307\u6807\u7ec4\u5408\uff0c\u662f\u6bcf\u4e2a\u673a\u5668\u5b66\u4e60\u4ece\u4e1a\u8005\u7684\u5fc5\u5907\u80fd\u529b\u3002\n<\/div>\n\n<\/div>\n\n\n<div class=\"lang-section\" id=\"lang-en\">\n<div class=\"hero\">\n <h1>Complete Guide to Classification Metrics<span class=\"sub\">From Confusion Matrix to Accuracy, Precision, Recall & F1-score<\/span><\/h1>\n <p>Understand the four core evaluation metrics in ML classification: principles, formulas, use cases, and trade-offs<\/p>\n<\/div>\n\n<div class=\"toc\">\n <h3>Contents<\/h3>\n <ol>\n <li><a href=\"#en-1\">1. Overview: Why Evaluation Metrics Matter<\/a><\/li>\n <li><a href=\"#en-2\">2. Confusion Matrix: The Foundation<\/a><\/li>\n <li><a href=\"#en-3\">3. Accuracy<\/a><\/li>\n <li><a href=\"#en-4\">4. Precision<\/a><\/li>\n <li><a href=\"#en-5\">5. Recall<\/a><\/li>\n <li><a href=\"#en-6\">6. F1-score<\/a><\/li>\n <li><a href=\"#en-7\">7. Relationships and Trade-offs<\/a><\/li>\n <li><a href=\"#en-8\">8. Imbalanced Dataset Challenges<\/a><\/li>\n <li><a href=\"#en-9\">9. Multi-class Extensions<\/a><\/li>\n <li><a href=\"#en-10\">10. Practical Guide & Code Examples<\/a><\/li>\n <\/ol>\n<\/div>\n\n\n<h2 id=\"en-1\">1. Overview: Why Evaluation Metrics Matter<\/h2>\n\n<p>In machine learning classification tasks, model predictions need objective, quantifiable metrics to assess quality. Knowing “the model got 95 correct” is insufficient\u2014we need to understand its performance on <strong>positive<\/strong> and <strong>negative<\/strong> classes separately, whether it’s biased, and whether it meets specific business requirements<sup><a href=\"#cite-1\">[1]<\/a><\/sup>.<\/p>\n\n<div class=\"info-box\">\n <strong>Core Problem:<\/strong> Different metrics measure different dimensions of model performance. There is no “universal metric”\u2014the choice depends on the specific business scenario, data distribution, and cost trade-offs. Understanding each metric’s <strong>definition, applicability, and limitations<\/strong> is the prerequisite for proper model evaluation.\n<\/div>\n\n<h3>1.1 Four Core Metrics at a Glance<\/h3>\n\n<div class=\"cmd-grid\">\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge acc\">Accuracy<\/span><\/h4>\n <span class=\"desc\">Overall correctness. Proportion of all predictions that are correct. Intuitive but vulnerable to imbalance.<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge pre\">Precision<\/span><\/h4>\n <span class=\"desc\">Of predicted positives, how many are actually positive. Focus: “purity of predictions.”<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge rec\">Recall<\/span><\/h4>\n <span class=\"desc\">Of actual positives, how many were correctly found. Focus: “did we miss any?”<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge f1\">F1-score<\/span><\/h4>\n <span class=\"desc\">Harmonic mean of precision and recall. A single balanced metric combining both.<\/span>\n <\/div>\n<\/div>\n\n<figure id=\"fig-1-en\">\n <div class=\"flow-diagram\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">Confusion Matrix<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item\">TP \/ TN \/ FP \/ FN<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.5rem\">\n <span class=\"flow-arrow\">\u2193<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">Accuracy<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item green\">Precision<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item yellow\">Recall<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item purple\">F1<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 1<\/strong> All four metrics derive from the four quantities in the confusion matrix<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"en-2\">2. Confusion Matrix: The Foundation<\/h2>\n\n<p>The <strong>Confusion Matrix<\/strong> is a 2\u00d72 table that cross-tabulates model predictions against ground truth labels, producing four fundamental quantities. All evaluation metrics are derived from these four<sup><a href=\"#cite-2\">[2]<\/a><\/sup>.<\/p>\n\n<h3>2.1 The Four Basic Quantities<\/h3>\n\n<div class=\"cm-table\">\n <div class=\"cm-cell cm-corner\"><\/div>\n <div class=\"cm-cell cm-axis\">Predicted Positive<\/div>\n <div class=\"cm-cell cm-axis\">Predicted Negative<\/div>\n\n <div class=\"cm-cell cm-axis\">Actual Positive<\/div>\n <div class=\"cm-cell cm-tp\">TP<span class=\"cm-label\">True Positive<\/span><\/div>\n <div class=\"cm-cell cm-fn\">FN<span class=\"cm-label\">False Negative<\/span><\/div>\n\n <div class=\"cm-cell cm-axis\">Actual Negative<\/div>\n <div class=\"cm-cell cm-fp\">FP<span class=\"cm-label\">False Positive<\/span><\/div>\n <div class=\"cm-cell cm-tn\">TN<span class=\"cm-label\">True Negative<\/span><\/div>\n<\/div>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 1<\/strong> Meaning of the four confusion matrix quantities<\/caption>\n <thead>\n <tr><th>Symbol<\/th><th>Name<\/th><th>Meaning<\/th><th>Plain English<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>TP<\/strong><\/td><td>True Positive<\/td><td>Actually positive, predicted positive<\/td><td>Correct hit<\/td><\/tr>\n <tr><td><strong>TN<\/strong><\/td><td>True Negative<\/td><td>Actually negative, predicted negative<\/td><td>Correct rejection<\/td><\/tr>\n <tr><td><strong>FP<\/strong><\/td><td>False Positive<\/td><td>Actually negative, predicted positive<\/td><td>False alarm (Type I error)<\/td><\/tr>\n <tr><td><strong>FN<\/strong><\/td><td>False Negative<\/td><td>Actually positive, predicted negative<\/td><td>Miss (Type II error)<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<h3>2.2 Memory Aid<\/h3>\n\n<div class=\"card\">\n <h4>Quick Rule<\/h4>\n <p><strong>T \/ F<\/strong> = whether the prediction is <strong>correct<\/strong> (True = correct, False = wrong)<\/p>\n <p><strong>P \/ N<\/strong> = the model’s <strong>predicted class<\/strong> (Positive = predicted positive, Negative = predicted negative)<\/p>\n <p>Combined: <strong>TP<\/strong> = correct prediction of positive; <strong>FP<\/strong> = wrong prediction of positive (actually negative).<\/p>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>Key Relationship:<\/strong> Total samples = TP + TN + FP + FN. Where <strong>TP + FN<\/strong> = total actual positives, and <strong>TP + FP<\/strong> = total predicted positives. These two relationships are the foundation for deriving all metrics.\n<\/div>\n\n\n<h2 id=\"en-3\">3. Accuracy<\/h2>\n\n<p><strong>Accuracy<\/strong> is the most intuitive evaluation metric\u2014the proportion of all samples that the model predicted correctly<sup><a href=\"#cite-3\">[3]<\/a><\/sup>.<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Accuracy Formula<\/div>\n <div class=\"formula\">Accuracy = (TP + TN) \/ (TP + TN + FP + FN)<\/div>\n<\/div>\n\n<h3>3.1 Intuitive Understanding<\/h3>\n\n<p>Accuracy answers: <strong>“How does the model perform overall?”<\/strong> It treats correct predictions of positive and negative classes equally in the numerator, and is the only metric that considers TN.<\/p>\n\n<figure id=\"fig-2-en\">\n <div class=\"metric-bar-container\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"metric-bar\">\n <span class=\"label\">TP (60)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:60%;background:var(--accent)\">Hits<\/div><\/div>\n <span class=\"value\">60<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">TN (30)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:30%;background:var(--accent2)\">Correct rejects<\/div><\/div>\n <span class=\"value\">30<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">FP (5)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:5%;background:var(--accent4)\">False alarm<\/div><\/div>\n <span class=\"value\">5<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">FN (5)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:5%;background:var(--accent3)\">Miss<\/div><\/div>\n <span class=\"value\">5<\/span>\n <\/div>\n <div class=\"metric-bar\" style=\"margin-top:.8rem;border-top:1px solid var(--rule);padding-top:.6rem\">\n <span class=\"label\" style=\"color:var(--accent)\">Accuracy<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:90%;background:var(--accent)\">90 \/ 100<\/div><\/div>\n <span class=\"value\" style=\"color:var(--accent)\">90%<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 2<\/strong> Accuracy example: 90 of 100 predictions correct (TP=60 + TN=30), accuracy = 90%<\/figcaption>\n<\/figure>\n\n<h3>3.2 The Fatal Pitfall of Accuracy<\/h3>\n\n<div class=\"info-box danger\">\n <strong>Imbalanced Data Trap:<\/strong> When data is severely imbalanced, Accuracy becomes misleading. For example, of 1000 emails, 950 are normal and 50 are spam. A classifier that does <strong>nothing<\/strong> (labels everything as “normal”) achieves Accuracy = 950\/1000 = <strong>95%<\/strong>, yet it catches zero spam<sup><a href=\"#cite-3\">[3]<\/a><\/sup>.\n<\/div>\n\n<div class=\"compare-box\">\n <div class=\"compare-col good\">\n <h4>\u2705 When to Use<\/h4>\n <p>Classes are roughly balanced<\/p>\n <p>FP and FN costs are similar<\/p>\n <p>Quick overall performance check needed<\/p>\n <p>Initial reference for multi-class tasks<\/p>\n <\/div>\n <div class=\"compare-col bad\">\n <h4>\u274c When NOT to Use<\/h4>\n <p>Severely imbalanced data (fraud, rare disease)<\/p>\n <p>Positive class is rare but critical (high FN cost)<\/p>\n <p>Using Accuracy as the sole metric<\/p>\n <p>Need to distinguish different error types<\/p>\n <\/div>\n<\/div>\n\n\n<h2 id=\"en-4\">4. Precision<\/h2>\n\n<p><strong>Precision<\/strong> measures: <strong>of all samples predicted as positive, what fraction is actually positive<\/strong><sup><a href=\"#cite-1\">[1]<\/a><\/sup>.<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Precision Formula<\/div>\n <div class=\"formula\">Precision = TP \/ (TP + FP)<\/div>\n<\/div>\n\n<h3>4.1 Intuitive Understanding<\/h3>\n\n<p>Precision answers: <strong>“When the model says ‘yes’, how trustworthy is it?”<\/strong> It focuses on the <strong>purity<\/strong> of positive predictions.<\/p>\n\n<div class=\"card\">\n <h4>Spam Filter Example<\/h4>\n <p>The model flags 20 emails as “spam”\u201416 are actually spam, 4 are normal emails misclassified. Precision = 16 \/ 20 = <strong>80%<\/strong>.<\/p>\n <p>Higher Precision means fewer normal emails are wrongly flagged as spam\u2014users won’t lose important emails.<\/p>\n<\/div>\n\n<h3>4.2 Precision Characteristics<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 2<\/strong> Precision metric characteristics<\/caption>\n <thead>\n <tr><th>Dimension<\/th><th>Description<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>Focus<\/td><td>Purity of positive predictions (minimize FP)<\/td><\/tr>\n <tr><td>Numerator<\/td><td>TP (correctly predicted positives)<\/td><\/tr>\n <tr><td>Denominator<\/td><td>TP + FP (all predicted positives)<\/td><\/tr>\n <tr><td>Excludes TN<\/td><td>Doesn’t consider correctly rejected negatives<\/td><\/tr>\n <tr><td>Extreme value<\/td><td>FP=0 \u2192 Precision=1 (better to miss than misfire)<\/td><\/tr>\n <tr><td>How to improve<\/td><td>Raise threshold, predict positive only when most confident<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box warn\">\n <strong>Precision’s Limitation:<\/strong> High Precision doesn’t necessarily mean a good model. If the model is extremely conservative\u2014predicting positive for only 1 sample it’s most sure about (and it’s correct)\u2014Precision = 1\/1 = 100%, but it may have missed 999 actual positives. High Precision often comes at the cost of Recall.\n<\/div>\n\n\n<h2 id=\"en-5\">5. Recall<\/h2>\n\n<p><strong>Recall<\/strong> (also known as Sensitivity, Hit Rate, or True Positive Rate) measures: <strong>of all actual positive samples, what fraction was correctly predicted as positive<\/strong><sup><a href=\"#cite-4\">[4]<\/a><\/sup>.<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Recall Formula<\/div>\n <div class=\"formula\">Recall = TP \/ (TP + FN)<\/div>\n<\/div>\n\n<h3>5.1 Intuitive Understanding<\/h3>\n\n<p>Recall answers: <strong>“Of all actual positives, how many did the model find?”<\/strong> It focuses on <strong>coverage<\/strong>\u2014did we miss any positives?<\/p>\n\n<div class=\"card\">\n <h4>Cancer Detection Example<\/h4>\n <p>Of 100 cancer patients, the model correctly identifies 85 and misses 15. Recall = 85 \/ 100 = <strong>85%<\/strong>.<\/p>\n <p>Higher Recall means fewer missed diagnoses. In medical settings, the cost of missing a patient (FN) is far higher than a false alarm (FP)\u2014better to run one more test than miss a patient.<\/p>\n<\/div>\n\n<h3>5.2 Recall Characteristics<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 3<\/strong> Recall metric characteristics<\/caption>\n <thead>\n <tr><th>Dimension<\/th><th>Description<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>Focus<\/td><td>Coverage of positive class (minimize FN)<\/td><\/tr>\n <tr><td>Numerator<\/td><td>TP (found positives)<\/td><\/tr>\n <tr><td>Denominator<\/td><td>TP + FN (all actual positives)<\/td><\/tr>\n <tr><td>Excludes TN<\/td><td>Doesn’t consider correctly rejected negatives<\/td><\/tr>\n <tr><td>Extreme value<\/td><td>FN=0 \u2192 Recall=1 (find everything, even false alarms)<\/td><\/tr>\n <tr><td>How to improve<\/td><td>Lower threshold, predict positive for any possibly positive sample<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box warn\">\n <strong>Recall’s Limitation:<\/strong> High Recall doesn’t necessarily mean a good model. If the model predicts positive for all samples, FN=0, Recall=100%, but it generates massive FP. High Recall often comes at the cost of Precision.\n<\/div>\n\n\n<h2 id=\"en-6\">6. F1-score<\/h2>\n\n<p><strong>F1-score<\/strong> is the <strong>harmonic mean<\/strong> of Precision and Recall, designed to balance the two<sup><a href=\"#cite-5\">[5]<\/a><\/sup>.<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">F1-score Formula<\/div>\n <div class=\"formula\">F1 = 2 \u00d7 (Precision \u00d7 Recall) \/ (Precision + Recall)<\/div>\n<\/div>\n\n<p>Equivalent form:<\/p>\n\n<pre class=\"code-block\">F1 = 2 \u00d7 TP \/ (2 \u00d7 TP + FP + FN)<\/pre>\n\n<h3>6.1 Why Harmonic Mean?<\/h3>\n\n<p>The key difference between harmonic and arithmetic mean: <strong>harmonic mean is more sensitive to extreme values<\/strong>. If Precision=0.01 and Recall=1.0, the arithmetic mean = 0.505 (looks okay), but the harmonic mean F1 = 0.0198 (exposes the low Precision)<sup><a href=\"#cite-5\">[5]<\/a><\/sup>.<\/p>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 4<\/strong> Comparison of averaging methods<\/caption>\n <thead>\n <tr><th>Precision<\/th><th>Recall<\/th><th>Arithmetic Mean<\/th><th>F1 (Harmonic)<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>0.80<\/td><td>0.80<\/td><td>0.80<\/td><td><strong>0.80<\/strong><\/td><\/tr>\n <tr><td>0.90<\/td><td>0.50<\/td><td>0.70<\/td><td><strong>0.643<\/strong><\/td><\/tr>\n <tr><td>1.00<\/td><td>0.50<\/td><td>0.75<\/td><td><strong>0.667<\/strong><\/td><\/tr>\n <tr><td>0.01<\/td><td>1.00<\/td><td>0.505<\/td><td><strong>0.0198<\/strong><\/td><\/tr>\n <tr><td>0.00<\/td><td>1.00<\/td><td>0.50<\/td><td><strong>0.00<\/strong><\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box\">\n <strong>Harmonic Mean’s Punishment:<\/strong> When either Precision or Recall is 0, F1 must be 0. This means F1 requires the model to perform decently on both dimensions\u2014no “one-legged” walking. The arithmetic mean would mask an extreme low value.\n<\/div>\n\n<h3>6.2 F-beta Generalization<\/h3>\n\n<p>F1 is a special case of the more general <strong>F-\u03b2<\/strong> metric (\u03b2=1). \u03b2 controls Recall’s weight relative to Precision:<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">F-\u03b2 Formula<\/div>\n <div class=\"formula\">F\u03b2 = (1 + \u03b2\u00b2) \u00d7 (Precision \u00d7 Recall) \/ (\u03b2\u00b2 \u00d7 Precision + Recall)<\/div>\n<\/div>\n\n<div class=\"cmd-grid\">\n <div class=\"cmd-card\">\n <h4>F1 (\u03b2=1)<\/h4>\n <span class=\"desc\">Equal weight to Precision and Recall. Most common composite metric.<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4>F2 (\u03b2=2)<\/h4>\n <span class=\"desc\">Recall weighted higher. For high FN-cost scenarios (e.g., medical).<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4>F0.5 (\u03b2=0.5)<\/h4>\n <span class=\"desc\">Precision weighted higher. For high FP-cost scenarios (e.g., spam).<\/span>\n <\/div>\n<\/div>\n\n\n<h2 id=\"en-7\">7. Relationships and Trade-offs<\/h2>\n\n<h3>7.1 The Precision-Recall Seesaw<\/h3>\n\n<p>There is a natural <strong>trade-off<\/strong> between Precision and Recall. By adjusting the classification threshold, you can improve one metric but typically at the expense of the other<sup><a href=\"#cite-4\">[4]<\/a><\/sup>.<\/p>\n\n<figure id=\"fig-3-en\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item yellow\">Lower threshold<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">More positive predictions<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">Recall \u2191<\/span>\n <span class=\"flow-arrow\">+<\/span>\n <span class=\"flow-item red\">FP \u2191<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item red\">Precision \u2193<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.6rem\">\n <span class=\"flow-item yellow\">Raise threshold<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item\">Fewer positive predictions<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">Precision \u2191<\/span>\n <span class=\"flow-arrow\">+<\/span>\n <span class=\"flow-item red\">FN \u2191<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item red\">Recall \u2193<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 3<\/strong> Precision-Recall trade-off: adjusting threshold is like a seesaw<\/figcaption>\n<\/figure>\n\n<h3>7.2 Four-Metric Comparison<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 5<\/strong> Core comparison of the four metrics<\/caption>\n <thead>\n <tr><th>Metric<\/th><th>Formula<\/th><th>Focus<\/th><th>Excludes<\/th><th>Most afraid of<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>Accuracy<\/strong><\/td><td>(TP+TN)\/All<\/td><td>Overall correctness<\/td><td>\u2014<\/td><td>Imbalanced data<\/td><\/tr>\n <tr><td><strong>Precision<\/strong><\/td><td>TP\/(TP+FP)<\/td><td>Prediction purity<\/td><td>TN<\/td><td>Too many FP<\/td><\/tr>\n <tr><td><strong>Recall<\/strong><\/td><td>TP\/(TP+FN)<\/td><td>Positive coverage<\/td><td>TN<\/td><td>Too many FN<\/td><\/tr>\n <tr><td><strong>F1<\/strong><\/td><td>2PR\/(P+R)<\/td><td>P\/R balance<\/td><td>TN<\/td><td>Extreme P or R<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>Key Insight:<\/strong> Precision, Recall, and F1 all <strong>exclude TN<\/strong>. This means in scenarios with abundant negative samples (e.g., fraud detection where 99.9% are normal), TN is huge but doesn’t participate in these three metrics\u2014so they are not directly affected by data imbalance. This is why they’re preferred over Accuracy for imbalanced data.\n<\/div>\n\n<h3>7.3 Numerical Example: Multi-dimensional Evaluation<\/h3>\n\n<div class=\"card\">\n <h4>Scenario: Disease Screening<\/h4>\n <p>Of 1000 people, 100 are actually sick. The model predicts 120 as “sick” (80 correctly, 40 false alarms), the remaining 880 as “healthy” (20 missed, 860 correctly excluded).<\/p>\n <ul style=\"margin-left:1.5rem;margin-bottom:.5rem\">\n <li>TP=80, FP=40, FN=20, TN=860<\/li>\n <li><strong>Accuracy<\/strong> = (80+860)\/1000 = <strong>94%<\/strong> (looks good)<\/li>\n <li><strong>Precision<\/strong> = 80\/(80+40) = <strong>66.7%<\/strong> (1 in 3 diagnoses is false alarm)<\/li>\n <li><strong>Recall<\/strong> = 80\/(80+20) = <strong>80%<\/strong> (found 80 of 100 patients)<\/li>\n <li><strong>F1<\/strong> = 2\u00d7(0.667\u00d70.80)\/(0.667+0.80) = <strong>72.7%<\/strong><\/li>\n <\/ul>\n<\/div>\n\n<figure id=\"fig-4-en\">\n <div class=\"metric-bar-container\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent)\">Accuracy<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:94%;background:var(--accent)\">94%<\/div><\/div>\n <span class=\"value\">94%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent2)\">Precision<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:66.7%;background:var(--accent2)\">66.7%<\/div><\/div>\n <span class=\"value\">66.7%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent4);color:#1a1a2e\">Recall<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:80%;background:var(--accent4)\">80%<\/div><\/div>\n <span class=\"value\">80%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent5)\">F1<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:72.7%;background:var(--accent5)\">72.7%<\/div><\/div>\n <span class=\"value\">72.7%<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 4<\/strong> Same model across four metrics: Accuracy is inflated, F1 reflects true composite performance<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"en-8\">8. Imbalanced Dataset Challenges<\/h2>\n\n<p>When positive\/negative ratios are extreme (fraud 1:1000, rare disease 1:10000), Accuracy fails. We need Precision, Recall, and F1<sup><a href=\"#cite-6\">[6]<\/a><\/sup>.<\/p>\n\n<h3>8.1 Accuracy Failure Demo<\/h3>\n\n<div class=\"compare-box\">\n <div class=\"compare-col bad\">\n <h4>\u274c Looking at Accuracy Only<\/h4>\n <p>Of 10000 transactions, 10 are fraud. Model predicts all as “normal.”<\/p>\n <p>TP=0, FP=0, FN=10, TN=9990<\/p>\n <p><strong>Accuracy = 9990\/10000 = 99.9%<\/strong><\/p>\n <p>Looks great\u2014but caught zero fraud.<\/p>\n <\/div>\n <div class=\"compare-col good\">\n <h4>\u2705 Looking at P\/R\/F1<\/h4>\n <p>Same model:<\/p>\n <p><strong>Precision<\/strong> = 0\/(0+0) = <strong>undefined<\/strong><\/p>\n <p><strong>Recall<\/strong> = 0\/(0+10) = <strong>0%<\/strong><\/p>\n <p><strong>F1<\/strong> = <strong>0%<\/strong> (or undefined)<\/p>\n <p>Immediately exposes model is useless.<\/p>\n <\/div>\n<\/div>\n\n<h3>8.2 Strategies for Imbalanced Data<\/h3>\n\n<ol class=\"steps\">\n <li>\n <strong>Choose the Right Metric<\/strong>\n <span class=\"note\">Use Precision, Recall, F1 instead of Accuracy. Consider PR-AUC (area under Precision-Recall curve).<\/span>\n <\/li>\n <li>\n <strong>Resampling<\/strong>\n <span class=\"note\">Oversample minority class (SMOTE) or undersample majority class to balance training data.<\/span>\n <\/li>\n <li>\n <strong>Class Weighting<\/strong>\n <span class=\"note\">Assign higher weight to minority class in loss function to make the model care more about its errors.<\/span>\n <\/li>\n <li>\n <strong>Threshold Tuning<\/strong>\n <span class=\"note\">Default 0.5 threshold may not be optimal; adjust based on business needs to balance P\/R.<\/span>\n <\/li>\n <li>\n <strong>Use Appropriate Algorithms<\/strong>\n <span class=\"note\">Ensemble methods (XGBoost) and anomaly detection approaches are more robust to imbalance.<\/span>\n <\/li>\n<\/ol>\n\n\n<h2 id=\"en-9\">9. Multi-class Extensions<\/h2>\n\n<p>In multi-class tasks (e.g., digit recognition 0-9), the confusion matrix expands to N\u00d7N. How do we extend binary metrics to multi-class? Three common averaging strategies<sup><a href=\"#cite-7\">[7]<\/a><\/sup>:<\/p>\n\n<h3>9.1 Three Averaging Strategies<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 6<\/strong> Multi-class averaging strategies compared<\/caption>\n <thead>\n <tr><th>Strategy<\/th><th>Calculation<\/th><th>Characteristics<\/th><th>Use Case<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>Macro<\/strong><\/td><td>Compute per-class metrics, then arithmetic mean<\/td><td>Equal weight per class; emphasizes rare classes<\/td><td>All classes equally important<\/td><\/tr>\n <tr><td><strong>Micro<\/strong><\/td><td>Aggregate all TP\/FP\/FN, then compute global metric<\/td><td>Larger classes dominate<\/td><td>Overall performance<\/td><\/tr>\n <tr><td><strong>Weighted<\/strong><\/td><td>Per-class metrics weighted by sample count<\/td><td>Accounts for class proportions<\/td><td>Imbalanced multi-class<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<h3>9.2 Macro vs Micro Example<\/h3>\n\n<div class=\"card\">\n <h4>Three-class Example<\/h4>\n <p>3 classes A, B, C with 100, 50, 10 samples respectively.<\/p>\n <pre class=\"code-block\">Per-class Recall:\n Class A (100 samples): Recall = 90\/100 = 0.90\n Class B ( 50 samples): Recall = 40\/50 = 0.80\n Class C ( 10 samples): Recall = 5\/10 = 0.50\n\nMacro-Recall = (0.90 + 0.80 + 0.50) \/ 3 = 0.733\n \u2192 Each class equally important; C's low Recall drags down average\n\nMicro-Recall = (90+40+5) \/ (100+50+10) = 135\/160 = 0.844\n \u2192 Sample-weighted; A's high proportion boosts the average\n\nWeighted-Recall = (0.90\u00d7100 + 0.80\u00d750 + 0.50\u00d710) \/ 160 = 0.844\n \u2192 Same as Micro (because of Recall's weighted nature)<\/pre>\n<\/div>\n\n<div class=\"info-box\">\n <strong>Selection Guide:<\/strong> If minority class performance matters equally (e.g., disease diagnosis), use <strong>Macro-F1<\/strong>; if overall prediction accuracy is the focus, use <strong>Micro-F1<\/strong>; if classes are imbalanced and proportions matter, use <strong>Weighted-F1<\/strong>.\n<\/div>\n\n<h3>9.3 One-vs-Rest Approach<\/h3>\n\n<p>Multi-class metrics are typically computed using the <strong>One-vs-Rest<\/strong> (OvR) strategy: treat each class as “positive” in turn, all others as “negative,” compute that class’s P\/R\/F1, then aggregate using one of the averaging strategies above.<\/p>\n\n<figure id=\"fig-5-en\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item\">Class A as positive<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (A)<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">Class B as positive<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (B)<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item purple\">Macro\/Micro\/Weighted<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">Class C as positive<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (C)<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 5<\/strong> One-vs-Rest strategy: converts N-class into N binary problems<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"en-10\">10. Practical Guide & Code Examples<\/h2>\n\n<h3>10.1 Scenario-Metric Matching Guide<\/h3>\n\n<div class=\"scenario-grid\">\n <div class=\"scenario-card medical\">\n <h4>\ud83c\udfe5 Medical Diagnosis<\/h4>\n <p class=\"priority\"><strong>Priority Metric:<\/strong>Recall \/ F2-score<\/p>\n <p class=\"reason\">Missing a diagnosis (FN) is far costlier than a false alarm (FP). Better to run extra tests than miss a patient.<\/p>\n <\/div>\n <div class=\"scenario-card spam\">\n <h4>\ud83d\udce7 Spam Filter<\/h4>\n <p class=\"priority\"><strong>Priority Metric:<\/strong>Precision \/ F0.5<\/p>\n <p class=\"reason\">Deleting a normal email (FP) is far costlier than letting spam through (FN).<\/p>\n <\/div>\n <div class=\"scenario-card fraud\">\n <h4>\ud83d\udcb3 Fraud Detection<\/h4>\n <p class=\"priority\"><strong>Priority Metric:<\/strong>Recall \/ PR-AUC<\/p>\n <p class=\"reason\">Missing fraud is hugely expensive; better to over-review. Extremely imbalanced data.<\/p>\n <\/div>\n <div class=\"scenario-card search\">\n <h4>\ud83d\udd0d Search Engine<\/h4>\n <p class=\"priority\"><strong>Priority Metric:<\/strong>Precision@K<\/p>\n <p class=\"reason\">Users only look at top results; precision of returned items matters more than coverage.<\/p>\n <\/div>\n<\/div>\n\n<h3>10.2 Decision Flowchart<\/h3>\n\n<figure id=\"fig-6-en\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">Is data balanced?<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item green\">Yes \u2192 Accuracy<\/span>\n <span class=\"flow-arrow\" style=\"margin:0 1rem\">|<\/span>\n <span class=\"flow-item yellow\">No \u2192 continue<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.3rem\">\n <span class=\"flow-arrow\">\u2193<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">Which costs more: FP or FN?<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">FP high \u2192 Precision<\/span>\n <span class=\"flow-arrow\">|<\/span>\n <span class=\"flow-item green\">FN high \u2192 Recall<\/span>\n <span class=\"flow-arrow\">|<\/span>\n <span class=\"flow-item purple\">Equal \u2192 F1<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 6<\/strong> Metric selection decision flow<\/figcaption>\n<\/figure>\n\n<h3>10.3 Python Code Example<\/h3>\n\n<pre class=\"terminal\"><span class=\"comment\"># Computing classification metrics with scikit-learn<\/span>\n<span class=\"keyword\">from<\/span> sklearn.metrics <span class=\"keyword\">import<\/span> (\n accuracy_score,\n precision_score,\n recall_score,\n f1_score,\n classification_report,\n confusion_matrix\n)\n<span class=\"keyword\">from<\/span> sklearn.datasets <span class=\"keyword\">import<\/span> make_classification\n<span class=\"keyword\">from<\/span> sklearn.model_selection <span class=\"keyword\">import<\/span> train_test_split\n<span class=\"keyword\">from<\/span> sklearn.ensemble <span class=\"keyword\">import<\/span> RandomForestClassifier\n\n<span class=\"comment\"># 1. Generate imbalanced data (1:9 ratio)<\/span>\nX, y = make_classification(\n n_samples=<span class=\"string\">1000<\/span>,\n weights=[<span class=\"string\">0.1<\/span>],\n random_state=<span class=\"string\">42<\/span>\n)\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=<span class=\"string\">0.3<\/span>)\n\n<span class=\"comment\"># 2. Train model<\/span>\nmodel = RandomForestClassifier(random_state=<span class=\"string\">42<\/span>)\nmodel.fit(X_train, y_train)\ny_pred = model.predict(X_test)\n\n<span class=\"comment\"># 3. Confusion matrix<\/span>\ncm = confusion_matrix(y_test, y_pred)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Confusion Matrix:\\n{cm}\"<\/span>)\n<span class=\"output\"># [[256 11]\n# [ 13 20]]<\/span>\n\ntn, fp, fn, tp = cm.ravel()\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"TP={tp}, TN={tn}, FP={fp}, FN={fn}\"<\/span>)\n<span class=\"output\"># TP=20, TN=256, FP=11, FN=13<\/span>\n\n<span class=\"comment\"># 4. Four core metrics<\/span>\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Accuracy: {accuracy_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Accuracy: 0.9200<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Precision: {precision_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Precision: 0.6452<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Recall: {recall_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Recall: 0.6061<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"F1-score: {f1_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># F1-score: 0.6250<\/span>\n\n<span class=\"comment\"># 5. Full classification report (with Macro\/Micro\/Weighted)<\/span>\n<span class=\"keyword\">print<\/span>(classification_report(y_test, y_pred, target_names=[<span class=\"string\">\"Negative\"<\/span>, <span class=\"string\">\"Positive\"<\/span>]))\n<span class=\"output\"># precision recall f1-score support\n# Negative 0.95 0.96 0.95 267\n# Positive 0.65 0.61 0.63 33\n# accuracy 0.92 300\n# macro avg 0.80 0.78 0.79 300\n# weighted avg 0.92 0.92 0.92 300<\/span>\n\n<span class=\"comment\"># 6. Cross-validation with average strategy<\/span>\n<span class=\"keyword\">from<\/span> sklearn.model_selection <span class=\"keyword\">import<\/span> cross_val_score\n\nmacro_f1 = cross_val_score(model, X, y, cv=<span class=\"string\">5<\/span>, scoring=<span class=\"string\">\"f1_macro\"<\/span>)\nweighted_f1 = cross_val_score(model, X, y, cv=<span class=\"string\">5<\/span>, scoring=<span class=\"string\">\"f1_weighted\"<\/span>)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Macro F1 CV: {macro_f1.mean():.4f}\"<\/span>)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Weighted F1 CV:{weighted_f1.mean():.4f}\"<\/span>)<\/pre>\n\n<h3>10.4 Common Pitfalls<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 7<\/strong> Common pitfalls and corrections<\/caption>\n <thead>\n <tr><th>Pitfall<\/th><th>Problem<\/th><th>Correction<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>Using only Accuracy<\/td><td>Inflated on imbalanced data<\/td><td>Pair with Precision\/Recall\/F1<\/td><\/tr>\n <tr><td>Chasing highest F1<\/td><td>May not match business needs<\/td><td>Choose F\u03b2 based on FP\/FN cost<\/td><\/tr>\n <tr><td>Ignoring threshold tuning<\/td><td>Default 0.5 may not be optimal<\/td><td>Use PR curve to select optimal threshold<\/td><\/tr>\n <tr><td>Imbalanced test set<\/td><td>Biased metrics<\/td><td>Use stratified sampling or stratified CV<\/td><\/tr>\n <tr><td>Ignoring TN effect<\/td><td>F1 excludes TN, may overestimate<\/td><td>Add MCC for extreme imbalance<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>Summary:<\/strong> Accuracy, Precision, Recall, and F1-score are the cornerstones of classification evaluation. Each has its applicable scenario\u2014there is no “best metric,” only the “most appropriate metric for the current business context.” Understanding the confusion matrix is the prerequisite for mastering all of them. Choosing the right metric combination based on data balance and FP\/FN cost trade-offs is an essential skill for every ML practitioner.\n<\/div>\n\n<\/div>\n\n\n<footer>\n <div class=\"sources\">\n <h2>Sources \/ \u53c2\u8003\u6765\u6e90<\/h2>\n <ol>\n <li id=\"cite-1\">\n <span class=\"src-title\">MetricGate, How to Interpret a Confusion Matrix \u2014 Accuracy, Precision, Recall, F1 formulas and explanations.<\/span>\n <a class=\"src-url\" href=\"https:\/\/metricgate.com\/blogs\/how-to-interpret-confusion-matrix\/\" target=\"_blank\" rel=\"noopener\">https:\/\/metricgate.com\/blogs\/how-to-interpret-confusion-matrix\/<\/a>\n <\/li>\n <li id=\"cite-2\">\n <span class=\"src-title\">IBM, What is a confusion matrix? \u2014 Definition, components, and role in classification evaluation.<\/span>\n <a class=\"src-url\" href=\"https:\/\/www.ibm.com\/think\/topics\/confusion-matrix\" target=\"_blank\" rel=\"noopener\">https:\/\/www.ibm.com\/think\/topics\/confusion-matrix<\/a>\n <\/li>\n <li id=\"cite-3\">\n <span class=\"src-title\">MetricGate, How to Interpret a Confusion Matrix \u2014 Accuracy’s limitation with imbalanced classes (95% accuracy catching zero spam example).<\/span>\n <a class=\"src-url\" href=\"https:\/\/metricgate.com\/blogs\/how-to-interpret-confusion-matrix\/\" target=\"_blank\" rel=\"noopener\">https:\/\/metricgate.com\/blogs\/how-to-interpret-confusion-matrix\/<\/a>\n <\/li>\n <li id=\"cite-4\">\n <span class=\"src-title\">CSDN, Accuracy\u3001Precision\u3001Recall\u3001F1-Score\u3001ROC AUC\u8be6\u89e3 \u2014 Comprehensive guide with medical\/spam examples and metric comparison table.<\/span>\n <a class=\"src-url\" href=\"https:\/\/blog.csdn.net\/2202_75569688\/article\/details\/151649058\" target=\"_blank\" rel=\"noopener\">https:\/\/blog.csdn.net\/2202_75569688\/article\/details\/151649058<\/a>\n <\/li>\n <li id=\"cite-5\">\n <span class=\"src-title\">PLOS ONE (PMC), S2 Method. Model Performance Metrics \u2014 F1 as harmonic mean of precision and recall, mathematical formulation.<\/span>\n <a class=\"src-url\" href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/instance\/11090298\/bin\/pone.0303287.s002.pdf\" target=\"_blank\" rel=\"noopener\">https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/instance\/11090298\/bin\/pone.0303287.s002.pdf<\/a>\n <\/li>\n <li id=\"cite-6\">\n <span class=\"src-title\">MetricGate, AUC vs. Accuracy vs. F1 Score \u2014 Scenario-based comparison: when accuracy is misleading, when F1 or AUC is recommended.<\/span>\n <a class=\"src-url\" href=\"https:\/\/metricgate.com\/blogs\/auc-vs-accuracy-vs-f1\/\" target=\"_blank\" rel=\"noopener\">https:\/\/metricgate.com\/blogs\/auc-vs-accuracy-vs-f1\/<\/a>\n <\/li>\n <li id=\"cite-7\">\n <span class=\"src-title\">Sarwan Pasha, Model Evaluation and Selection \u2014 Multi-class metrics, Macro\/Micro F1, and real-world application examples (medical, spam, fraud).<\/span>\n <a class=\"src-url\" href=\"https:\/\/sarwanpasha.github.io\/Courses\/ME_1.pdf\" target=\"_blank\" rel=\"noopener\">https:\/\/sarwanpasha.github.io\/Courses\/ME_1.pdf<\/a>\n <\/li>\n <\/ol>\n <\/div>\n<\/footer>\n\n<\/main>\n\n<button class=\"back-top\" onclick=\"scrollToTop()\" title=\"Back to top\">\u2191<\/button>\n\n<script>\nfunction setLang(lang) {\n document.querySelectorAll('.lang-section').forEach(s => s.classList.remove('active'));\n document.getElementById('lang-' + lang).classList.add('active');\n document.getElementById('btn-zh').classList.toggle('active', lang === 'zh');\n document.getElementById('btn-en').classList.toggle('active', lang === 'en');\n localStorage.setItem('cm-lang', lang);\n window.scrollTo(0, 0);\n}\n\nfunction toggleTheme() {\n const current = document.documentElement.getAttribute('data-theme');\n const next = current === 'dark' ? 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{"id":397,"date":"2026-08-18T10:40:53","date_gmt":"2026-08-18T02:40:53","guid":{"rendered":"https:\/\/numsimlab.com\/?p=397"},"modified":"2026-08-18T10:40:53","modified_gmt":"2026-08-18T02:40:53","slug":"%e5%88%86%e7%b1%bb%e8%af%84%e4%bc%b0%e6%8c%87%e6%a0%87%e5%ae%8c%e6%95%b4%e6%8c%87%e5%8d%97","status":"publish","type":"post","link":"https:\/\/numsimlab.com\/?p=397","title":{"rendered":"\u5206\u7c7b\u8bc4\u4f30\u6307\u6807\u5b8c\u6574\u6307\u5357"},"content":{"rendered":"\n\n\n\n\n\n\u5206\u7c7b\u8bc4\u4f30\u6307\u6807\u5b8c\u6574\u6307\u5357 \u00b7 Classification Metrics Guide<\/title>\n<style>\n*,*::before,*::after{box-sizing:border-box;margin:0;padding:0}\nhtml{scroll-behavior:smooth}\n:root{\n --bg:#f8f9fa;--bg2:#fff;--ink:#1a1a2e;--muted:#6c7086;--rule:#e2e4eb;\n --accent:#2563eb;--accent2:#16a34a;--accent3:#dc2626;--accent4:#d97706;--accent5:#7c3aed;\n --card-bg:#fff;--code-bg:#f1f3f5;--nav-bg:rgba(255,255,255,0.85);\n 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*\/\n.scenario-grid{display:grid;grid-template-columns:repeat(auto-fill,minmax(260px,1fr));gap:1rem;margin:1rem 0}\n.scenario-card{background:var(--card-bg);border:1px solid var(--rule);border-radius:var(--radius);padding:1.1rem;box-shadow:var(--shadow);border-top:4px solid var(--accent)}\n.scenario-card.spam{border-top-color:var(--accent4)}\n.scenario-card.medical{border-top-color:var(--accent3)}\n.scenario-card.search{border-top-color:var(--accent)}\n.scenario-card.fraud{border-top-color:var(--accent5)}\n.scenario-card h4{margin:0 0 .4rem;font-size:.9rem}\n.scenario-card .priority{font-size:.78rem;color:var(--muted);margin-bottom:.3rem}\n.scenario-card .reason{font-size:.8rem;color:var(--muted)}\n\/* Python terminal *\/\n.terminal{background:#1a1a2e;color:#a8e6cf;border-radius:var(--radius);padding:.9rem 1rem;font-family:\"SF Mono\",Consolas,\"Courier New\",monospace;font-size:.82rem;line-height:1.6;margin:.6rem 0;overflow-x:auto;border:1px solid #333}\n.terminal 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a{word-break:break-all}\n.back-top{position:fixed;bottom:2rem;right:2rem;width:42px;height:42px;border-radius:50%;background:var(--accent);color:#fff;border:none;cursor:pointer;font-size:1.2rem;display:flex;align-items:center;justify-content:center;opacity:0;transition:opacity .3s,transform .3s;z-index:99;box-shadow:var(--shadow)}\n.back-top.visible{opacity:1;transform:translateY(0)}\n.back-top:hover{transform:translateY(-3px)}\n@media(max-width:640px){\n h1{font-size:1.4rem}.toc ol{columns:1}.header-inner{padding:0 1rem}main{padding:72px 1rem 2rem}\n .steps li{padding-left:2.4rem}.steps li::before{left:-11px;width:22px;height:22px;font-size:.7rem}\n .two-col{grid-template-columns:1fr}.cmd-grid{grid-template-columns:1fr}.compare-box{grid-template-columns:1fr}\n .scenario-grid{grid-template-columns:1fr}\n .cm-table{max-width:100%}\n}\n<\/style>\n<\/head>\n<body>\n<div class=\"progress-bar\" id=\"progressBar\"><\/div>\n<header>\n <div class=\"header-inner\">\n <div class=\"logo\"><span>\ud83d\udcca<\/span> \u5206\u7c7b\u8bc4\u4f30\u6307\u6807<\/div>\n <div class=\"controls\">\n <div class=\"lang-switch\">\n <button class=\"active\" onclick=\"setLang('zh')\" id=\"btn-zh\">\u4e2d\u6587<\/button>\n <button onclick=\"setLang('en')\" id=\"btn-en\">English<\/button>\n <\/div>\n <button class=\"theme-toggle\" onclick=\"toggleTheme()\" title=\"\u5207\u6362\u660e\u6697\u4e3b\u9898\">☼<\/button>\n <\/div>\n <\/div>\n<\/header>\n<main>\n\n\n<div class=\"lang-section active\" id=\"lang-zh\">\n<div class=\"hero\">\n <h1>\u5206\u7c7b\u8bc4\u4f30\u6307\u6807\u5b8c\u6574\u6307\u5357<span class=\"sub\">\u4ece\u6df7\u6dc6\u77e9\u9635\u5230 Accuracy\u3001Precision\u3001Recall\u3001F1-score \u7684\u5168\u9762\u89e3\u6790<\/span><\/h1>\n <p>\u7406\u89e3\u673a\u5668\u5b66\u4e60\u5206\u7c7b\u4efb\u52a1\u4e2d\u56db\u5927\u6838\u5fc3\u8bc4\u4f30\u6307\u6807\u7684\u539f\u7406\u3001\u516c\u5f0f\u3001\u9002\u7528\u573a\u666f\u4e0e\u6743\u8861\u5173\u7cfb<\/p>\n<\/div>\n\n<div class=\"toc\">\n <h3>\u76ee\u5f55<\/h3>\n <ol>\n <li><a href=\"#zh-1\">\u4e00\u3001\u6982\u8ff0\uff1a\u4e3a\u4ec0\u4e48\u9700\u8981\u8bc4\u4f30\u6307\u6807<\/a><\/li>\n <li><a href=\"#zh-2\">\u4e8c\u3001\u6df7\u6dc6\u77e9\u9635\uff1a\u4e00\u5207\u7684\u57fa\u7840<\/a><\/li>\n <li><a href=\"#zh-3\">\u4e09\u3001Accuracy\uff08\u51c6\u786e\u7387\uff09<\/a><\/li>\n <li><a href=\"#zh-4\">\u56db\u3001Precision\uff08\u7cbe\u786e\u7387\uff09<\/a><\/li>\n <li><a href=\"#zh-5\">\u4e94\u3001Recall\uff08\u53ec\u56de\u7387\uff09<\/a><\/li>\n <li><a href=\"#zh-6\">\u516d\u3001F1-score\uff08F1 \u5206\u6570\uff09<\/a><\/li>\n <li><a href=\"#zh-7\">\u4e03\u3001\u6307\u6807\u95f4\u7684\u5173\u7cfb\u4e0e\u6743\u8861<\/a><\/li>\n <li><a href=\"#zh-8\">\u516b\u3001\u4e0d\u5747\u8861\u6570\u636e\u96c6\u7684\u6311\u6218<\/a><\/li>\n <li><a href=\"#zh-9\">\u4e5d\u3001\u591a\u5206\u7c7b\u573a\u666f\u6269\u5c55<\/a><\/li>\n <li><a href=\"#zh-10\">\u5341\u3001\u5b9e\u9645\u5e94\u7528\u6307\u5357\u4e0e\u4ee3\u7801\u793a\u4f8b<\/a><\/li>\n <\/ol>\n<\/div>\n\n\n<h2 id=\"zh-1\">\u4e00\u3001\u6982\u8ff0\uff1a\u4e3a\u4ec0\u4e48\u9700\u8981\u8bc4\u4f30\u6307\u6807<\/h2>\n\n<p>\u5728\u673a\u5668\u5b66\u4e60\u7684\u5206\u7c7b\u4efb\u52a1\u4e2d\uff0c\u6a21\u578b\u9884\u6d4b\u7684\u7ed3\u679c\u9700\u8981\u7528\u5ba2\u89c2\u3001\u91cf\u5316\u7684\u6307\u6807\u6765\u8bc4\u4f30\u597d\u574f\u3002\u4ec5\u4ec5\u77e5\u9053”\u6a21\u578b\u9884\u6d4b\u4e86 95 \u4e2a\u6b63\u786e”\u662f\u4e0d\u591f\u7684\u2014\u2014\u6211\u4eec\u9700\u8981\u77e5\u9053\u5b83\u5728<strong>\u6b63\u7c7b<\/strong>\u548c<strong>\u8d1f\u7c7b<\/strong>\u4e0a\u5206\u522b\u8868\u73b0\u5982\u4f55\uff0c\u662f\u5426\u504f\u5411\u67d0\u4e00\u7c7b\uff0c\u4ee5\u53ca\u5728\u7279\u5b9a\u4e1a\u52a1\u573a\u666f\u4e0b\u662f\u5426\u6ee1\u8db3\u8981\u6c42<sup><a href=\"#cite-1\">[1]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"info-box\">\n <strong>\u6838\u5fc3\u95ee\u9898\uff1a<\/strong>\u4e0d\u540c\u6307\u6807\u8861\u91cf\u7684\u662f\u6a21\u578b\u6027\u80fd\u7684\u4e0d\u540c\u7ef4\u5ea6\u3002\u6ca1\u6709”\u4e07\u80fd\u6307\u6807”\u2014\u2014\u9009\u62e9\u54ea\u4e2a\u6307\u6807\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u4e1a\u52a1\u573a\u666f\u3001\u6570\u636e\u5206\u5e03\u548c\u4ee3\u4ef7\u6743\u8861\u3002\u7406\u89e3\u6bcf\u4e2a\u6307\u6807\u7684<strong>\u5b9a\u4e49\u3001\u9002\u7528\u6761\u4ef6\u548c\u5c40\u9650\u6027<\/strong>\u662f\u6b63\u786e\u8bc4\u4f30\u6a21\u578b\u7684\u524d\u63d0\u3002\n<\/div>\n\n<h3>1.1 \u56db\u5927\u6838\u5fc3\u6307\u6807\u901f\u89c8<\/h3>\n\n<div class=\"cmd-grid\">\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge acc\">Accuracy<\/span><\/h4>\n <span class=\"desc\">\u6574\u4f53\u9884\u6d4b\u6b63\u786e\u7387\u3002\u6240\u6709\u9884\u6d4b\u4e2d\u6b63\u786e\u7684\u6bd4\u4f8b\u3002\u76f4\u89c2\u4f46\u60e7\u6015\u6570\u636e\u4e0d\u5747\u8861\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge pre\">Precision<\/span><\/h4>\n <span class=\"desc\">\u67e5\u51c6\u7387\u3002\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u771f\u6b63\u4e3a\u6b63\u7684\u6bd4\u4f8b\u3002\u5173\u6ce8”\u9884\u6d4b\u7684\u7eaf\u5ea6”\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge rec\">Recall<\/span><\/h4>\n <span class=\"desc\">\u67e5\u5168\u7387\u3002\u5b9e\u9645\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u88ab\u6b63\u786e\u9884\u6d4b\u7684\u6bd4\u4f8b\u3002\u5173\u6ce8”\u662f\u5426\u6f0f\u6389”\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge f1\">F1-score<\/span><\/h4>\n <span class=\"desc\">\u7cbe\u786e\u7387\u4e0e\u53ec\u56de\u7387\u7684\u8c03\u548c\u5e73\u5747\u3002\u7efc\u5408\u5e73\u8861\u4e24\u8005\u7684\u5355\u4e00\u6307\u6807\u3002<\/span>\n <\/div>\n<\/div>\n\n<figure id=\"fig-1\">\n <div class=\"flow-diagram\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">\u6df7\u6dc6\u77e9\u9635<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item\">TP \/ TN \/ FP \/ FN<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.5rem\">\n <span class=\"flow-arrow\">\u2193<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">Accuracy<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item green\">Precision<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item yellow\">Recall<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item purple\">F1<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 1<\/strong> \u56db\u5927\u8bc4\u4f30\u6307\u6807\u5747\u7531\u6df7\u6dc6\u77e9\u9635\u4e2d\u7684\u56db\u4e2a\u57fa\u672c\u91cf\u63a8\u5bfc\u800c\u6765<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"zh-2\">\u4e8c\u3001\u6df7\u6dc6\u77e9\u9635\uff1a\u4e00\u5207\u7684\u57fa\u7840<\/h2>\n\n<p><strong>\u6df7\u6dc6\u77e9\u9635<\/strong>\uff08Confusion Matrix\uff09\u662f\u4e00\u4e2a 2\u00d72 \u7684\u8868\u683c\uff0c\u5c06\u6a21\u578b\u9884\u6d4b\u7ed3\u679c\u4e0e\u771f\u5b9e\u6807\u7b7e\u4ea4\u53c9\u5bf9\u6bd4\uff0c\u4ea7\u751f\u56db\u4e2a\u57fa\u672c\u91cf\u3002\u6240\u6709\u8bc4\u4f30\u6307\u6807\u90fd\u4ece\u8fd9\u56db\u4e2a\u91cf\u63a8\u5bfc\u800c\u6765<sup><a href=\"#cite-2\">[2]<\/a><\/sup>\u3002<\/p>\n\n<h3>2.1 \u56db\u4e2a\u57fa\u672c\u91cf<\/h3>\n\n<div class=\"cm-table\">\n <div class=\"cm-cell cm-corner\"><\/div>\n <div class=\"cm-cell cm-axis\">\u9884\u6d4b\u4e3a\u6b63<\/div>\n <div class=\"cm-cell cm-axis\">\u9884\u6d4b\u4e3a\u8d1f<\/div>\n\n <div class=\"cm-cell cm-axis\">\u5b9e\u9645\u4e3a\u6b63<\/div>\n <div class=\"cm-cell cm-tp\">TP<span class=\"cm-label\">True Positive<\/span><\/div>\n <div class=\"cm-cell cm-fn\">FN<span class=\"cm-label\">False Negative<\/span><\/div>\n\n <div class=\"cm-cell cm-axis\">\u5b9e\u9645\u4e3a\u8d1f<\/div>\n <div class=\"cm-cell cm-fp\">FP<span class=\"cm-label\">False Positive<\/span><\/div>\n <div class=\"cm-cell cm-tn\">TN<span class=\"cm-label\">True Negative<\/span><\/div>\n<\/div>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 1<\/strong> \u6df7\u6dc6\u77e9\u9635\u56db\u4e2a\u57fa\u672c\u91cf\u7684\u542b\u4e49<\/caption>\n <thead>\n <tr><th>\u7b26\u53f7<\/th><th>\u540d\u79f0<\/th><th>\u542b\u4e49<\/th><th>\u901a\u4fd7\u7406\u89e3<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>TP<\/strong><\/td><td>True Positive<\/td><td>\u5b9e\u9645\u4e3a\u6b63\uff0c\u9884\u6d4b\u4e3a\u6b63<\/td><td>\u6b63\u786e\u53d1\u73b0\uff08\u547d\u4e2d\uff09<\/td><\/tr>\n <tr><td><strong>TN<\/strong><\/td><td>True Negative<\/td><td>\u5b9e\u9645\u4e3a\u8d1f\uff0c\u9884\u6d4b\u4e3a\u8d1f<\/td><td>\u6b63\u786e\u6392\u9664\uff08\u6b63\u786e\u62d2\u7edd\uff09<\/td><\/tr>\n <tr><td><strong>FP<\/strong><\/td><td>False Positive<\/td><td>\u5b9e\u9645\u4e3a\u8d1f\uff0c\u9884\u6d4b\u4e3a\u6b63<\/td><td>\u8bef\u62a5\uff08\u5047\u9633\u6027 \/ Type I \u9519\u8bef\uff09<\/td><\/tr>\n <tr><td><strong>FN<\/strong><\/td><td>False Negative<\/td><td>\u5b9e\u9645\u4e3a\u6b63\uff0c\u9884\u6d4b\u4e3a\u8d1f<\/td><td>\u6f0f\u62a5\uff08\u5047\u9634\u6027 \/ Type II \u9519\u8bef\uff09<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<h3>2.2 \u8bb0\u5fc6\u53e3\u8bc0<\/h3>\n\n<div class=\"card\">\n <h4>\u901f\u8bb0\u89c4\u5219<\/h4>\n <p><strong>T \/ F<\/strong> = \u9884\u6d4b\u662f\u5426<strong>\u6b63\u786e<\/strong>\uff08True = \u5bf9\u4e86\uff0cFalse = \u9519\u4e86\uff09<\/p>\n <p><strong>P \/ N<\/strong> = \u6a21\u578b\u7684<strong>\u9884\u6d4b\u7c7b\u522b<\/strong>\uff08Positive = \u9884\u6d4b\u4e3a\u6b63\uff0cNegative = \u9884\u6d4b\u4e3a\u8d1f\uff09<\/p>\n <p>\u7ec4\u5408\u8d77\u6765\uff1a<strong>TP<\/strong> = \u9884\u6d4b\u6b63\u786e\u4e14\u9884\u6d4b\u4e3a\u6b63\uff1b<strong>FP<\/strong> = \u9884\u6d4b\u9519\u8bef\u4e14\u9884\u6d4b\u4e3a\u6b63\uff08\u5b9e\u9645\u4e0a\u662f\u8d1f\uff09\u3002<\/p>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>\u5173\u952e\u5173\u7cfb\uff1a<\/strong>\u6837\u672c\u603b\u6570 = TP + TN + FP + FN\u3002\u5176\u4e2d <strong>TP + FN<\/strong> = \u5b9e\u9645\u6b63\u7c7b\u603b\u6570\uff0c<strong>TP + FP<\/strong> = \u9884\u6d4b\u6b63\u7c7b\u603b\u6570\u3002\u8fd9\u4e24\u4e2a\u5173\u7cfb\u662f\u63a8\u5bfc\u6240\u6709\u6307\u6807\u7684\u57fa\u77f3\u3002\n<\/div>\n\n\n<h2 id=\"zh-3\">\u4e09\u3001Accuracy\uff08\u51c6\u786e\u7387\uff09<\/h2>\n\n<p><strong>Accuracy<\/strong>\uff08\u51c6\u786e\u7387\uff09\u662f\u6700\u76f4\u89c2\u7684\u8bc4\u4f30\u6307\u6807\uff0c\u8868\u793a\u6240\u6709\u6837\u672c\u4e2d\u6a21\u578b\u9884\u6d4b\u6b63\u786e\u7684\u6bd4\u4f8b<sup><a href=\"#cite-3\">[3]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Accuracy \u516c\u5f0f<\/div>\n <div class=\"formula\">Accuracy = (TP + TN) \/ (TP + TN + FP + FN)<\/div>\n<\/div>\n\n<h3>3.1 \u76f4\u89c2\u7406\u89e3<\/h3>\n\n<p>Accuracy \u56de\u7b54\u7684\u95ee\u9898\u662f\uff1a<strong>“\u6a21\u578b\u6574\u4f53\u8868\u73b0\u5982\u4f55\uff1f”<\/strong> \u5b83\u5c06\u6b63\u7c7b\u548c\u8d1f\u7c7b\u7684\u6b63\u786e\u9884\u6d4b\u4e00\u89c6\u540c\u4ec1\u5730\u8ba1\u5165\u5206\u5b50\uff0c\u662f\u552f\u4e00\u540c\u65f6\u8003\u8651 TN \u7684\u6307\u6807\u3002<\/p>\n\n<figure id=\"fig-2\">\n <div class=\"metric-bar-container\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"metric-bar\">\n <span class=\"label\">TP (60)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:60%;background:var(--accent)\">\u547d\u4e2d<\/div><\/div>\n <span class=\"value\">60<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">TN (30)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:30%;background:var(--accent2)\">\u6b63\u786e\u6392\u9664<\/div><\/div>\n <span class=\"value\">30<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">FP (5)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:5%;background:var(--accent4)\">\u8bef\u62a5<\/div><\/div>\n <span class=\"value\">5<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">FN (5)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:5%;background:var(--accent3)\">\u6f0f\u62a5<\/div><\/div>\n <span class=\"value\">5<\/span>\n <\/div>\n <div class=\"metric-bar\" style=\"margin-top:.8rem;border-top:1px solid var(--rule);padding-top:.6rem\">\n <span class=\"label\" style=\"color:var(--accent)\">Accuracy<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:90%;background:var(--accent)\">90 \/ 100<\/div><\/div>\n <span class=\"value\" style=\"color:var(--accent)\">90%<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 2<\/strong> Accuracy \u793a\u4f8b\uff1a100 \u4e2a\u6837\u672c\u4e2d 90 \u4e2a\u9884\u6d4b\u6b63\u786e\uff08TP=60 + TN=30\uff09\uff0c\u51c6\u786e\u7387 = 90%<\/figcaption>\n<\/figure>\n\n<h3>3.2 Accuracy \u7684\u81f4\u547d\u9677\u9631<\/h3>\n\n<div class=\"info-box danger\">\n <strong>\u4e0d\u5747\u8861\u6570\u636e\u7684\u9677\u9631\uff1a<\/strong>\u5f53\u6570\u636e\u4e25\u91cd\u4e0d\u5747\u8861\u65f6\uff0cAccuracy \u4f1a\u4ea7\u751f\u8bef\u5bfc\u3002\u4f8b\u5982\uff0c1000 \u5c01\u90ae\u4ef6\u4e2d 950 \u5c01\u662f\u6b63\u5e38\u90ae\u4ef6\u300150 \u5c01\u662f\u5783\u573e\u90ae\u4ef6\u3002\u4e00\u4e2a<strong>\u4ec0\u4e48\u90fd\u4e0d\u505a<\/strong>\u7684\u5206\u7c7b\u5668\uff08\u5168\u90e8\u5224\u4e3a”\u6b63\u5e38”\uff09\u7684 Accuracy = 950\/1000 = <strong>95%<\/strong>\uff0c\u4f46\u5b83\u5b8c\u5168\u6ca1\u6709\u8bc6\u522b\u51fa\u4efb\u4f55\u5783\u573e\u90ae\u4ef6<sup><a href=\"#cite-3\">[3]<\/a><\/sup>\u3002\n<\/div>\n\n<div class=\"compare-box\">\n <div class=\"compare-col good\">\n <h4>\u2705 \u9002\u7528\u573a\u666f<\/h4>\n <p>\u5404\u7c7b\u522b\u6837\u672c\u6570\u91cf\u5927\u81f4\u5747\u8861<\/p>\n <p>\u6b63\u7c7b\u548c\u8d1f\u7c7b\u7684\u9519\u8bef\u4ee3\u4ef7\u76f8\u8fd1<\/p>\n <p>\u9700\u8981\u5feb\u901f\u4e86\u89e3\u6574\u4f53\u8868\u73b0<\/p>\n <p>\u591a\u5206\u7c7b\u4efb\u52a1\u7684\u521d\u59cb\u53c2\u8003<\/p>\n <\/div>\n <div class=\"compare-col bad\">\n <h4>\u274c \u4e0d\u9002\u7528\u573a\u666f<\/h4>\n <p>\u6570\u636e\u4e25\u91cd\u4e0d\u5747\u8861\uff08\u5982\u6b3a\u8bc8\u68c0\u6d4b\u3001\u7f55\u89c1\u75c5\u8bca\u65ad\uff09<\/p>\n <p>\u6b63\u7c7b\u6781\u5c11\u4f46\u6781\u91cd\u8981\uff08\u6f0f\u62a5\u4ee3\u4ef7\u9ad8\uff09<\/p>\n <p>\u5355\u72ec\u4f7f\u7528 Accuracy \u4f5c\u4e3a\u552f\u4e00\u6307\u6807<\/p>\n <p>\u9700\u8981\u533a\u5206\u4e0d\u540c\u7c7b\u578b\u9519\u8bef\u7684\u573a\u666f<\/p>\n <\/div>\n<\/div>\n\n\n<h2 id=\"zh-4\">\u56db\u3001Precision\uff08\u7cbe\u786e\u7387 \/ \u67e5\u51c6\u7387\uff09<\/h2>\n\n<p><strong>Precision<\/strong>\uff08\u7cbe\u786e\u7387\uff0c\u53c8\u79f0\u67e5\u51c6\u7387\uff09\u8861\u91cf\u7684\u662f\uff1a<strong>\u5728\u6240\u6709\u88ab\u6a21\u578b\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u5b9e\u9645\u4e3a\u6b63\u7684\u6bd4\u4f8b<\/strong><sup><a href=\"#cite-1\">[1]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Precision \u516c\u5f0f<\/div>\n <div class=\"formula\">Precision = TP \/ (TP + FP)<\/div>\n<\/div>\n\n<h3>4.1 \u76f4\u89c2\u7406\u89e3<\/h3>\n\n<p>Precision \u56de\u7b54\u7684\u95ee\u9898\u662f\uff1a<strong>“\u6a21\u578b\u8bf4’\u662f’\u7684\u65f6\u5019\uff0c\u6709\u591a\u53ef\u4fe1\uff1f”<\/strong> \u5b83\u5173\u6ce8\u7684\u662f\u9884\u6d4b\u7684<strong>\u7eaf\u5ea6<\/strong>\u2014\u2014\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u6709\u591a\u5c11\u662f\u771f\u6b63\u7684\u6b63\u6837\u672c\u3002<\/p>\n\n<div class=\"card\">\n <h4>\u5783\u573e\u90ae\u4ef6\u8fc7\u6ee4\u7684\u4f8b\u5b50<\/h4>\n <p>\u6a21\u578b\u6807\u8bb0\u4e86 20 \u5c01\u90ae\u4ef6\u4e3a”\u5783\u573e\u90ae\u4ef6”\uff0c\u5176\u4e2d 16 \u5c01\u786e\u5b9e\u662f\u5783\u573e\u90ae\u4ef6\uff0c4 \u5c01\u662f\u6b63\u5e38\u90ae\u4ef6\u88ab\u8bef\u5224\u3002\u5219 Precision = 16 \/ 20 = <strong>80%<\/strong>\u3002<\/p>\n <p>Precision \u8d8a\u9ad8\uff0c\u610f\u5473\u7740\u6b63\u5e38\u90ae\u4ef6\u88ab\u8bef\u5224\u4e3a\u5783\u573e\u90ae\u4ef6\u7684\u53ef\u80fd\u6027\u8d8a\u4f4e\u2014\u2014\u7528\u6237\u4e0d\u4f1a\u56e0\u4e3a\u91cd\u8981\u90ae\u4ef6\u88ab\u8bef\u5220\u800c\u53d7\u635f\u5931\u3002<\/p>\n<\/div>\n\n<h3>4.2 Precision \u7684\u7279\u6027<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 2<\/strong> Precision \u6307\u6807\u7279\u6027\u5206\u6790<\/caption>\n <thead>\n <tr><th>\u7ef4\u5ea6<\/th><th>\u8bf4\u660e<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>\u5173\u6ce8\u7126\u70b9<\/td><td>\u9884\u6d4b\u4e3a\u6b63\u7684\u7eaf\u5ea6\uff08\u51cf\u5c11 FP\uff09<\/td><\/tr>\n <tr><td>\u5206\u5b50<\/td><td>TP\uff08\u6b63\u786e\u9884\u6d4b\u7684\u6b63\u6837\u672c\uff09<\/td><\/tr>\n <tr><td>\u5206\u6bcd<\/td><td>TP + FP\uff08\u6240\u6709\u9884\u6d4b\u4e3a\u6b63\u7684\u6837\u672c\uff09<\/td><\/tr>\n <tr><td>\u4e0d\u542b TN<\/td><td>\u4e0d\u5173\u5fc3\u6b63\u786e\u6392\u9664\u7684\u8d1f\u6837\u672c<\/td><\/tr>\n <tr><td>\u6781\u7aef\u503c<\/td><td>FP=0 \u65f6 Precision=1\uff08\u5b81\u53ef\u5c11\u62a5\u4e5f\u4e0d\u9519\u62a5\uff09<\/td><\/tr>\n <tr><td>\u63d0\u9ad8\u65b9\u5f0f<\/td><td>\u63d0\u9ad8\u5224\u65ad\u95e8\u69db\uff0c\u53ea\u5bf9\u6700\u6709\u628a\u63e1\u7684\u6837\u672c\u9884\u6d4b\u4e3a\u6b63<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box warn\">\n <strong>Precision \u7684\u5c40\u9650\uff1a<\/strong>\u9ad8 Precision \u4e0d\u4e00\u5b9a\u4ee3\u8868\u597d\u6a21\u578b\u3002\u5982\u679c\u6a21\u578b\u6781\u5ea6\u4fdd\u5b88\uff0c\u53ea\u5bf9 1 \u4e2a\u6700\u786e\u4fe1\u7684\u6837\u672c\u9884\u6d4b\u4e3a\u6b63\uff08\u4e14\u786e\u5b9e\u4e3a\u6b63\uff09\uff0cPrecision = 1\/1 = 100%\uff0c\u4f46\u5b83\u53ef\u80fd\u6f0f\u6389\u4e86 999 \u4e2a\u6b63\u6837\u672c\u3002\u9ad8 Precision \u53ef\u80fd\u4ee5\u727a\u7272 Recall \u4e3a\u4ee3\u4ef7\u3002\n<\/div>\n\n\n<h2 id=\"zh-5\">\u4e94\u3001Recall\uff08\u53ec\u56de\u7387 \/ \u67e5\u5168\u7387\uff09<\/h2>\n\n<p><strong>Recall<\/strong>\uff08\u53ec\u56de\u7387\uff0c\u53c8\u79f0\u67e5\u5168\u7387\u3001\u7075\u654f\u5ea6 Sensitivity\u3001\u771f\u9633\u6027\u7387 TPR\uff09\u8861\u91cf\u7684\u662f\uff1a<strong>\u5728\u6240\u6709\u5b9e\u9645\u4e3a\u6b63\u7684\u6837\u672c\u4e2d\uff0c\u88ab\u6a21\u578b\u6b63\u786e\u9884\u6d4b\u4e3a\u6b63\u7684\u6bd4\u4f8b<\/strong><sup><a href=\"#cite-4\">[4]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Recall \u516c\u5f0f<\/div>\n <div class=\"formula\">Recall = TP \/ (TP + FN)<\/div>\n<\/div>\n\n<h3>5.1 \u76f4\u89c2\u7406\u89e3<\/h3>\n\n<p>Recall \u56de\u7b54\u7684\u95ee\u9898\u662f\uff1a<strong>“\u6240\u6709\u771f\u6b63\u7684\u6b63\u6837\u672c\uff0c\u6a21\u578b\u627e\u5230\u4e86\u591a\u5c11\uff1f”<\/strong> \u5b83\u5173\u6ce8\u7684\u662f<strong>\u67e5\u5168\u7387<\/strong>\u2014\u2014\u6709\u6ca1\u6709\u6f0f\u6389\u5e94\u8be5\u88ab\u53d1\u73b0\u7684\u6b63\u6837\u672c\u3002<\/p>\n\n<div class=\"card\">\n <h4>\u764c\u75c7\u68c0\u6d4b\u7684\u4f8b\u5b50<\/h4>\n <p>100 \u4e2a\u60a3\u764c\u75c5\u4eba\u4e2d\uff0c\u6a21\u578b\u6b63\u786e\u8bc6\u522b\u4e86 85 \u4e2a\uff0c\u6f0f\u6389\u4e86 15 \u4e2a\u3002\u5219 Recall = 85 \/ 100 = <strong>85%<\/strong>\u3002<\/p>\n <p>Recall \u8d8a\u9ad8\uff0c\u610f\u5473\u7740\u8d8a\u5c11\u7684\u75c5\u4eba\u88ab\u6f0f\u8bca\u3002\u5728\u533b\u7597\u573a\u666f\u4e2d\uff0c\u6f0f\u8bca\uff08FN\uff09\u7684\u4ee3\u4ef7\u8fdc\u9ad8\u4e8e\u8bef\u8bca\uff08FP\uff09\u2014\u2014\u5b81\u53ef\u591a\u505a\u4e00\u6b21\u68c0\u67e5\uff0c\u4e5f\u4e0d\u80fd\u653e\u8fc7\u4e00\u4e2a\u75c5\u4eba\u3002<\/p>\n<\/div>\n\n<h3>5.2 Recall \u7684\u7279\u6027<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 3<\/strong> Recall \u6307\u6807\u7279\u6027\u5206\u6790<\/caption>\n <thead>\n <tr><th>\u7ef4\u5ea6<\/th><th>\u8bf4\u660e<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>\u5173\u6ce8\u7126\u70b9<\/td><td>\u6b63\u6837\u672c\u7684\u8986\u76d6\u7387\uff08\u51cf\u5c11 FN\uff09<\/td><\/tr>\n <tr><td>\u5206\u5b50<\/td><td>TP\uff08\u88ab\u627e\u5230\u7684\u6b63\u6837\u672c\uff09<\/td><\/tr>\n <tr><td>\u5206\u6bcd<\/td><td>TP + FN\uff08\u6240\u6709\u5b9e\u9645\u4e3a\u6b63\u7684\u6837\u672c\uff09<\/td><\/tr>\n <tr><td>\u4e0d\u542b TN<\/td><td>\u4e0d\u5173\u5fc3\u6b63\u786e\u6392\u9664\u7684\u8d1f\u6837\u672c<\/td><\/tr>\n <tr><td>\u6781\u7aef\u503c<\/td><td>FN=0 \u65f6 Recall=1\uff08\u5168\u90e8\u627e\u5230\uff0c\u5b81\u53ef\u9519\u62a5\uff09<\/td><\/tr>\n <tr><td>\u63d0\u9ad8\u65b9\u5f0f<\/td><td>\u964d\u4f4e\u5224\u65ad\u95e8\u69db\uff0c\u5bf9\u6240\u6709\u53ef\u80fd\u4e3a\u6b63\u7684\u6837\u672c\u90fd\u9884\u6d4b\u4e3a\u6b63<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box warn\">\n <strong>Recall \u7684\u5c40\u9650\uff1a<\/strong>\u9ad8 Recall \u4e0d\u4e00\u5b9a\u4ee3\u8868\u597d\u6a21\u578b\u3002\u5982\u679c\u6a21\u578b\u5bf9\u6240\u6709\u6837\u672c\u90fd\u9884\u6d4b\u4e3a\u6b63\uff0c\u5219 FN=0\uff0cRecall=100%\uff0c\u4f46\u5b83\u4ea7\u751f\u4e86\u5927\u91cf FP\u3002\u9ad8 Recall \u53ef\u80fd\u4ee5\u727a\u7272 Precision \u4e3a\u4ee3\u4ef7\u3002\n<\/div>\n\n\n<h2 id=\"zh-6\">\u516d\u3001F1-score\uff08F1 \u5206\u6570\uff09<\/h2>\n\n<p><strong>F1-score<\/strong> \u662f Precision \u548c Recall \u7684<strong>\u8c03\u548c\u5e73\u5747<\/strong>\uff08Harmonic Mean\uff09\uff0c\u7528\u4e8e\u5728\u4e24\u8005\u4e4b\u95f4\u53d6\u5f97\u5e73\u8861<sup><a href=\"#cite-5\">[5]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">F1-score \u516c\u5f0f<\/div>\n <div class=\"formula\">F1 = 2 \u00d7 (Precision \u00d7 Recall) \/ (Precision + Recall)<\/div>\n<\/div>\n\n<p>\u7b49\u4ef7\u5f62\u5f0f\uff1a<\/p>\n\n<pre class=\"code-block\">F1 = 2 \u00d7 TP \/ (2 \u00d7 TP + FP + FN)<\/pre>\n\n<h3>6.1 \u4e3a\u4ec0\u4e48\u7528\u8c03\u548c\u5e73\u5747\uff1f<\/h3>\n\n<p>\u8c03\u548c\u5e73\u5747\u4e0e\u7b97\u672f\u5e73\u5747\u7684\u5173\u952e\u533a\u522b\u5728\u4e8e\uff1a<strong>\u5b83\u5bf9\u6781\u7aef\u503c\u66f4\u654f\u611f<\/strong>\u3002\u5982\u679c Precision=0.01 \u800c Recall=1.0\uff0c\u7b97\u672f\u5e73\u5747 = 0.505\uff08\u770b\u8d77\u6765\u8fd8\u884c\uff09\uff0c\u4f46\u8c03\u548c\u5e73\u5747 F1 = 0.0198\uff08\u66b4\u9732\u4e86 Precision \u6781\u4f4e\u7684\u95ee\u9898\uff09<sup><a href=\"#cite-5\">[5]<\/a><\/sup>\u3002<\/p>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 4<\/strong> \u4e0d\u540c\u5e73\u5747\u65b9\u5f0f\u5bf9\u6bd4<\/caption>\n <thead>\n <tr><th>Precision<\/th><th>Recall<\/th><th>\u7b97\u672f\u5e73\u5747<\/th><th>F1\uff08\u8c03\u548c\u5e73\u5747\uff09<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>0.80<\/td><td>0.80<\/td><td>0.80<\/td><td><strong>0.80<\/strong><\/td><\/tr>\n <tr><td>0.90<\/td><td>0.50<\/td><td>0.70<\/td><td><strong>0.643<\/strong><\/td><\/tr>\n <tr><td>1.00<\/td><td>0.50<\/td><td>0.75<\/td><td><strong>0.667<\/strong><\/td><\/tr>\n <tr><td>0.01<\/td><td>1.00<\/td><td>0.505<\/td><td><strong>0.0198<\/strong><\/td><\/tr>\n <tr><td>0.00<\/td><td>1.00<\/td><td>0.50<\/td><td><strong>0.00<\/strong><\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box\">\n <strong>\u8c03\u548c\u5e73\u5747\u7684\u60e9\u7f5a\u6027\uff1a<\/strong>\u5f53 Precision \u6216 Recall \u4efb\u4e00\u4e3a 0 \u65f6\uff0cF1 \u4e00\u5b9a\u4e3a 0\u3002\u8fd9\u610f\u5473\u7740 F1 \u8981\u6c42\u6a21\u578b\u5728\u4e24\u4e2a\u7ef4\u5ea6\u4e0a\u90fd\u8868\u73b0\u4e0d\u9519\uff0c\u4e0d\u5141\u8bb8”\u4e00\u6761\u817f\u8d70\u8def”\u3002\u800c\u7b97\u672f\u5e73\u5747\u4f1a\u63a9\u76d6\u4e00\u4e2a\u6781\u7aef\u4f4e\u503c\u7684\u95ee\u9898\u3002\n<\/div>\n\n<h3>6.2 F-beta \u63a8\u5e7f<\/h3>\n\n<p>F1 \u662f\u66f4\u4e00\u822c\u7684 <strong>F-\u03b2<\/strong> \u6307\u6807\u7684\u7279\u4f8b\uff08\u03b2=1\uff09\u3002\u03b2 \u63a7\u5236\u4e86 Recall \u76f8\u5bf9\u4e8e Precision \u7684\u6743\u91cd\uff1a<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">F-\u03b2 \u516c\u5f0f<\/div>\n <div class=\"formula\">F\u03b2 = (1 + \u03b2\u00b2) \u00d7 (Precision \u00d7 Recall) \/ (\u03b2\u00b2 \u00d7 Precision + Recall)<\/div>\n<\/div>\n\n<div class=\"cmd-grid\">\n <div class=\"cmd-card\">\n <h4>F1 (\u03b2=1)<\/h4>\n <span class=\"desc\">Precision \u548c Recall \u7b49\u6743\u3002\u6700\u5e38\u7528\u7684\u7efc\u5408\u6307\u6807\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4>F2 (\u03b2=2)<\/h4>\n <span class=\"desc\">Recall \u6743\u91cd\u66f4\u9ad8\u3002\u9002\u7528\u4e8e\u6f0f\u62a5\u4ee3\u4ef7\u9ad8\u7684\u573a\u666f\uff08\u5982\u533b\u7597\uff09\u3002<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4>F0.5 (\u03b2=0.5)<\/h4>\n <span class=\"desc\">Precision \u6743\u91cd\u66f4\u9ad8\u3002\u9002\u7528\u4e8e\u8bef\u62a5\u4ee3\u4ef7\u9ad8\u7684\u573a\u666f\uff08\u5982\u5783\u573e\u90ae\u4ef6\uff09\u3002<\/span>\n <\/div>\n<\/div>\n\n\n<h2 id=\"zh-7\">\u4e03\u3001\u6307\u6807\u95f4\u7684\u5173\u7cfb\u4e0e\u6743\u8861<\/h2>\n\n<h3>7.1 Precision-Recall \u7684\u8df7\u8df7\u677f\u6548\u5e94<\/h3>\n\n<p>Precision \u548c Recall \u4e4b\u95f4\u5b58\u5728\u5929\u7136\u7684<strong>\u6743\u8861\u5173\u7cfb<\/strong>\uff08Trade-off\uff09\u3002\u901a\u8fc7\u8c03\u6574\u5206\u7c7b\u9608\u503c\uff0c\u53ef\u4ee5\u63d0\u9ad8\u4e00\u4e2a\u6307\u6807\u4f46\u901a\u5e38\u4f1a\u964d\u4f4e\u53e6\u4e00\u4e2a<sup><a href=\"#cite-4\">[4]<\/a><\/sup>\u3002<\/p>\n\n<figure id=\"fig-3\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item yellow\">\u964d\u4f4e\u9608\u503c<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">\u9884\u6d4b\u66f4\u591a\u6b63\u6837\u672c<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">Recall \u2191<\/span>\n <span class=\"flow-arrow\">+<\/span>\n <span class=\"flow-item red\">FP \u2191<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item red\">Precision \u2193<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.6rem\">\n <span class=\"flow-item yellow\">\u63d0\u9ad8\u9608\u503c<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item\">\u9884\u6d4b\u66f4\u5c11\u6b63\u6837\u672c<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">Precision \u2191<\/span>\n <span class=\"flow-arrow\">+<\/span>\n <span class=\"flow-item red\">FN \u2191<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item red\">Recall \u2193<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 3<\/strong> Precision-Recall \u6743\u8861\uff1a\u8c03\u6574\u9608\u503c\u5982\u8e29\u8df7\u8df7\u677f\uff0c\u4e00\u7aef\u4e0a\u5347\u5219\u53e6\u4e00\u7aef\u4e0b\u964d<\/figcaption>\n<\/figure>\n\n<h3>7.2 \u56db\u6307\u6807\u5173\u7cfb\u56fe<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 5<\/strong> \u56db\u5927\u6307\u6807\u7684\u6838\u5fc3\u5bf9\u6bd4<\/caption>\n <thead>\n <tr><th>\u6307\u6807<\/th><th>\u516c\u5f0f<\/th><th>\u5173\u6ce8<\/th><th>\u4e0d\u5305\u542b<\/th><th>\u6700\u6015<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>Accuracy<\/strong><\/td><td>(TP+TN)\/All<\/td><td>\u6574\u4f53\u6b63\u786e\u7387<\/td><td>\u2014<\/td><td>\u6570\u636e\u4e0d\u5747\u8861<\/td><\/tr>\n <tr><td><strong>Precision<\/strong><\/td><td>TP\/(TP+FP)<\/td><td>\u9884\u6d4b\u7eaf\u5ea6<\/td><td>TN<\/td><td>FP \u8fc7\u591a<\/td><\/tr>\n <tr><td><strong>Recall<\/strong><\/td><td>TP\/(TP+FN)<\/td><td>\u6b63\u7c7b\u8986\u76d6<\/td><td>TN<\/td><td>FN \u8fc7\u591a<\/td><\/tr>\n <tr><td><strong>F1<\/strong><\/td><td>2PR\/(P+R)<\/td><td>P\/R \u5e73\u8861<\/td><td>TN<\/td><td>P \u6216 R \u6781\u7aef<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>\u5173\u952e\u6d1e\u5bdf\uff1a<\/strong>Precision\u3001Recall\u3001F1 \u4e09\u4e2a\u6307\u6807\u90fd<strong>\u4e0d\u5305\u542b TN<\/strong>\u3002\u8fd9\u610f\u5473\u7740\u5728\u8d1f\u6837\u672c\u6781\u591a\u7684\u573a\u666f\u4e0b\uff08\u5982\u6b3a\u8bc8\u68c0\u6d4b\uff0c99.9% \u662f\u6b63\u5e38\u4ea4\u6613\uff09\uff0cTN \u867d\u7136\u5de8\u5927\u4f46\u4e0d\u53c2\u4e0e\u8fd9\u4e09\u4e2a\u6307\u6807\u7684\u8ba1\u7b97\uff0c\u56e0\u6b64\u5b83\u4eec\u4e0d\u53d7\u6570\u636e\u4e0d\u5747\u8861\u7684\u76f4\u63a5\u5f71\u54cd\u2014\u2014\u8fd9\u662f\u5b83\u4eec\u6bd4 Accuracy \u66f4\u9002\u5408\u4e0d\u5747\u8861\u6570\u636e\u7684\u539f\u56e0\u3002\n<\/div>\n\n<h3>7.3 \u6570\u503c\u793a\u4f8b\uff1a\u540c\u4e00\u6a21\u578b\u7684\u591a\u7ef4\u8bc4\u4f30<\/h3>\n\n<div class=\"card\">\n <h4>\u573a\u666f\uff1a\u75be\u75c5\u7b5b\u67e5<\/h4>\n <p>1000 \u4eba\u4e2d\u5b9e\u9645 100 \u4eba\u60a3\u75c5\u3002\u6a21\u578b\u9884\u6d4b 120 \u4eba\u4e3a”\u60a3\u75c5”\uff08\u5176\u4e2d 80 \u4eba\u786e\u5b9e\u60a3\u75c5\uff0c40 \u4eba\u8bef\u62a5\uff09\uff0c\u5176\u4f59 880 \u4eba\u4e3a”\u5065\u5eb7”\uff08\u5176\u4e2d 20 \u4eba\u6f0f\u8bca\uff0c860 \u4eba\u6b63\u786e\u6392\u9664\uff09\u3002<\/p>\n <ul style=\"margin-left:1.5rem;margin-bottom:.5rem\">\n <li>TP=80, FP=40, FN=20, TN=860<\/li>\n <li><strong>Accuracy<\/strong> = (80+860)\/1000 = <strong>94%<\/strong>\uff08\u770b\u4f3c\u4e0d\u9519\uff09<\/li>\n <li><strong>Precision<\/strong> = 80\/(80+40) = <strong>66.7%<\/strong>\uff08\u6bcf 3 \u4e2a\u8bca\u65ad\u4e2d 1 \u4e2a\u8bef\u62a5\uff09<\/li>\n <li><strong>Recall<\/strong> = 80\/(80+20) = <strong>80%<\/strong>\uff08100 \u4e2a\u60a3\u8005\u627e\u5230 80 \u4e2a\uff09<\/li>\n <li><strong>F1<\/strong> = 2\u00d7(0.667\u00d70.80)\/(0.667+0.80) = <strong>72.7%<\/strong><\/li>\n <\/ul>\n<\/div>\n\n<figure id=\"fig-4\">\n <div class=\"metric-bar-container\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent)\">Accuracy<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:94%;background:var(--accent)\">94%<\/div><\/div>\n <span class=\"value\">94%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent2)\">Precision<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:66.7%;background:var(--accent2)\">66.7%<\/div><\/div>\n <span class=\"value\">66.7%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent4);color:#1a1a2e\">Recall<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:80%;background:var(--accent4)\">80%<\/div><\/div>\n <span class=\"value\">80%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent5)\">F1<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:72.7%;background:var(--accent5)\">72.7%<\/div><\/div>\n <span class=\"value\">72.7%<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 4<\/strong> \u540c\u4e00\u6a21\u578b\u5728\u56db\u4e2a\u6307\u6807\u4e0a\u7684\u8868\u73b0\u5dee\u5f02\uff1aAccuracy \u865a\u9ad8\uff0cF1 \u53cd\u6620\u771f\u5b9e\u7efc\u5408\u6c34\u5e73<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"zh-8\">\u516b\u3001\u4e0d\u5747\u8861\u6570\u636e\u96c6\u7684\u6311\u6218<\/h2>\n\n<p>\u5f53\u6b63\u8d1f\u6837\u672c\u6bd4\u4f8b\u60ac\u6b8a\u65f6\uff08\u5982\u6b3a\u8bc8\u68c0\u6d4b 1:1000\u3001\u7f55\u89c1\u75c5 1:10000\uff09\uff0cAccuracy \u4f1a\u5931\u6548\uff0c\u9700\u8981\u4f9d\u8d56 Precision\u3001Recall \u548c F1<sup><a href=\"#cite-6\">[6]<\/a><\/sup>\u3002<\/p>\n\n<h3>8.1 Accuracy \u5931\u6548\u6f14\u793a<\/h3>\n\n<div class=\"compare-box\">\n <div class=\"compare-col bad\">\n <h4>\u274c \u4ec5\u770b Accuracy<\/h4>\n <p>10000 \u7b14\u4ea4\u6613\u4e2d 10 \u7b14\u662f\u6b3a\u8bc8\u3002\u6a21\u578b\u5168\u90e8\u9884\u6d4b\u4e3a”\u6b63\u5e38”\u3002<\/p>\n <p>TP=0, FP=0, FN=10, TN=9990<\/p>\n <p><strong>Accuracy = 9990\/10000 = 99.9%<\/strong><\/p>\n <p>\u770b\u8d77\u6765\u975e\u5e38\u597d\u2014\u2014\u4f46\u4e00\u4e2a\u6b3a\u8bc8\u90fd\u6ca1\u6293\u5230\u3002<\/p>\n <\/div>\n <div class=\"compare-col good\">\n <h4>\u2705 \u770b Precision\/Recall\/F1<\/h4>\n <p>\u540c\u4e00\u6a21\u578b\uff1a<\/p>\n <p><strong>Precision<\/strong> = 0\/(0+0) = <strong>\u672a\u5b9a\u4e49<\/strong>\uff08\u65e0\u9884\u6d4b\u6b63\u6837\u672c\uff09<\/p>\n <p><strong>Recall<\/strong> = 0\/(0+10) = <strong>0%<\/strong><\/p>\n <p><strong>F1<\/strong> = <strong>0%<\/strong>\uff08\u6216\u672a\u5b9a\u4e49\uff09<\/p>\n <p>\u7acb\u523b\u66b4\u9732\u4e86\u6a21\u578b\u5b8c\u5168\u65e0\u6548\u3002<\/p>\n <\/div>\n<\/div>\n\n<h3>8.2 \u4e0d\u5747\u8861\u6570\u636e\u7684\u5e94\u5bf9\u7b56\u7565<\/h3>\n\n<ol class=\"steps\">\n <li>\n <strong>\u9009\u62e9\u6b63\u786e\u7684\u6307\u6807<\/strong>\n <span class=\"note\">\u4f7f\u7528 Precision\u3001Recall\u3001F1 \u66ff\u4ee3 Accuracy\u3002\u8003\u8651 PR-AUC\uff08Precision-Recall \u66f2\u7ebf\u4e0b\u9762\u79ef\uff09\u3002<\/span>\n <\/li>\n <li>\n <strong>\u91cd\u91c7\u6837\uff08Resampling\uff09<\/strong>\n <span class=\"note\">\u8fc7\u91c7\u6837\u5c11\u6570\u7c7b\uff08SMOTE\uff09\u6216\u6b20\u91c7\u6837\u591a\u6570\u7c7b\uff0c\u4f7f\u8bad\u7ec3\u96c6\u66f4\u5747\u8861\u3002<\/span>\n <\/li>\n <li>\n <strong>\u7c7b\u522b\u6743\u91cd\uff08Class Weight\uff09<\/strong>\n <span class=\"note\">\u5728\u635f\u5931\u51fd\u6570\u4e2d\u7ed9\u5c11\u6570\u7c7b\u66f4\u9ad8\u6743\u91cd\uff0c\u8ba9\u6a21\u578b\u66f4\u91cd\u89c6\u5c11\u6570\u7c7b\u7684\u9519\u8bef\u3002<\/span>\n <\/li>\n <li>\n <strong>\u8c03\u6574\u51b3\u7b56\u9608\u503c<\/strong>\n <span class=\"note\">\u9ed8\u8ba4\u9608\u503c 0.5 \u4e0d\u4e00\u5b9a\u6700\u4f18\uff0c\u53ef\u6839\u636e\u4e1a\u52a1\u9700\u6c42\u8c03\u6574\u4ee5\u5e73\u8861 P\/R\u3002<\/span>\n <\/li>\n <li>\n <strong>\u4f7f\u7528\u9002\u5408\u7684\u7b97\u6cd5<\/strong>\n <span class=\"note\">\u96c6\u6210\u65b9\u6cd5\uff08\u5982 XGBoost\uff09\u3001\u5f02\u5e38\u68c0\u6d4b\u65b9\u6cd5\u5bf9\u4e0d\u5747\u8861\u6570\u636e\u66f4\u9c81\u68d2\u3002<\/span>\n <\/li>\n<\/ol>\n\n\n<h2 id=\"zh-9\">\u4e5d\u3001\u591a\u5206\u7c7b\u573a\u666f\u6269\u5c55<\/h2>\n\n<p>\u5728\u591a\u5206\u7c7b\u4efb\u52a1\u4e2d\uff08\u5982\u624b\u5199\u6570\u5b57\u8bc6\u522b 0-9\uff09\uff0c\u6df7\u6dc6\u77e9\u9635\u6269\u5c55\u4e3a N\u00d7N\u3002\u5982\u4f55\u5c06\u4e8c\u5206\u7c7b\u6307\u6807\u6269\u5c55\u5230\u591a\u5206\u7c7b\uff1f\u6709\u4e09\u79cd\u5e38\u89c1\u5e73\u5747\u65b9\u5f0f<sup><a href=\"#cite-7\">[7]<\/a><\/sup>\uff1a<\/p>\n\n<h3>9.1 \u4e09\u79cd\u5e73\u5747\u7b56\u7565<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 6<\/strong> \u591a\u5206\u7c7b\u5e73\u5747\u7b56\u7565\u5bf9\u6bd4<\/caption>\n <thead>\n <tr><th>\u7b56\u7565<\/th><th>\u8ba1\u7b97\u65b9\u5f0f<\/th><th>\u7279\u70b9<\/th><th>\u9002\u7528\u573a\u666f<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>Macro<\/strong><\/td><td>\u5404\u7c7b\u522b\u6307\u6807\u5206\u522b\u8ba1\u7b97\u540e\u53d6\u7b97\u672f\u5e73\u5747<\/td><td>\u5404\u7c7b\u522b\u7b49\u6743\uff0c\u91cd\u89c6\u5c11\u6570\u7c7b<\/td><td>\u5404\u7c7b\u522b\u540c\u7b49\u91cd\u8981<\/td><\/tr>\n <tr><td><strong>Micro<\/strong><\/td><td>\u6240\u6709\u7c7b\u522b TP\/FP\/FN \u6c47\u603b\u540e\u8ba1\u7b97\u5168\u5c40\u6307\u6807<\/td><td>\u6837\u672c\u591a\u7684\u7c7b\u6743\u91cd\u66f4\u5927<\/td><td>\u6574\u4f53\u6027\u80fd\u8bc4\u4f30<\/td><\/tr>\n <tr><td><strong>Weighted<\/strong><\/td><td>\u5404\u7c7b\u522b\u6307\u6807\u6309\u6837\u672c\u91cf\u52a0\u6743\u5e73\u5747<\/td><td>\u517c\u987e\u7c7b\u522b\u6bd4\u4f8b<\/td><td>\u4e0d\u5747\u8861\u591a\u5206\u7c7b<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<h3>9.2 Macro vs Micro \u793a\u4f8b<\/h3>\n\n<div class=\"card\">\n <h4>\u4e09\u5206\u7c7b\u793a\u4f8b<\/h4>\n <p>3 \u4e2a\u7c7b\u522b A\u3001B\u3001C\uff0c\u6837\u672c\u6570\u5206\u522b\u4e3a 100\u300150\u300110\u3002<\/p>\n <pre class=\"code-block\">\u5404\u7c7b\u522b\u7684 Recall:\n \u7c7b\u522b A (100\u6837\u672c): Recall = 90\/100 = 0.90\n \u7c7b\u522b B ( 50\u6837\u672c): Recall = 40\/50 = 0.80\n \u7c7b\u522b C ( 10\u6837\u672c): Recall = 5\/10 = 0.50\n\nMacro-Recall = (0.90 + 0.80 + 0.50) \/ 3 = 0.733\n \u2192 \u6bcf\u4e2a\u7c7b\u522b\u540c\u7b49\u91cd\u8981\uff0cC \u7684\u4f4e Recall \u62c9\u4f4e\u4e86\u5747\u503c\n\nMicro-Recall = (90+40+5) \/ (100+50+10) = 135\/160 = 0.844\n \u2192 \u6309\u6837\u672c\u52a0\u6743\uff0cA \u7684\u9ad8\u5360\u6bd4\u63a8\u9ad8\u4e86\u5747\u503c\n\nWeighted-Recall = (0.90\u00d7100 + 0.80\u00d750 + 0.50\u00d710) \/ 160 = 0.844\n \u2192 \u4e0e Micro \u76f8\u540c\uff08\u56e0\u4e3a Recall \u7684\u52a0\u6743\u672c\u8d28\uff09<\/pre>\n<\/div>\n\n<div class=\"info-box\">\n <strong>\u9009\u62e9\u5efa\u8bae\uff1a<\/strong>\u5982\u679c\u5c11\u6570\u7c7b\u7684\u8868\u73b0\u540c\u6837\u91cd\u8981\uff08\u5982\u5404\u75be\u75c5\u8bca\u65ad\uff09\uff0c\u7528 <strong>Macro-F1<\/strong>\uff1b\u5982\u679c\u5173\u6ce8\u6574\u4f53\u9884\u6d4b\u51c6\u786e\u5ea6\uff0c\u7528 <strong>Micro-F1<\/strong>\uff1b\u5982\u679c\u7c7b\u522b\u95f4\u4e0d\u5747\u8861\u4e14\u9700\u517c\u987e\u6bd4\u4f8b\uff0c\u7528 <strong>Weighted-F1<\/strong>\u3002\n<\/div>\n\n<h3>9.3 One-vs-Rest \u601d\u8def<\/h3>\n\n<p>\u591a\u5206\u7c7b\u6307\u6807\u7684\u5e95\u5c42\u8ba1\u7b97\u901a\u5e38\u91c7\u7528 <strong>One-vs-Rest<\/strong>\uff08OvR\uff09\u7b56\u7565\uff1a\u5c06\u6bcf\u4e2a\u7c7b\u522b\u4f9d\u6b21\u89c6\u4e3a”\u6b63\u7c7b”\uff0c\u5176\u4f59\u6240\u6709\u7c7b\u522b\u89c6\u4e3a”\u8d1f\u7c7b”\uff0c\u8ba1\u7b97\u8be5\u7c7b\u7684 Precision\/Recall\/F1\uff0c\u518d\u6309\u4e0a\u8ff0\u5e73\u5747\u65b9\u5f0f\u6c47\u603b\u3002<\/p>\n\n<figure id=\"fig-5\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item\">\u7c7b\u522b A \u4e3a\u6b63<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (A)<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">\u7c7b\u522b B \u4e3a\u6b63<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (B)<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item purple\">Macro\/Micro\/Weighted \u5e73\u5747<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">\u7c7b\u522b C \u4e3a\u6b63<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (C)<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 5<\/strong> One-vs-Rest \u7b56\u7565\uff1a\u5c06 N \u5206\u7c7b\u8f6c\u5316\u4e3a N \u4e2a\u4e8c\u5206\u7c7b\u95ee\u9898<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"zh-10\">\u5341\u3001\u5b9e\u9645\u5e94\u7528\u6307\u5357\u4e0e\u4ee3\u7801\u793a\u4f8b<\/h2>\n\n<h3>10.1 \u573a\u666f-\u6307\u6807\u5339\u914d\u6307\u5357<\/h3>\n\n<div class=\"scenario-grid\">\n <div class=\"scenario-card medical\">\n <h4>\ud83c\udfe5 \u533b\u7597\u8bca\u65ad<\/h4>\n <p class=\"priority\"><strong>\u4f18\u5148\u6307\u6807\uff1a<\/strong>Recall \/ F2-score<\/p>\n <p class=\"reason\">\u6f0f\u8bca\uff08FN\uff09\u4ee3\u4ef7\u8fdc\u9ad8\u4e8e\u8bef\u8bca\uff08FP\uff09\u3002\u5b81\u53ef\u591a\u505a\u68c0\u67e5\uff0c\u4e0d\u53ef\u653e\u8fc7\u4e00\u4e2a\u75c5\u4eba\u3002<\/p>\n <\/div>\n <div class=\"scenario-card spam\">\n <h4>\ud83d\udce7 \u5783\u573e\u90ae\u4ef6\u8fc7\u6ee4<\/h4>\n <p class=\"priority\"><strong>\u4f18\u5148\u6307\u6807\uff1a<\/strong>Precision \/ F0.5<\/p>\n <p class=\"reason\">\u8bef\u5220\u6b63\u5e38\u90ae\u4ef6\uff08FP\uff09\u4ee3\u4ef7\u8fdc\u9ad8\u4e8e\u653e\u8fc7\u4e00\u5c01\u5783\u573e\u90ae\u4ef6\uff08FN\uff09\u3002<\/p>\n <\/div>\n <div class=\"scenario-card fraud\">\n <h4>\ud83d\udcb3 \u6b3a\u8bc8\u68c0\u6d4b<\/h4>\n <p class=\"priority\"><strong>\u4f18\u5148\u6307\u6807\uff1a<\/strong>Recall \/ PR-AUC<\/p>\n <p class=\"reason\">\u6f0f\u6389\u4e00\u7b14\u6b3a\u8bc8\u635f\u5931\u5de8\u5927\uff0c\u5b81\u53ef\u591a\u5ba1\u6838\u3002\u6570\u636e\u6781\u5ea6\u4e0d\u5747\u8861\u3002<\/p>\n <\/div>\n <div class=\"scenario-card search\">\n <h4>\ud83d\udd0d \u641c\u7d22\u5f15\u64ce<\/h4>\n <p class=\"priority\"><strong>\u4f18\u5148\u6307\u6807\uff1a<\/strong>Precision@K<\/p>\n <p class=\"reason\">\u7528\u6237\u53ea\u770b\u524d\u51e0\u6761\u7ed3\u679c\uff0c\u8fd4\u56de\u7684\u7cbe\u786e\u5ea6\u6bd4\u8986\u76d6\u7387\u66f4\u91cd\u8981\u3002<\/p>\n <\/div>\n<\/div>\n\n<h3>10.2 \u51b3\u7b56\u6d41\u7a0b\u56fe<\/h3>\n\n<figure id=\"fig-6\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">\u6570\u636e\u662f\u5426\u5747\u8861\uff1f<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item green\">\u662f \u2192 Accuracy<\/span>\n <span class=\"flow-arrow\" style=\"margin:0 1rem\">|<\/span>\n <span class=\"flow-item yellow\">\u5426 \u2192 \u7ee7\u7eed<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.3rem\">\n <span class=\"flow-arrow\">\u2193<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">FP \u548c FN \u54ea\u4e2a\u4ee3\u4ef7\u9ad8\uff1f<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">FP \u9ad8 \u2192 Precision<\/span>\n <span class=\"flow-arrow\">|<\/span>\n <span class=\"flow-item green\">FN \u9ad8 \u2192 Recall<\/span>\n <span class=\"flow-arrow\">|<\/span>\n <span class=\"flow-item purple\">\u76f8\u5f53 \u2192 F1<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>\u56fe 6<\/strong> \u6307\u6807\u9009\u62e9\u51b3\u7b56\u6d41\u7a0b<\/figcaption>\n<\/figure>\n\n<h3>10.3 Python \u4ee3\u7801\u793a\u4f8b<\/h3>\n\n<pre class=\"terminal\"><span class=\"comment\"># \u4f7f\u7528 scikit-learn \u8ba1\u7b97\u5206\u7c7b\u8bc4\u4f30\u6307\u6807<\/span>\n<span class=\"keyword\">from<\/span> sklearn.metrics <span class=\"keyword\">import<\/span> (\n accuracy_score,\n precision_score,\n recall_score,\n f1_score,\n classification_report,\n confusion_matrix\n)\n<span class=\"keyword\">from<\/span> sklearn.datasets <span class=\"keyword\">import<\/span> make_classification\n<span class=\"keyword\">from<\/span> sklearn.model_selection <span class=\"keyword\">import<\/span> train_test_split\n<span class=\"keyword\">from<\/span> sklearn.ensemble <span class=\"keyword\">import<\/span> RandomForestClassifier\n\n<span class=\"comment\"># 1. \u751f\u6210\u4e0d\u5747\u8861\u6570\u636e\uff08\u6b63\u8d1f\u6bd4 1:9\uff09<\/span>\nX, y = make_classification(\n n_samples=<span class=\"string\">1000<\/span>,\n weights=[<span class=\"string\">0.1<\/span>],\n random_state=<span class=\"string\">42<\/span>\n)\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=<span class=\"string\">0.3<\/span>)\n\n<span class=\"comment\"># 2. \u8bad\u7ec3\u6a21\u578b<\/span>\nmodel = RandomForestClassifier(random_state=<span class=\"string\">42<\/span>)\nmodel.fit(X_train, y_train)\ny_pred = model.predict(X_test)\n\n<span class=\"comment\"># 3. \u6df7\u6dc6\u77e9\u9635<\/span>\ncm = confusion_matrix(y_test, y_pred)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Confusion Matrix:\\n{cm}\"<\/span>)\n<span class=\"output\"># [[256 11]\n# [ 13 20]]<\/span>\n\ntn, fp, fn, tp = cm.ravel()\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"TP={tp}, TN={tn}, FP={fp}, FN={fn}\"<\/span>)\n<span class=\"output\"># TP=20, TN=256, FP=11, FN=13<\/span>\n\n<span class=\"comment\"># 4. \u56db\u5927\u6307\u6807<\/span>\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Accuracy: {accuracy_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Accuracy: 0.9200<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Precision: {precision_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Precision: 0.6452<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Recall: {recall_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Recall: 0.6061<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"F1-score: {f1_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># F1-score: 0.6250<\/span>\n\n<span class=\"comment\"># 5. \u591a\u5206\u7c7b\u62a5\u544a\uff08\u542b Macro\/Micro\/Weighted\uff09<\/span>\n<span class=\"keyword\">print<\/span>(classification_report(y_test, y_pred, target_names=[<span class=\"string\">\"Negative\"<\/span>, <span class=\"string\">\"Positive\"<\/span>]))\n<span class=\"output\"># precision recall f1-score support\n# Negative 0.95 0.96 0.95 267\n# Positive 0.65 0.61 0.63 33\n# accuracy 0.92 300\n# macro avg 0.80 0.78 0.79 300\n# weighted avg 0.92 0.92 0.92 300<\/span>\n\n<span class=\"comment\"># 6. \u4ea4\u53c9\u9a8c\u8bc1\u4e2d\u6307\u5b9a average \u7b56\u7565<\/span>\n<span class=\"keyword\">from<\/span> sklearn.model_selection <span class=\"keyword\">import<\/span> cross_val_score\n\nmacro_f1 = cross_val_score(model, X, y, cv=<span class=\"string\">5<\/span>, scoring=<span class=\"string\">\"f1_macro\"<\/span>)\nweighted_f1 = cross_val_score(model, X, y, cv=<span class=\"string\">5<\/span>, scoring=<span class=\"string\">\"f1_weighted\"<\/span>)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Macro F1 CV: {macro_f1.mean():.4f}\"<\/span>)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Weighted F1 CV:{weighted_f1.mean():.4f}\"<\/span>)<\/pre>\n\n<h3>10.4 \u5e38\u89c1\u8bef\u533a<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>\u8868 7<\/strong> \u5e38\u89c1\u8bef\u533a\u4e0e\u7ea0\u6b63<\/caption>\n <thead>\n <tr><th>\u8bef\u533a<\/th><th>\u95ee\u9898<\/th><th>\u7ea0\u6b63<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>\u53ea\u7528 Accuracy<\/td><td>\u4e0d\u5747\u8861\u6570\u636e\u4e0b\u865a\u9ad8<\/td><td>\u642d\u914d Precision\/Recall\/F1 \u4f7f\u7528<\/td><\/tr>\n <tr><td>\u8ffd\u6c42 F1 \u6700\u9ad8<\/td><td>\u53ef\u80fd\u4e0d\u7b26\u5408\u4e1a\u52a1\u9700\u6c42<\/td><td>\u6839\u636e FP\/FN \u4ee3\u4ef7\u9009\u62e9 F\u03b2<\/td><\/tr>\n <tr><td>\u5ffd\u7565\u9608\u503c\u8c03\u4f18<\/td><td>\u9ed8\u8ba4 0.5 \u9608\u503c\u672a\u5fc5\u6700\u4f18<\/td><td>\u7528 PR \u66f2\u7ebf\u9009\u62e9\u4e1a\u52a1\u6700\u4f18\u9608\u503c<\/td><\/tr>\n <tr><td>\u6d4b\u8bd5\u96c6\u4e0d\u5747\u8861<\/td><td>\u6307\u6807\u6709\u504f<\/td><td>\u5206\u5c42\u62bd\u6837\u4fdd\u6301\u6bd4\u4f8b\uff0c\u6216\u4f7f\u7528\u5206\u5c42\u4ea4\u53c9\u9a8c\u8bc1<\/td><\/tr>\n <tr><td>\u5ffd\u89c6 TN \u5f71\u54cd<\/td><td>F1 \u4e0d\u542b TN\uff0c\u53ef\u80fd\u9ad8\u4f30<\/td><td>\u6781\u7aef\u4e0d\u5747\u8861\u65f6\u8865\u5145 MCC \u6307\u6807<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>\u603b\u7ed3\uff1a<\/strong>Accuracy\u3001Precision\u3001Recall\u3001F1-score \u662f\u5206\u7c7b\u8bc4\u4f30\u7684\u57fa\u77f3\u3002\u5b83\u4eec\u5404\u6709\u9002\u7528\u573a\u666f\uff0c\u4e0d\u5b58\u5728”\u6700\u597d\u7684\u6307\u6807”\u2014\u2014\u53ea\u6709”\u6700\u9002\u5408\u5f53\u524d\u4e1a\u52a1\u573a\u666f\u7684\u6307\u6807”\u3002\u7406\u89e3\u6df7\u6dc6\u77e9\u9635\u662f\u638c\u63e1\u4e00\u5207\u7684\u524d\u63d0\uff0c\u800c\u6839\u636e\u6570\u636e\u5747\u8861\u6027\u3001FP\/FN \u4ee3\u4ef7\u6743\u8861\u9009\u62e9\u5408\u9002\u7684\u6307\u6807\u7ec4\u5408\uff0c\u662f\u6bcf\u4e2a\u673a\u5668\u5b66\u4e60\u4ece\u4e1a\u8005\u7684\u5fc5\u5907\u80fd\u529b\u3002\n<\/div>\n\n<\/div>\n\n\n<div class=\"lang-section\" id=\"lang-en\">\n<div class=\"hero\">\n <h1>Complete Guide to Classification Metrics<span class=\"sub\">From Confusion Matrix to Accuracy, Precision, Recall & F1-score<\/span><\/h1>\n <p>Understand the four core evaluation metrics in ML classification: principles, formulas, use cases, and trade-offs<\/p>\n<\/div>\n\n<div class=\"toc\">\n <h3>Contents<\/h3>\n <ol>\n <li><a href=\"#en-1\">1. Overview: Why Evaluation Metrics Matter<\/a><\/li>\n <li><a href=\"#en-2\">2. Confusion Matrix: The Foundation<\/a><\/li>\n <li><a href=\"#en-3\">3. Accuracy<\/a><\/li>\n <li><a href=\"#en-4\">4. Precision<\/a><\/li>\n <li><a href=\"#en-5\">5. Recall<\/a><\/li>\n <li><a href=\"#en-6\">6. F1-score<\/a><\/li>\n <li><a href=\"#en-7\">7. Relationships and Trade-offs<\/a><\/li>\n <li><a href=\"#en-8\">8. Imbalanced Dataset Challenges<\/a><\/li>\n <li><a href=\"#en-9\">9. Multi-class Extensions<\/a><\/li>\n <li><a href=\"#en-10\">10. Practical Guide & Code Examples<\/a><\/li>\n <\/ol>\n<\/div>\n\n\n<h2 id=\"en-1\">1. Overview: Why Evaluation Metrics Matter<\/h2>\n\n<p>In machine learning classification tasks, model predictions need objective, quantifiable metrics to assess quality. Knowing “the model got 95 correct” is insufficient\u2014we need to understand its performance on <strong>positive<\/strong> and <strong>negative<\/strong> classes separately, whether it’s biased, and whether it meets specific business requirements<sup><a href=\"#cite-1\">[1]<\/a><\/sup>.<\/p>\n\n<div class=\"info-box\">\n <strong>Core Problem:<\/strong> Different metrics measure different dimensions of model performance. There is no “universal metric”\u2014the choice depends on the specific business scenario, data distribution, and cost trade-offs. Understanding each metric’s <strong>definition, applicability, and limitations<\/strong> is the prerequisite for proper model evaluation.\n<\/div>\n\n<h3>1.1 Four Core Metrics at a Glance<\/h3>\n\n<div class=\"cmd-grid\">\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge acc\">Accuracy<\/span><\/h4>\n <span class=\"desc\">Overall correctness. Proportion of all predictions that are correct. Intuitive but vulnerable to imbalance.<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge pre\">Precision<\/span><\/h4>\n <span class=\"desc\">Of predicted positives, how many are actually positive. Focus: “purity of predictions.”<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge rec\">Recall<\/span><\/h4>\n <span class=\"desc\">Of actual positives, how many were correctly found. Focus: “did we miss any?”<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4><span class=\"metric-badge f1\">F1-score<\/span><\/h4>\n <span class=\"desc\">Harmonic mean of precision and recall. A single balanced metric combining both.<\/span>\n <\/div>\n<\/div>\n\n<figure id=\"fig-1-en\">\n <div class=\"flow-diagram\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">Confusion Matrix<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item\">TP \/ TN \/ FP \/ FN<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.5rem\">\n <span class=\"flow-arrow\">\u2193<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">Accuracy<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item green\">Precision<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item yellow\">Recall<\/span>\n <span class=\"flow-arrow\">\u00b7<\/span>\n <span class=\"flow-item purple\">F1<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 1<\/strong> All four metrics derive from the four quantities in the confusion matrix<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"en-2\">2. Confusion Matrix: The Foundation<\/h2>\n\n<p>The <strong>Confusion Matrix<\/strong> is a 2\u00d72 table that cross-tabulates model predictions against ground truth labels, producing four fundamental quantities. All evaluation metrics are derived from these four<sup><a href=\"#cite-2\">[2]<\/a><\/sup>.<\/p>\n\n<h3>2.1 The Four Basic Quantities<\/h3>\n\n<div class=\"cm-table\">\n <div class=\"cm-cell cm-corner\"><\/div>\n <div class=\"cm-cell cm-axis\">Predicted Positive<\/div>\n <div class=\"cm-cell cm-axis\">Predicted Negative<\/div>\n\n <div class=\"cm-cell cm-axis\">Actual Positive<\/div>\n <div class=\"cm-cell cm-tp\">TP<span class=\"cm-label\">True Positive<\/span><\/div>\n <div class=\"cm-cell cm-fn\">FN<span class=\"cm-label\">False Negative<\/span><\/div>\n\n <div class=\"cm-cell cm-axis\">Actual Negative<\/div>\n <div class=\"cm-cell cm-fp\">FP<span class=\"cm-label\">False Positive<\/span><\/div>\n <div class=\"cm-cell cm-tn\">TN<span class=\"cm-label\">True Negative<\/span><\/div>\n<\/div>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 1<\/strong> Meaning of the four confusion matrix quantities<\/caption>\n <thead>\n <tr><th>Symbol<\/th><th>Name<\/th><th>Meaning<\/th><th>Plain English<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>TP<\/strong><\/td><td>True Positive<\/td><td>Actually positive, predicted positive<\/td><td>Correct hit<\/td><\/tr>\n <tr><td><strong>TN<\/strong><\/td><td>True Negative<\/td><td>Actually negative, predicted negative<\/td><td>Correct rejection<\/td><\/tr>\n <tr><td><strong>FP<\/strong><\/td><td>False Positive<\/td><td>Actually negative, predicted positive<\/td><td>False alarm (Type I error)<\/td><\/tr>\n <tr><td><strong>FN<\/strong><\/td><td>False Negative<\/td><td>Actually positive, predicted negative<\/td><td>Miss (Type II error)<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<h3>2.2 Memory Aid<\/h3>\n\n<div class=\"card\">\n <h4>Quick Rule<\/h4>\n <p><strong>T \/ F<\/strong> = whether the prediction is <strong>correct<\/strong> (True = correct, False = wrong)<\/p>\n <p><strong>P \/ N<\/strong> = the model’s <strong>predicted class<\/strong> (Positive = predicted positive, Negative = predicted negative)<\/p>\n <p>Combined: <strong>TP<\/strong> = correct prediction of positive; <strong>FP<\/strong> = wrong prediction of positive (actually negative).<\/p>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>Key Relationship:<\/strong> Total samples = TP + TN + FP + FN. Where <strong>TP + FN<\/strong> = total actual positives, and <strong>TP + FP<\/strong> = total predicted positives. These two relationships are the foundation for deriving all metrics.\n<\/div>\n\n\n<h2 id=\"en-3\">3. Accuracy<\/h2>\n\n<p><strong>Accuracy<\/strong> is the most intuitive evaluation metric\u2014the proportion of all samples that the model predicted correctly<sup><a href=\"#cite-3\">[3]<\/a><\/sup>.<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Accuracy Formula<\/div>\n <div class=\"formula\">Accuracy = (TP + TN) \/ (TP + TN + FP + FN)<\/div>\n<\/div>\n\n<h3>3.1 Intuitive Understanding<\/h3>\n\n<p>Accuracy answers: <strong>“How does the model perform overall?”<\/strong> It treats correct predictions of positive and negative classes equally in the numerator, and is the only metric that considers TN.<\/p>\n\n<figure id=\"fig-2-en\">\n <div class=\"metric-bar-container\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"metric-bar\">\n <span class=\"label\">TP (60)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:60%;background:var(--accent)\">Hits<\/div><\/div>\n <span class=\"value\">60<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">TN (30)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:30%;background:var(--accent2)\">Correct rejects<\/div><\/div>\n <span class=\"value\">30<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">FP (5)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:5%;background:var(--accent4)\">False alarm<\/div><\/div>\n <span class=\"value\">5<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\">FN (5)<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:5%;background:var(--accent3)\">Miss<\/div><\/div>\n <span class=\"value\">5<\/span>\n <\/div>\n <div class=\"metric-bar\" style=\"margin-top:.8rem;border-top:1px solid var(--rule);padding-top:.6rem\">\n <span class=\"label\" style=\"color:var(--accent)\">Accuracy<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:90%;background:var(--accent)\">90 \/ 100<\/div><\/div>\n <span class=\"value\" style=\"color:var(--accent)\">90%<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 2<\/strong> Accuracy example: 90 of 100 predictions correct (TP=60 + TN=30), accuracy = 90%<\/figcaption>\n<\/figure>\n\n<h3>3.2 The Fatal Pitfall of Accuracy<\/h3>\n\n<div class=\"info-box danger\">\n <strong>Imbalanced Data Trap:<\/strong> When data is severely imbalanced, Accuracy becomes misleading. For example, of 1000 emails, 950 are normal and 50 are spam. A classifier that does <strong>nothing<\/strong> (labels everything as “normal”) achieves Accuracy = 950\/1000 = <strong>95%<\/strong>, yet it catches zero spam<sup><a href=\"#cite-3\">[3]<\/a><\/sup>.\n<\/div>\n\n<div class=\"compare-box\">\n <div class=\"compare-col good\">\n <h4>\u2705 When to Use<\/h4>\n <p>Classes are roughly balanced<\/p>\n <p>FP and FN costs are similar<\/p>\n <p>Quick overall performance check needed<\/p>\n <p>Initial reference for multi-class tasks<\/p>\n <\/div>\n <div class=\"compare-col bad\">\n <h4>\u274c When NOT to Use<\/h4>\n <p>Severely imbalanced data (fraud, rare disease)<\/p>\n <p>Positive class is rare but critical (high FN cost)<\/p>\n <p>Using Accuracy as the sole metric<\/p>\n <p>Need to distinguish different error types<\/p>\n <\/div>\n<\/div>\n\n\n<h2 id=\"en-4\">4. Precision<\/h2>\n\n<p><strong>Precision<\/strong> measures: <strong>of all samples predicted as positive, what fraction is actually positive<\/strong><sup><a href=\"#cite-1\">[1]<\/a><\/sup>.<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Precision Formula<\/div>\n <div class=\"formula\">Precision = TP \/ (TP + FP)<\/div>\n<\/div>\n\n<h3>4.1 Intuitive Understanding<\/h3>\n\n<p>Precision answers: <strong>“When the model says ‘yes’, how trustworthy is it?”<\/strong> It focuses on the <strong>purity<\/strong> of positive predictions.<\/p>\n\n<div class=\"card\">\n <h4>Spam Filter Example<\/h4>\n <p>The model flags 20 emails as “spam”\u201416 are actually spam, 4 are normal emails misclassified. Precision = 16 \/ 20 = <strong>80%<\/strong>.<\/p>\n <p>Higher Precision means fewer normal emails are wrongly flagged as spam\u2014users won’t lose important emails.<\/p>\n<\/div>\n\n<h3>4.2 Precision Characteristics<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 2<\/strong> Precision metric characteristics<\/caption>\n <thead>\n <tr><th>Dimension<\/th><th>Description<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>Focus<\/td><td>Purity of positive predictions (minimize FP)<\/td><\/tr>\n <tr><td>Numerator<\/td><td>TP (correctly predicted positives)<\/td><\/tr>\n <tr><td>Denominator<\/td><td>TP + FP (all predicted positives)<\/td><\/tr>\n <tr><td>Excludes TN<\/td><td>Doesn’t consider correctly rejected negatives<\/td><\/tr>\n <tr><td>Extreme value<\/td><td>FP=0 \u2192 Precision=1 (better to miss than misfire)<\/td><\/tr>\n <tr><td>How to improve<\/td><td>Raise threshold, predict positive only when most confident<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box warn\">\n <strong>Precision’s Limitation:<\/strong> High Precision doesn’t necessarily mean a good model. If the model is extremely conservative\u2014predicting positive for only 1 sample it’s most sure about (and it’s correct)\u2014Precision = 1\/1 = 100%, but it may have missed 999 actual positives. High Precision often comes at the cost of Recall.\n<\/div>\n\n\n<h2 id=\"en-5\">5. Recall<\/h2>\n\n<p><strong>Recall<\/strong> (also known as Sensitivity, Hit Rate, or True Positive Rate) measures: <strong>of all actual positive samples, what fraction was correctly predicted as positive<\/strong><sup><a href=\"#cite-4\">[4]<\/a><\/sup>.<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">Recall Formula<\/div>\n <div class=\"formula\">Recall = TP \/ (TP + FN)<\/div>\n<\/div>\n\n<h3>5.1 Intuitive Understanding<\/h3>\n\n<p>Recall answers: <strong>“Of all actual positives, how many did the model find?”<\/strong> It focuses on <strong>coverage<\/strong>\u2014did we miss any positives?<\/p>\n\n<div class=\"card\">\n <h4>Cancer Detection Example<\/h4>\n <p>Of 100 cancer patients, the model correctly identifies 85 and misses 15. Recall = 85 \/ 100 = <strong>85%<\/strong>.<\/p>\n <p>Higher Recall means fewer missed diagnoses. In medical settings, the cost of missing a patient (FN) is far higher than a false alarm (FP)\u2014better to run one more test than miss a patient.<\/p>\n<\/div>\n\n<h3>5.2 Recall Characteristics<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 3<\/strong> Recall metric characteristics<\/caption>\n <thead>\n <tr><th>Dimension<\/th><th>Description<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>Focus<\/td><td>Coverage of positive class (minimize FN)<\/td><\/tr>\n <tr><td>Numerator<\/td><td>TP (found positives)<\/td><\/tr>\n <tr><td>Denominator<\/td><td>TP + FN (all actual positives)<\/td><\/tr>\n <tr><td>Excludes TN<\/td><td>Doesn’t consider correctly rejected negatives<\/td><\/tr>\n <tr><td>Extreme value<\/td><td>FN=0 \u2192 Recall=1 (find everything, even false alarms)<\/td><\/tr>\n <tr><td>How to improve<\/td><td>Lower threshold, predict positive for any possibly positive sample<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box warn\">\n <strong>Recall’s Limitation:<\/strong> High Recall doesn’t necessarily mean a good model. If the model predicts positive for all samples, FN=0, Recall=100%, but it generates massive FP. High Recall often comes at the cost of Precision.\n<\/div>\n\n\n<h2 id=\"en-6\">6. F1-score<\/h2>\n\n<p><strong>F1-score<\/strong> is the <strong>harmonic mean<\/strong> of Precision and Recall, designed to balance the two<sup><a href=\"#cite-5\">[5]<\/a><\/sup>.<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">F1-score Formula<\/div>\n <div class=\"formula\">F1 = 2 \u00d7 (Precision \u00d7 Recall) \/ (Precision + Recall)<\/div>\n<\/div>\n\n<p>Equivalent form:<\/p>\n\n<pre class=\"code-block\">F1 = 2 \u00d7 TP \/ (2 \u00d7 TP + FP + FN)<\/pre>\n\n<h3>6.1 Why Harmonic Mean?<\/h3>\n\n<p>The key difference between harmonic and arithmetic mean: <strong>harmonic mean is more sensitive to extreme values<\/strong>. If Precision=0.01 and Recall=1.0, the arithmetic mean = 0.505 (looks okay), but the harmonic mean F1 = 0.0198 (exposes the low Precision)<sup><a href=\"#cite-5\">[5]<\/a><\/sup>.<\/p>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 4<\/strong> Comparison of averaging methods<\/caption>\n <thead>\n <tr><th>Precision<\/th><th>Recall<\/th><th>Arithmetic Mean<\/th><th>F1 (Harmonic)<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>0.80<\/td><td>0.80<\/td><td>0.80<\/td><td><strong>0.80<\/strong><\/td><\/tr>\n <tr><td>0.90<\/td><td>0.50<\/td><td>0.70<\/td><td><strong>0.643<\/strong><\/td><\/tr>\n <tr><td>1.00<\/td><td>0.50<\/td><td>0.75<\/td><td><strong>0.667<\/strong><\/td><\/tr>\n <tr><td>0.01<\/td><td>1.00<\/td><td>0.505<\/td><td><strong>0.0198<\/strong><\/td><\/tr>\n <tr><td>0.00<\/td><td>1.00<\/td><td>0.50<\/td><td><strong>0.00<\/strong><\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box\">\n <strong>Harmonic Mean’s Punishment:<\/strong> When either Precision or Recall is 0, F1 must be 0. This means F1 requires the model to perform decently on both dimensions\u2014no “one-legged” walking. The arithmetic mean would mask an extreme low value.\n<\/div>\n\n<h3>6.2 F-beta Generalization<\/h3>\n\n<p>F1 is a special case of the more general <strong>F-\u03b2<\/strong> metric (\u03b2=1). \u03b2 controls Recall’s weight relative to Precision:<\/p>\n\n<div class=\"formula-box\">\n <div class=\"formula-name\">F-\u03b2 Formula<\/div>\n <div class=\"formula\">F\u03b2 = (1 + \u03b2\u00b2) \u00d7 (Precision \u00d7 Recall) \/ (\u03b2\u00b2 \u00d7 Precision + Recall)<\/div>\n<\/div>\n\n<div class=\"cmd-grid\">\n <div class=\"cmd-card\">\n <h4>F1 (\u03b2=1)<\/h4>\n <span class=\"desc\">Equal weight to Precision and Recall. Most common composite metric.<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4>F2 (\u03b2=2)<\/h4>\n <span class=\"desc\">Recall weighted higher. For high FN-cost scenarios (e.g., medical).<\/span>\n <\/div>\n <div class=\"cmd-card\">\n <h4>F0.5 (\u03b2=0.5)<\/h4>\n <span class=\"desc\">Precision weighted higher. For high FP-cost scenarios (e.g., spam).<\/span>\n <\/div>\n<\/div>\n\n\n<h2 id=\"en-7\">7. Relationships and Trade-offs<\/h2>\n\n<h3>7.1 The Precision-Recall Seesaw<\/h3>\n\n<p>There is a natural <strong>trade-off<\/strong> between Precision and Recall. By adjusting the classification threshold, you can improve one metric but typically at the expense of the other<sup><a href=\"#cite-4\">[4]<\/a><\/sup>.<\/p>\n\n<figure id=\"fig-3-en\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item yellow\">Lower threshold<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">More positive predictions<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">Recall \u2191<\/span>\n <span class=\"flow-arrow\">+<\/span>\n <span class=\"flow-item red\">FP \u2191<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item red\">Precision \u2193<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.6rem\">\n <span class=\"flow-item yellow\">Raise threshold<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item\">Fewer positive predictions<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">Precision \u2191<\/span>\n <span class=\"flow-arrow\">+<\/span>\n <span class=\"flow-item red\">FN \u2191<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item red\">Recall \u2193<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 3<\/strong> Precision-Recall trade-off: adjusting threshold is like a seesaw<\/figcaption>\n<\/figure>\n\n<h3>7.2 Four-Metric Comparison<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 5<\/strong> Core comparison of the four metrics<\/caption>\n <thead>\n <tr><th>Metric<\/th><th>Formula<\/th><th>Focus<\/th><th>Excludes<\/th><th>Most afraid of<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>Accuracy<\/strong><\/td><td>(TP+TN)\/All<\/td><td>Overall correctness<\/td><td>\u2014<\/td><td>Imbalanced data<\/td><\/tr>\n <tr><td><strong>Precision<\/strong><\/td><td>TP\/(TP+FP)<\/td><td>Prediction purity<\/td><td>TN<\/td><td>Too many FP<\/td><\/tr>\n <tr><td><strong>Recall<\/strong><\/td><td>TP\/(TP+FN)<\/td><td>Positive coverage<\/td><td>TN<\/td><td>Too many FN<\/td><\/tr>\n <tr><td><strong>F1<\/strong><\/td><td>2PR\/(P+R)<\/td><td>P\/R balance<\/td><td>TN<\/td><td>Extreme P or R<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>Key Insight:<\/strong> Precision, Recall, and F1 all <strong>exclude TN<\/strong>. This means in scenarios with abundant negative samples (e.g., fraud detection where 99.9% are normal), TN is huge but doesn’t participate in these three metrics\u2014so they are not directly affected by data imbalance. This is why they’re preferred over Accuracy for imbalanced data.\n<\/div>\n\n<h3>7.3 Numerical Example: Multi-dimensional Evaluation<\/h3>\n\n<div class=\"card\">\n <h4>Scenario: Disease Screening<\/h4>\n <p>Of 1000 people, 100 are actually sick. The model predicts 120 as “sick” (80 correctly, 40 false alarms), the remaining 880 as “healthy” (20 missed, 860 correctly excluded).<\/p>\n <ul style=\"margin-left:1.5rem;margin-bottom:.5rem\">\n <li>TP=80, FP=40, FN=20, TN=860<\/li>\n <li><strong>Accuracy<\/strong> = (80+860)\/1000 = <strong>94%<\/strong> (looks good)<\/li>\n <li><strong>Precision<\/strong> = 80\/(80+40) = <strong>66.7%<\/strong> (1 in 3 diagnoses is false alarm)<\/li>\n <li><strong>Recall<\/strong> = 80\/(80+20) = <strong>80%<\/strong> (found 80 of 100 patients)<\/li>\n <li><strong>F1<\/strong> = 2\u00d7(0.667\u00d70.80)\/(0.667+0.80) = <strong>72.7%<\/strong><\/li>\n <\/ul>\n<\/div>\n\n<figure id=\"fig-4-en\">\n <div class=\"metric-bar-container\" style=\"border:none;box-shadow:none;padding:0\">\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent)\">Accuracy<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:94%;background:var(--accent)\">94%<\/div><\/div>\n <span class=\"value\">94%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent2)\">Precision<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:66.7%;background:var(--accent2)\">66.7%<\/div><\/div>\n <span class=\"value\">66.7%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent4);color:#1a1a2e\">Recall<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:80%;background:var(--accent4)\">80%<\/div><\/div>\n <span class=\"value\">80%<\/span>\n <\/div>\n <div class=\"metric-bar\">\n <span class=\"label\" style=\"color:var(--accent5)\">F1<\/span>\n <div class=\"bar-bg\"><div class=\"bar-fill\" style=\"width:72.7%;background:var(--accent5)\">72.7%<\/div><\/div>\n <span class=\"value\">72.7%<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 4<\/strong> Same model across four metrics: Accuracy is inflated, F1 reflects true composite performance<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"en-8\">8. Imbalanced Dataset Challenges<\/h2>\n\n<p>When positive\/negative ratios are extreme (fraud 1:1000, rare disease 1:10000), Accuracy fails. We need Precision, Recall, and F1<sup><a href=\"#cite-6\">[6]<\/a><\/sup>.<\/p>\n\n<h3>8.1 Accuracy Failure Demo<\/h3>\n\n<div class=\"compare-box\">\n <div class=\"compare-col bad\">\n <h4>\u274c Looking at Accuracy Only<\/h4>\n <p>Of 10000 transactions, 10 are fraud. Model predicts all as “normal.”<\/p>\n <p>TP=0, FP=0, FN=10, TN=9990<\/p>\n <p><strong>Accuracy = 9990\/10000 = 99.9%<\/strong><\/p>\n <p>Looks great\u2014but caught zero fraud.<\/p>\n <\/div>\n <div class=\"compare-col good\">\n <h4>\u2705 Looking at P\/R\/F1<\/h4>\n <p>Same model:<\/p>\n <p><strong>Precision<\/strong> = 0\/(0+0) = <strong>undefined<\/strong><\/p>\n <p><strong>Recall<\/strong> = 0\/(0+10) = <strong>0%<\/strong><\/p>\n <p><strong>F1<\/strong> = <strong>0%<\/strong> (or undefined)<\/p>\n <p>Immediately exposes model is useless.<\/p>\n <\/div>\n<\/div>\n\n<h3>8.2 Strategies for Imbalanced Data<\/h3>\n\n<ol class=\"steps\">\n <li>\n <strong>Choose the Right Metric<\/strong>\n <span class=\"note\">Use Precision, Recall, F1 instead of Accuracy. Consider PR-AUC (area under Precision-Recall curve).<\/span>\n <\/li>\n <li>\n <strong>Resampling<\/strong>\n <span class=\"note\">Oversample minority class (SMOTE) or undersample majority class to balance training data.<\/span>\n <\/li>\n <li>\n <strong>Class Weighting<\/strong>\n <span class=\"note\">Assign higher weight to minority class in loss function to make the model care more about its errors.<\/span>\n <\/li>\n <li>\n <strong>Threshold Tuning<\/strong>\n <span class=\"note\">Default 0.5 threshold may not be optimal; adjust based on business needs to balance P\/R.<\/span>\n <\/li>\n <li>\n <strong>Use Appropriate Algorithms<\/strong>\n <span class=\"note\">Ensemble methods (XGBoost) and anomaly detection approaches are more robust to imbalance.<\/span>\n <\/li>\n<\/ol>\n\n\n<h2 id=\"en-9\">9. Multi-class Extensions<\/h2>\n\n<p>In multi-class tasks (e.g., digit recognition 0-9), the confusion matrix expands to N\u00d7N. How do we extend binary metrics to multi-class? Three common averaging strategies<sup><a href=\"#cite-7\">[7]<\/a><\/sup>:<\/p>\n\n<h3>9.1 Three Averaging Strategies<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 6<\/strong> Multi-class averaging strategies compared<\/caption>\n <thead>\n <tr><th>Strategy<\/th><th>Calculation<\/th><th>Characteristics<\/th><th>Use Case<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td><strong>Macro<\/strong><\/td><td>Compute per-class metrics, then arithmetic mean<\/td><td>Equal weight per class; emphasizes rare classes<\/td><td>All classes equally important<\/td><\/tr>\n <tr><td><strong>Micro<\/strong><\/td><td>Aggregate all TP\/FP\/FN, then compute global metric<\/td><td>Larger classes dominate<\/td><td>Overall performance<\/td><\/tr>\n <tr><td><strong>Weighted<\/strong><\/td><td>Per-class metrics weighted by sample count<\/td><td>Accounts for class proportions<\/td><td>Imbalanced multi-class<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<h3>9.2 Macro vs Micro Example<\/h3>\n\n<div class=\"card\">\n <h4>Three-class Example<\/h4>\n <p>3 classes A, B, C with 100, 50, 10 samples respectively.<\/p>\n <pre class=\"code-block\">Per-class Recall:\n Class A (100 samples): Recall = 90\/100 = 0.90\n Class B ( 50 samples): Recall = 40\/50 = 0.80\n Class C ( 10 samples): Recall = 5\/10 = 0.50\n\nMacro-Recall = (0.90 + 0.80 + 0.50) \/ 3 = 0.733\n \u2192 Each class equally important; C's low Recall drags down average\n\nMicro-Recall = (90+40+5) \/ (100+50+10) = 135\/160 = 0.844\n \u2192 Sample-weighted; A's high proportion boosts the average\n\nWeighted-Recall = (0.90\u00d7100 + 0.80\u00d750 + 0.50\u00d710) \/ 160 = 0.844\n \u2192 Same as Micro (because of Recall's weighted nature)<\/pre>\n<\/div>\n\n<div class=\"info-box\">\n <strong>Selection Guide:<\/strong> If minority class performance matters equally (e.g., disease diagnosis), use <strong>Macro-F1<\/strong>; if overall prediction accuracy is the focus, use <strong>Micro-F1<\/strong>; if classes are imbalanced and proportions matter, use <strong>Weighted-F1<\/strong>.\n<\/div>\n\n<h3>9.3 One-vs-Rest Approach<\/h3>\n\n<p>Multi-class metrics are typically computed using the <strong>One-vs-Rest<\/strong> (OvR) strategy: treat each class as “positive” in turn, all others as “negative,” compute that class’s P\/R\/F1, then aggregate using one of the averaging strategies above.<\/p>\n\n<figure id=\"fig-5-en\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item\">Class A as positive<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (A)<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">Class B as positive<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (B)<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item purple\">Macro\/Micro\/Weighted<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">Class C as positive<\/span>\n <span class=\"flow-arrow\">\u2192<\/span>\n <span class=\"flow-item green\">P\/R\/F1 (C)<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 5<\/strong> One-vs-Rest strategy: converts N-class into N binary problems<\/figcaption>\n<\/figure>\n\n\n<h2 id=\"en-10\">10. Practical Guide & Code Examples<\/h2>\n\n<h3>10.1 Scenario-Metric Matching Guide<\/h3>\n\n<div class=\"scenario-grid\">\n <div class=\"scenario-card medical\">\n <h4>\ud83c\udfe5 Medical Diagnosis<\/h4>\n <p class=\"priority\"><strong>Priority Metric:<\/strong>Recall \/ F2-score<\/p>\n <p class=\"reason\">Missing a diagnosis (FN) is far costlier than a false alarm (FP). Better to run extra tests than miss a patient.<\/p>\n <\/div>\n <div class=\"scenario-card spam\">\n <h4>\ud83d\udce7 Spam Filter<\/h4>\n <p class=\"priority\"><strong>Priority Metric:<\/strong>Precision \/ F0.5<\/p>\n <p class=\"reason\">Deleting a normal email (FP) is far costlier than letting spam through (FN).<\/p>\n <\/div>\n <div class=\"scenario-card fraud\">\n <h4>\ud83d\udcb3 Fraud Detection<\/h4>\n <p class=\"priority\"><strong>Priority Metric:<\/strong>Recall \/ PR-AUC<\/p>\n <p class=\"reason\">Missing fraud is hugely expensive; better to over-review. Extremely imbalanced data.<\/p>\n <\/div>\n <div class=\"scenario-card search\">\n <h4>\ud83d\udd0d Search Engine<\/h4>\n <p class=\"priority\"><strong>Priority Metric:<\/strong>Precision@K<\/p>\n <p class=\"reason\">Users only look at top results; precision of returned items matters more than coverage.<\/p>\n <\/div>\n<\/div>\n\n<h3>10.2 Decision Flowchart<\/h3>\n\n<figure id=\"fig-6-en\">\n <div class=\"flow-diagram\">\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">Is data balanced?<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item green\">Yes \u2192 Accuracy<\/span>\n <span class=\"flow-arrow\" style=\"margin:0 1rem\">|<\/span>\n <span class=\"flow-item yellow\">No \u2192 continue<\/span>\n <\/div>\n <div class=\"flow-row\" style=\"margin-top:.3rem\">\n <span class=\"flow-arrow\">\u2193<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item purple\">Which costs more: FP or FN?<\/span>\n <\/div>\n <div class=\"flow-row\">\n <span class=\"flow-item\">FP high \u2192 Precision<\/span>\n <span class=\"flow-arrow\">|<\/span>\n <span class=\"flow-item green\">FN high \u2192 Recall<\/span>\n <span class=\"flow-arrow\">|<\/span>\n <span class=\"flow-item purple\">Equal \u2192 F1<\/span>\n <\/div>\n <\/div>\n <figcaption><strong>Figure 6<\/strong> Metric selection decision flow<\/figcaption>\n<\/figure>\n\n<h3>10.3 Python Code Example<\/h3>\n\n<pre class=\"terminal\"><span class=\"comment\"># Computing classification metrics with scikit-learn<\/span>\n<span class=\"keyword\">from<\/span> sklearn.metrics <span class=\"keyword\">import<\/span> (\n accuracy_score,\n precision_score,\n recall_score,\n f1_score,\n classification_report,\n confusion_matrix\n)\n<span class=\"keyword\">from<\/span> sklearn.datasets <span class=\"keyword\">import<\/span> make_classification\n<span class=\"keyword\">from<\/span> sklearn.model_selection <span class=\"keyword\">import<\/span> train_test_split\n<span class=\"keyword\">from<\/span> sklearn.ensemble <span class=\"keyword\">import<\/span> RandomForestClassifier\n\n<span class=\"comment\"># 1. Generate imbalanced data (1:9 ratio)<\/span>\nX, y = make_classification(\n n_samples=<span class=\"string\">1000<\/span>,\n weights=[<span class=\"string\">0.1<\/span>],\n random_state=<span class=\"string\">42<\/span>\n)\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=<span class=\"string\">0.3<\/span>)\n\n<span class=\"comment\"># 2. Train model<\/span>\nmodel = RandomForestClassifier(random_state=<span class=\"string\">42<\/span>)\nmodel.fit(X_train, y_train)\ny_pred = model.predict(X_test)\n\n<span class=\"comment\"># 3. Confusion matrix<\/span>\ncm = confusion_matrix(y_test, y_pred)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Confusion Matrix:\\n{cm}\"<\/span>)\n<span class=\"output\"># [[256 11]\n# [ 13 20]]<\/span>\n\ntn, fp, fn, tp = cm.ravel()\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"TP={tp}, TN={tn}, FP={fp}, FN={fn}\"<\/span>)\n<span class=\"output\"># TP=20, TN=256, FP=11, FN=13<\/span>\n\n<span class=\"comment\"># 4. Four core metrics<\/span>\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Accuracy: {accuracy_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Accuracy: 0.9200<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Precision: {precision_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Precision: 0.6452<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Recall: {recall_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># Recall: 0.6061<\/span>\n\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"F1-score: {f1_score(y_test, y_pred):.4f}\"<\/span>)\n<span class=\"output\"># F1-score: 0.6250<\/span>\n\n<span class=\"comment\"># 5. Full classification report (with Macro\/Micro\/Weighted)<\/span>\n<span class=\"keyword\">print<\/span>(classification_report(y_test, y_pred, target_names=[<span class=\"string\">\"Negative\"<\/span>, <span class=\"string\">\"Positive\"<\/span>]))\n<span class=\"output\"># precision recall f1-score support\n# Negative 0.95 0.96 0.95 267\n# Positive 0.65 0.61 0.63 33\n# accuracy 0.92 300\n# macro avg 0.80 0.78 0.79 300\n# weighted avg 0.92 0.92 0.92 300<\/span>\n\n<span class=\"comment\"># 6. Cross-validation with average strategy<\/span>\n<span class=\"keyword\">from<\/span> sklearn.model_selection <span class=\"keyword\">import<\/span> cross_val_score\n\nmacro_f1 = cross_val_score(model, X, y, cv=<span class=\"string\">5<\/span>, scoring=<span class=\"string\">\"f1_macro\"<\/span>)\nweighted_f1 = cross_val_score(model, X, y, cv=<span class=\"string\">5<\/span>, scoring=<span class=\"string\">\"f1_weighted\"<\/span>)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Macro F1 CV: {macro_f1.mean():.4f}\"<\/span>)\n<span class=\"keyword\">print<\/span>(<span class=\"string\">f\"Weighted F1 CV:{weighted_f1.mean():.4f}\"<\/span>)<\/pre>\n\n<h3>10.4 Common Pitfalls<\/h3>\n\n<div class=\"table-wrap\">\n <table>\n <caption><strong>Table 7<\/strong> Common pitfalls and corrections<\/caption>\n <thead>\n <tr><th>Pitfall<\/th><th>Problem<\/th><th>Correction<\/th><\/tr>\n <\/thead>\n <tbody>\n <tr><td>Using only Accuracy<\/td><td>Inflated on imbalanced data<\/td><td>Pair with Precision\/Recall\/F1<\/td><\/tr>\n <tr><td>Chasing highest F1<\/td><td>May not match business needs<\/td><td>Choose F\u03b2 based on FP\/FN cost<\/td><\/tr>\n <tr><td>Ignoring threshold tuning<\/td><td>Default 0.5 may not be optimal<\/td><td>Use PR curve to select optimal threshold<\/td><\/tr>\n <tr><td>Imbalanced test set<\/td><td>Biased metrics<\/td><td>Use stratified sampling or stratified CV<\/td><\/tr>\n <tr><td>Ignoring TN effect<\/td><td>F1 excludes TN, may overestimate<\/td><td>Add MCC for extreme imbalance<\/td><\/tr>\n <\/tbody>\n <\/table>\n<\/div>\n\n<div class=\"info-box success\">\n <strong>Summary:<\/strong> Accuracy, Precision, Recall, and F1-score are the cornerstones of classification evaluation. Each has its applicable scenario\u2014there is no “best metric,” only the “most appropriate metric for the current business context.” Understanding the confusion matrix is the prerequisite for mastering all of them. Choosing the right metric combination based on data balance and FP\/FN cost trade-offs is an essential skill for every ML practitioner.\n<\/div>\n\n<\/div>\n\n\n<footer>\n <div class=\"sources\">\n <h2>Sources \/ \u53c2\u8003\u6765\u6e90<\/h2>\n <ol>\n <li id=\"cite-1\">\n <span class=\"src-title\">MetricGate, How to Interpret a Confusion Matrix \u2014 Accuracy, Precision, Recall, F1 formulas and explanations.<\/span>\n <a class=\"src-url\" href=\"https:\/\/metricgate.com\/blogs\/how-to-interpret-confusion-matrix\/\" target=\"_blank\" rel=\"noopener\">https:\/\/metricgate.com\/blogs\/how-to-interpret-confusion-matrix\/<\/a>\n <\/li>\n <li id=\"cite-2\">\n <span class=\"src-title\">IBM, What is a confusion matrix? \u2014 Definition, components, and role in classification evaluation.<\/span>\n <a class=\"src-url\" href=\"https:\/\/www.ibm.com\/think\/topics\/confusion-matrix\" target=\"_blank\" rel=\"noopener\">https:\/\/www.ibm.com\/think\/topics\/confusion-matrix<\/a>\n <\/li>\n <li id=\"cite-3\">\n <span class=\"src-title\">MetricGate, How to Interpret a Confusion Matrix \u2014 Accuracy’s limitation with imbalanced classes (95% accuracy catching zero spam example).<\/span>\n <a class=\"src-url\" href=\"https:\/\/metricgate.com\/blogs\/how-to-interpret-confusion-matrix\/\" target=\"_blank\" rel=\"noopener\">https:\/\/metricgate.com\/blogs\/how-to-interpret-confusion-matrix\/<\/a>\n <\/li>\n <li id=\"cite-4\">\n <span class=\"src-title\">CSDN, Accuracy\u3001Precision\u3001Recall\u3001F1-Score\u3001ROC AUC\u8be6\u89e3 \u2014 Comprehensive guide with medical\/spam examples and metric comparison table.<\/span>\n <a class=\"src-url\" href=\"https:\/\/blog.csdn.net\/2202_75569688\/article\/details\/151649058\" target=\"_blank\" rel=\"noopener\">https:\/\/blog.csdn.net\/2202_75569688\/article\/details\/151649058<\/a>\n <\/li>\n <li id=\"cite-5\">\n <span class=\"src-title\">PLOS ONE (PMC), S2 Method. Model Performance Metrics \u2014 F1 as harmonic mean of precision and recall, mathematical formulation.<\/span>\n <a class=\"src-url\" href=\"https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/instance\/11090298\/bin\/pone.0303287.s002.pdf\" target=\"_blank\" rel=\"noopener\">https:\/\/pmc.ncbi.nlm.nih.gov\/articles\/instance\/11090298\/bin\/pone.0303287.s002.pdf<\/a>\n <\/li>\n <li id=\"cite-6\">\n <span class=\"src-title\">MetricGate, AUC vs. Accuracy vs. F1 Score \u2014 Scenario-based comparison: when accuracy is misleading, when F1 or AUC is recommended.<\/span>\n <a class=\"src-url\" href=\"https:\/\/metricgate.com\/blogs\/auc-vs-accuracy-vs-f1\/\" target=\"_blank\" rel=\"noopener\">https:\/\/metricgate.com\/blogs\/auc-vs-accuracy-vs-f1\/<\/a>\n <\/li>\n <li id=\"cite-7\">\n <span class=\"src-title\">Sarwan Pasha, Model Evaluation and Selection \u2014 Multi-class metrics, Macro\/Micro F1, and real-world application examples (medical, spam, fraud).<\/span>\n <a class=\"src-url\" href=\"https:\/\/sarwanpasha.github.io\/Courses\/ME_1.pdf\" target=\"_blank\" rel=\"noopener\">https:\/\/sarwanpasha.github.io\/Courses\/ME_1.pdf<\/a>\n <\/li>\n <\/ol>\n <\/div>\n<\/footer>\n\n<\/main>\n\n<button class=\"back-top\" onclick=\"scrollToTop()\" title=\"Back to top\">\u2191<\/button>\n\n<script>\nfunction setLang(lang) {\n document.querySelectorAll('.lang-section').forEach(s => s.classList.remove('active'));\n document.getElementById('lang-' + lang).classList.add('active');\n document.getElementById('btn-zh').classList.toggle('active', lang === 'zh');\n document.getElementById('btn-en').classList.toggle('active', lang === 'en');\n localStorage.setItem('cm-lang', lang);\n window.scrollTo(0, 0);\n}\n\nfunction toggleTheme() {\n const current = document.documentElement.getAttribute('data-theme');\n const next = current === 'dark' ? 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