{"id":2567,"date":"2023-01-03T23:49:27","date_gmt":"2023-01-03T22:49:27","guid":{"rendered":"https:\/\/ff.mhrooz.xyz\/?p=2567"},"modified":"2023-01-04T14:52:34","modified_gmt":"2023-01-04T13:52:34","slug":"clustering_-_partitioning_methods","status":"publish","type":"post","link":"https:\/\/blog.mhrooz.xyz\/index.php\/2023\/01\/03\/clustering_-_partitioning_methods\/","title":{"rendered":"Clustering &#8211; Partitioning Methods"},"content":{"rendered":"\n<!doctype html>\n<html>\n<head>\n<meta charset='UTF-8'><meta name='viewport' content='width=device-width initial-scale=1'>\n\n<link href='https:\/\/fonts.loli.net\/css?family=PT+Serif:400,400italic,700,700italic&#038;subset=latin,cyrillic-ext,cyrillic,latin-ext' rel='stylesheet' type='text\/css' \/><style type='text\/css'>html {overflow-x: initial !important;}:root { --bg-color: #ffffff; --text-color: #333333; --select-text-bg-color: #B5D6FC; --select-text-font-color: auto; --monospace: \"Lucida 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button;\n}\n\ninput {\n\tborder: 1px solid #aaa;\n}\n\n.megamenu-menu-header #megamenu-menu-header-title,\n.megamenu-menu-header:hover, \n.megamenu-menu-header:focus {\n\tcolor: inherit;\n}\n\n.dropdown-menu .divider {\n\tborder-color: #e5e5e5;\n\topacity: 1;\n}\n\n\/* https:\/\/github.com\/typora\/typora-issues\/issues\/2046 *\/\n.os-windows-7 strong,\n.os-windows-7 strong  {\n\tfont-weight: 760;\n}\n\n.ty-preferences .btn-default {\n\tbackground: transparent;\n}\n\n.ty-preferences .window-header {\n\tborder-bottom: 1px dashed #202B33;\n\tbox-shadow: none;\n}\n\n#sidebar-loading-template, #sidebar-loading-template.file-list-item {\n\tcolor: #777;\n}\n\n.searchpanel-search-option-btn.active {\n\tbackground: #777;\n\tcolor: white;\n}\n\n.export-detail, .light .export-detail, \n.light .export-item.active, \n.light .export-items-list-control {\n\tbackground: #e0e0e0;\n\tborder-radius: 2px;\n\tfont-weight: 700;\n\tcolor: inherit\n}\n\n\n\nmjx-container[jax=\"SVG\"] {\n  direction: 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0;\n\t\t\t\t\t\t} @media print { @page {margin: 0 0 0 0;} body.typora-export {padding-left: 0; padding-right: 0;} #write {padding:0;}}\n<\/style><title>4_1_Partitioning_Methods<\/title>\n<\/head>\n<body class='typora-export'><div class='typora-export-content'>\n<div id='write'  class=''><div class='md-toc' mdtype='toc'><p class=\"md-toc-content\" role=\"list\"><span role=\"listitem\" class=\"md-toc-item md-toc-h1\" data-ref=\"n0\"><a class=\"md-toc-inner\" style=\"\" href=\"#clustering---partitioning-methods\">Clustering &#8211; Partitioning Methods<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h2\" data-ref=\"n414\"><a class=\"md-toc-inner\" style=\"\" href=\"#\u5b9a\u4e49\">\u5b9a\u4e49<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h3\" data-ref=\"n67\"><a class=\"md-toc-inner\" style=\"\" href=\"#partitioning-method\">Partitioning method<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h3\" data-ref=\"n68\"><a class=\"md-toc-inner\" style=\"\" href=\"#\u5f62\u5fc3-centroid-of-a-cluster\">\u5f62\u5fc3 centroid of a cluster<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h2\" data-ref=\"n18\"><a class=\"md-toc-inner\" style=\"\" href=\"#k-mean\">K-mean<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h3\" data-ref=\"n88\"><a class=\"md-toc-inner\" style=\"\" href=\"#\u7b26\u53f7\u89c4\u5b9a\">\u7b26\u53f7\u89c4\u5b9a<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h3\" data-ref=\"n175\"><a class=\"md-toc-inner\" style=\"\" href=\"#\u7b97\u6cd5\">\u7b97\u6cd5<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h3\" data-ref=\"n248\"><a class=\"md-toc-inner\" style=\"\" href=\"#\u5206\u6790\">\u5206\u6790<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h2\" data-ref=\"n362\"><a class=\"md-toc-inner\" style=\"\" href=\"#k-median\">k-Median<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h2\" data-ref=\"n387\"><a class=\"md-toc-inner\" style=\"\" href=\"#silhouette-coefficient\">Silhouette-Coefficient<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h3\" data-ref=\"n433\"><a class=\"md-toc-inner\" style=\"\" href=\"#evaluating\">Evaluating<\/a><\/span><span role=\"listitem\" class=\"md-toc-item md-toc-h2\" data-ref=\"n75\"><a class=\"md-toc-inner\" style=\"\" href=\"#reference\">Reference<\/a><\/span><\/p><\/div><p><span>\u5212\u5206\u65b9\u6cd5\u662f\u4e00\u79cd\u805a\u7c7b\u7b97\u6cd5\uff0c\u53ef\u4ee5\u7528\u6765\u4e3a\u5927\u6570\u636e\u6d1e\u5bdf\u6570\u636e\u7684\u5206\u5e03\uff0c\u505a\u81ea\u52a8\u5f52\u7c7b\u7b49\u4f5c\u7528\u3002<\/span><\/p><h2 id='\u5b9a\u4e49'><span>\u5b9a\u4e49<\/span><\/h2><h3 id='partitioning-method'><span>Partitioning method<\/span><\/h3><p><span>\u7ed9\u5b9a\u4e00\u4e2a<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-572-TEX-I-1D45B\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D45B\" xlink:href=\"#MJX-572-TEX-I-1D45B\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">n<\/script><span>\u4e2a\u5bf9\u8c61\u7684\u96c6\u5408\uff0c\u5212\u5206\u65b9\u6cd5(Partitioning method)\u5c06\u4f1a\u6784\u5efa\u6570\u636e\u7684k\u4e2a\u5206\u533a\uff0c\u5176\u4e2d\u6bcf\u4e2a\u5206\u533a\u8868\u793a\u4e00\u4e2a\u7c07(cluster)\uff0c\u5e76\u4e14<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.553ex\" height=\"1.882ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 2454.6 832\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.312ex;\"><defs><path id=\"MJX-15-TEX-I-1D458\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path id=\"MJX-15-TEX-N-2264\" d=\"M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z\"><\/path><path id=\"MJX-15-TEX-I-1D45B\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D458\" xlink:href=\"#MJX-15-TEX-I-1D458\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(798.8,0)\"><use data-c=\"2264\" xlink:href=\"#MJX-15-TEX-N-2264\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(1854.6,0)\"><use data-c=\"1D45B\" xlink:href=\"#MJX-15-TEX-I-1D45B\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><mo>\u2264<\/mo><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">k\\leq n<\/script><span>\u3002<\/span><\/p><p><span>\u4e5f\u5c31\u662f\u8bf4\uff0c\u5212\u5206\u65b9\u6cd5\u628a\u6570\u636e\u5212\u5206\u6210\u4e86<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.179ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 521 705\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-602-TEX-I-1D458\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D458\" xlink:href=\"#MJX-602-TEX-I-1D458\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">k<\/script><span>\u4e2a\u7ec4\uff0c\u5e76\u4e14\u4f7f\u5f97\u6bcf\u4e2a\u7ec4\u81f3\u5c11\u5305\u542b\u4e00\u4e2a\u5bf9\u8c61\u3002\u6700\u5178\u578b\u7684\u4f8b\u5b50\u662f<\/span><em><span>\u4e92\u65a5\u7684\u7c07\u5212\u5206<\/span><\/em><span> (<\/span><em><span>exclusive cluster separation<\/span><\/em><span>)\u3002\u5728\u8fd9\u79cd\u65b9\u6cd5\u4e0b\uff0c\u6211\u4eec\u8981\u6c42\u6bcf\u4e2a\u5bf9\u8c61\u5fc5\u987b\u6070\u597d\u5c5e\u4e8e\u4e00\u4e2a\u7ec4\u3002<\/span><\/p><p><span>\u5212\u5206\u65b9\u6cd5\u7684\u4e00\u4e2a\u51c6\u5219\u662f(\u6216\u8005\u5224\u65ad\u4e00\u4e2a\u5212\u5206\u662f\u5426\u662f\u4e00\u4e2a\u597d\u7684\u5212\u5206\u7684\u6807\u51c6\u662f)\uff1a\u540c\u4e00\u4e2a\u7c07\u4e2d\u7684\u5bf9\u8c61\u5c3d\u53ef\u80fd\u76f8\u5173\uff0c\u4e0d\u540c\u7c07\u7684\u5bf9\u8c61\u5c3d\u53ef\u80fd\u65e0\u5173\u3002<\/span><\/p><p><span>\u57fa\u4e8e\u5212\u5206\u7684\u805a\u7c7b\u53ef\u80fd\u662f\u6548\u7387\u4f4e\u4e0b\u7684\uff0c\u56e0\u4e3a\u904d\u5386\u6240\u6709\u7684\u9879\u901a\u5e38\u5f88\u6162\u3002\u53ef\u4ee5\u4f7f\u7528\u542f\u53d1\u5f0f\u7b97\u6cd5\u6765\u63d0\u5347\u6548\u7387\u3002<\/span><\/p><p><span>\u76ee\u524d\u6d41\u884c\u7684\u542f\u53d1\u5f0f\u7b97\u6cd5\u8fc7\u7a0b\u5982\u4e0b\uff1a<\/span><\/p><ul><li><p><span>\u7ed9\u6bcf\u4e2a\u7c07\u6311\u9009<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.179ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 521 705\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-602-TEX-I-1D458\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D458\" xlink:href=\"#MJX-602-TEX-I-1D458\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">k<\/script><span>\u4e2a\u4ee3\u8868\uff0c\u53ef\u4ee5\u968f\u673a\u6311\u9009\u6216\u8005\u7528\u5176\u4ed6\u7b97\u6cd5\u3002<\/span><\/p><\/li><li><p><span>\u9012\u5f52\u5730\u6539\u5584\u521a\u521a\u6311\u9009\u5230\u7684\u7c07\uff1a<\/span><\/p><ul><li><span>\u5728\u5f53\u524d\u7684\u805a\u7c7b(clustering)\u4e0b\uff0c\u628a\u6bcf\u4e2a\u5bf9\u8c61\u5206\u914d\u5230\u6700\u5408\u9002\u7684\u7c07(cluster)\u4e2d<\/span><\/li><li><span>\u57fa\u4e8e\u521a\u624d\u7684\u91cd\u65b0\u805a\u7c7b\uff0c\u91cd\u65b0\u8ba1\u7b97\u65b0\u7684\u7c07\u7684\u4ee3\u8868\u3002<\/span><\/li><li><span>\u91cd\u590d\u5230\u4e0d\u518d\u6539\u53d8<\/span><\/li><\/ul><\/li><\/ul><p><span>\u542f\u53d1\u5f0f\u7b97\u6cd5\u4f1a\u6e10\u8fd1\u5730\u63d0\u9ad8\u805a\u7c7b\u7684\u8d28\u91cf\uff0c\u8fdb\u800c\u903c\u8fd1\u5c40\u90e8\u6700\u4f18\u89e3\u3002\u672c\u5c0f\u8282\u4ecb\u7ecd\u7684<\/span><em><span>k-mean<\/span><\/em><span>\u7b97\u6cd5\u5c31\u662f\u4e00\u79cd\u542f\u53d1\u5f0f\u7b97\u6cd5\u3002<\/span><\/p><p><span>\u6570\u5b66\u7684\u5b9a\u4e49\u5982\u4e0b\uff1a<\/span><\/p><p><span>Given a set <\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: 0px;\"><defs><path id=\"MJX-1231-TEX-I-1D437\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D437\" xlink:href=\"#MJX-1231-TEX-I-1D437\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">D<\/script><span>, a partitioning <\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.746ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 7401.8 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-61-TEX-C-43\" d=\"M201 -25Q167 -25 136 -14T75 23T29 94T12 202Q12 290 50 394T161 574Q227 642 303 673T433 704Q435 705 457 705Q533 701 533 640Q533 606 507 548T464 474Q431 444 396 444Q381 444 381 453Q381 459 388 473T407 513T428 563Q433 580 433 594Q433 636 381 636Q314 636 260 594T175 489T128 363T112 247Q112 157 153 101T273 44Q347 44 398 121Q413 144 437 157T481 171Q496 171 496 160Q496 150 476 123Q426 56 350 16T201 -25Z\"><\/path><path id=\"MJX-61-TEX-N-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path id=\"MJX-61-TEX-N-7B\" d=\"M434 -231Q434 -244 428 -250H410Q281 -250 230 -184Q225 -177 222 -172T217 -161T213 -148T211 -133T210 -111T209 -84T209 -47T209 0Q209 21 209 53Q208 142 204 153Q203 154 203 155Q189 191 153 211T82 231Q71 231 68 234T65 250T68 266T82 269Q116 269 152 289T203 345Q208 356 208 377T209 529V579Q209 634 215 656T244 698Q270 724 324 740Q361 748 377 749Q379 749 390 749T408 750H428Q434 744 434 732Q434 719 431 716Q429 713 415 713Q362 710 332 689T296 647Q291 634 291 499V417Q291 370 288 353T271 314Q240 271 184 255L170 250L184 245Q202 239 220 230T262 196T290 137Q291 131 291 1Q291 -134 296 -147Q306 -174 339 -192T415 -213Q429 -213 431 -216Q434 -219 434 -231Z\"><\/path><path id=\"MJX-61-TEX-I-1D436\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><path id=\"MJX-61-TEX-N-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path id=\"MJX-61-TEX-N-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><path id=\"MJX-61-TEX-N-2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><path id=\"MJX-61-TEX-I-1D458\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path id=\"MJX-61-TEX-N-7D\" d=\"M65 731Q65 745 68 747T88 750Q171 750 216 725T279 670Q288 649 289 635T291 501Q292 362 293 357Q306 312 345 291T417 269Q428 269 431 266T434 250T431 234T417 231Q380 231 345 210T298 157Q293 143 292 121T291 -28V-79Q291 -134 285 -156T256 -198Q202 -250 89 -250Q71 -250 68 -247T65 -230Q65 -224 65 -223T66 -218T69 -214T77 -213Q91 -213 108 -210T146 -200T183 -177T207 -139Q208 -134 209 3L210 139Q223 196 280 230Q315 247 330 250Q305 257 280 270Q225 304 212 352L210 362L209 498Q208 635 207 640Q195 680 154 696T77 713Q68 713 67 716T65 731Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"mi\"><use data-c=\"43\" xlink:href=\"#MJX-61-TEX-C-43\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(804.8,0)\"><use data-c=\"3D\" xlink:href=\"#MJX-61-TEX-N-3D\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(1860.6,0)\"><use data-c=\"7B\" xlink:href=\"#MJX-61-TEX-N-7B\"><\/use><\/g><g data-mml-node=\"msub\" transform=\"translate(2360.6,0)\"><g data-mml-node=\"mi\"><use data-c=\"1D436\" xlink:href=\"#MJX-61-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(748,-150) scale(0.707)\"><use data-c=\"31\" xlink:href=\"#MJX-61-TEX-N-31\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3512.1,0)\"><use data-c=\"2C\" xlink:href=\"#MJX-61-TEX-N-2C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3956.8,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-61-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4401.4,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-61-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4846.1,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-61-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5290.8,0)\"><use data-c=\"2C\" xlink:href=\"#MJX-61-TEX-N-2C\"><\/use><\/g><g data-mml-node=\"msub\" transform=\"translate(5735.4,0)\"><g data-mml-node=\"mi\"><use data-c=\"1D436\" xlink:href=\"#MJX-61-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(748,-150) scale(0.707)\"><use data-c=\"1D458\" xlink:href=\"#MJX-61-TEX-I-1D458\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(6901.8,0)\"><use data-c=\"7D\" xlink:href=\"#MJX-61-TEX-N-7D\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo>=<\/mo><mo fence=\"false\" stretchy=\"false\">{<\/mo><msub><mi>C<\/mi><mn>1<\/mn><\/msub><mo>,<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>,<\/mo><msub><mi>C<\/mi><mi>k<\/mi><\/msub><mo fence=\"false\" stretchy=\"false\">}<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">\\mathcal{C}=\\{C_1,...,C_k\\}<\/script><span> of <\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: 0px;\"><defs><path id=\"MJX-1231-TEX-I-1D437\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D437\" xlink:href=\"#MJX-1231-TEX-I-1D437\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">D<\/script><span> fulfills:<\/span><\/p><ul><li><span> <\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.248ex\" height=\"1.952ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 3203.5 862.8\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.357ex;\"><defs><path id=\"MJX-78-TEX-I-1D436\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><path id=\"MJX-78-TEX-I-1D456\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><path id=\"MJX-78-TEX-N-2286\" d=\"M84 346Q84 468 166 546T360 635Q361 635 370 635T395 635T430 636T475 636T524 636H679Q694 628 694 616Q694 607 681 597L522 596H470H441Q366 596 338 592T266 568Q244 557 224 542T179 500T139 433T124 346V341Q124 253 185 185Q244 121 328 103Q348 98 366 98T522 96H681Q694 86 694 76Q694 64 679 56H526Q510 56 480 56T434 55Q350 55 289 71T172 141Q84 223 84 346ZM104 -131T104 -118T118 -98H679Q694 -106 694 -118T679 -138H118Q104 -131 104 -118Z\"><\/path><path id=\"MJX-78-TEX-I-1D437\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><use data-c=\"1D436\" xlink:href=\"#MJX-78-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(748,-150) scale(0.707)\"><use data-c=\"1D456\" xlink:href=\"#MJX-78-TEX-I-1D456\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1319.7,0)\"><use data-c=\"2286\" xlink:href=\"#MJX-78-TEX-N-2286\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(2375.5,0)\"><use data-c=\"1D437\" xlink:href=\"#MJX-78-TEX-I-1D437\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>C<\/mi><mi>i<\/mi><\/msub><mo>\u2286<\/mo><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">C_i\\subseteq D<\/script><span> for all <\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.125ex\" height=\"1.882ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 4033.1 832\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.312ex;\"><defs><path id=\"MJX-91-TEX-N-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path id=\"MJX-91-TEX-N-2264\" d=\"M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z\"><\/path><path id=\"MJX-91-TEX-I-1D456\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><path id=\"MJX-91-TEX-I-1D458\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><use data-c=\"31\" xlink:href=\"#MJX-91-TEX-N-31\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(777.8,0)\"><use data-c=\"2264\" xlink:href=\"#MJX-91-TEX-N-2264\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(1833.6,0)\"><use data-c=\"1D456\" xlink:href=\"#MJX-91-TEX-I-1D456\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2456.3,0)\"><use data-c=\"2264\" xlink:href=\"#MJX-91-TEX-N-2264\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(3512.1,0)\"><use data-c=\"1D458\" xlink:href=\"#MJX-91-TEX-I-1D458\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>1<\/mn><mo>\u2264<\/mo><mi>i<\/mi><mo>\u2264<\/mo><mi>k<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">1\\leq i \\leq k<\/script><\/li><li><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"19.734ex\" height=\"2.412ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -772 8722.4 1066.2\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.666ex;\"><defs><path id=\"MJX-145-TEX-I-1D436\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><path id=\"MJX-145-TEX-I-1D456\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><path id=\"MJX-145-TEX-N-2229\" d=\"M88 -21T75 -21T55 -7V200Q55 231 55 280Q56 414 60 428Q61 430 61 431Q77 500 152 549T332 598Q443 598 522 544T610 405Q611 399 611 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d=\"M331 696Q335 708 339 722T345 744T350 759T357 769T367 772Q374 772 381 767T388 754Q388 746 377 712L366 673L378 661Q460 575 460 344Q460 281 456 234T432 126T373 27Q319 -22 250 -22Q214 -22 180 -7Q168 -3 168 -4L159 -33Q148 -71 142 -75Q138 -78 132 -78Q124 -78 118 -72T111 -60Q111 -52 122 -18L133 21L125 29Q39 111 39 344Q39 596 137 675Q187 716 251 716Q265 716 278 714T296 710T315 703T331 696ZM276 676Q264 679 246 679Q196 679 159 631Q134 597 128 536T121 356Q121 234 127 174T151 80L234 366Q253 430 275 506T308 618L318 654Q318 656 294 669L276 676ZM181 42Q207 16 250 16Q291 16 324 47Q354 78 366 136T378 356Q378 470 372 528T349 616L348 613Q348 611 264 326L181 42Z\"><\/path><path id=\"MJX-145-TEX-N-21D4\" d=\"M308 524Q318 526 323 526Q340 526 340 514Q340 507 336 499Q326 476 314 454T292 417T274 391T260 374L255 368Q255 367 500 367Q744 367 744 368L739 374Q734 379 726 390T707 416T685 453T663 499Q658 511 658 515Q658 525 680 525Q687 524 690 523T695 519T701 507Q766 359 902 287Q921 276 939 269T961 259T966 250Q966 246 965 244T960 240T949 236T930 228T902 213Q763 137 701 -7Q697 -16 695 -19T690 -23T680 -25Q658 -25 658 -15Q658 -11 663 1Q673 24 685 46T707 83T725 109T739 126L744 132Q744 133 500 133Q255 133 255 132L260 126Q265 121 273 110T292 84T314 47T336 1Q341 -11 341 -15Q341 -25 319 -25Q312 -24 309 -23T304 -19T298 -7Q233 141 97 213Q83 221 70 227T51 235T41 239T35 243T34 250T35 256T40 261T51 265T70 273T97 287Q235 363 299 509Q305 522 308 524ZM792 319L783 327H216Q183 294 120 256L110 250L120 244Q173 212 207 181L216 173H783L792 181Q826 212 879 244L889 250L879 256Q826 288 792 319Z\"><\/path><path id=\"MJX-145-TEX-N-2260\" d=\"M166 -215T159 -215T147 -212T141 -204T139 -197Q139 -190 144 -183L306 133H70Q56 140 56 153Q56 168 72 173H327L406 327H72Q56 332 56 347Q56 360 70 367H426Q597 702 602 707Q605 716 618 716Q625 716 630 712T636 703T638 696Q638 692 471 367H707Q722 359 722 347Q722 336 708 328L451 327L371 173H708Q722 163 722 153Q722 140 707 133H351Q175 -210 170 -212Q166 -215 159 -215Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><use data-c=\"1D436\" xlink:href=\"#MJX-145-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(748,-150) scale(0.707)\"><use data-c=\"1D456\" xlink:href=\"#MJX-145-TEX-I-1D456\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(1264.2,0)\"><use data-c=\"2229\" xlink:href=\"#MJX-145-TEX-N-2229\"><\/use><\/g><g data-mml-node=\"msub\" transform=\"translate(2153.4,0)\"><g data-mml-node=\"mi\"><use data-c=\"1D436\" xlink:href=\"#MJX-145-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(748,-150) scale(0.707)\"><use data-c=\"1D457\" xlink:href=\"#MJX-145-TEX-I-1D457\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3520.5,0)\"><use data-c=\"3D\" xlink:href=\"#MJX-145-TEX-N-3D\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(4576.3,0)\"><use data-c=\"2205\" xlink:href=\"#MJX-145-TEX-N-2205\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5354.1,0)\"><use data-c=\"21D4\" xlink:href=\"#MJX-145-TEX-N-21D4\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(6631.8,0)\"><use data-c=\"1D456\" xlink:href=\"#MJX-145-TEX-I-1D456\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(7254.6,0)\"><use data-c=\"2260\" xlink:href=\"#MJX-145-TEX-N-2260\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(8310.4,0)\"><use data-c=\"1D457\" xlink:href=\"#MJX-145-TEX-I-1D457\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>C<\/mi><mi>i<\/mi><\/msub><mo>\u2229<\/mo><msub><mi>C<\/mi><mi>j<\/mi><\/msub><mo>=<\/mo><mi mathvariant=\"normal\">\u2205<\/mi><mo stretchy=\"false\">\u21d4<\/mo><mi>i<\/mi><mo>\u2260<\/mo><mi>j<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">C_i\\cap C_j = \\empty \\Leftrightarrow i\\neq j<\/script><\/li><li><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"9.509ex\" height=\"2.26ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -749.5 4203.2 999\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.564ex;\"><defs><path id=\"MJX-159-TEX-SO-22C3\" d=\"M96 750Q103 750 109 748T120 744T127 737T133 730T137 723T139 718V395L140 73L142 60Q159 -43 237 -104T416 -166Q521 -166 597 -103T690 60L692 73L694 718Q708 749 735 749Q765 749 775 720Q777 714 777 398Q777 78 776 71Q766 -51 680 -140Q571 -249 416 -249H411Q261 -249 152 -140Q66 -51 56 71Q55 78 55 398Q55 714 57 720Q60 734 70 740Q80 750 96 750Z\"><\/path><path id=\"MJX-159-TEX-I-1D436\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><path id=\"MJX-159-TEX-I-1D456\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><path id=\"MJX-159-TEX-N-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path id=\"MJX-159-TEX-I-1D437\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mo\" transform=\"translate(0 -0.5)\"><use data-c=\"22C3\" xlink:href=\"#MJX-159-TEX-SO-22C3\"><\/use><\/g><g data-mml-node=\"msub\" transform=\"translate(999.7,0)\"><g data-mml-node=\"mi\"><use data-c=\"1D436\" xlink:href=\"#MJX-159-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(748,-150) scale(0.707)\"><use data-c=\"1D456\" xlink:href=\"#MJX-159-TEX-I-1D456\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2319.4,0)\"><use data-c=\"3D\" xlink:href=\"#MJX-159-TEX-N-3D\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(3375.2,0)\"><use data-c=\"1D437\" xlink:href=\"#MJX-159-TEX-I-1D437\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo data-mjx-texclass=\"OP\">\u22c3<\/mo><msub><mi>C<\/mi><mi>i<\/mi><\/msub><mo>=<\/mo><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">\\bigcup C_i=D<\/script><\/li><\/ul><p><span>i.e. each element of <\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.873ex\" height=\"1.545ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -683 828 683\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: 0px;\"><defs><path id=\"MJX-1231-TEX-I-1D437\" d=\"M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D437\" xlink:href=\"#MJX-1231-TEX-I-1D437\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>D<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">D<\/script><span> is in exactly one set <\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.357ex\" height=\"1.952ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 1042 862.8\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.357ex;\"><defs><path id=\"MJX-162-TEX-I-1D436\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><path id=\"MJX-162-TEX-I-1D456\" d=\"M184 600Q184 624 203 642T247 661Q265 661 277 649T290 619Q290 596 270 577T226 557Q211 557 198 567T184 600ZM21 287Q21 295 30 318T54 369T98 420T158 442Q197 442 223 419T250 357Q250 340 236 301T196 196T154 83Q149 61 149 51Q149 26 166 26Q175 26 185 29T208 43T235 78T260 137Q263 149 265 151T282 153Q302 153 302 143Q302 135 293 112T268 61T223 11T161 -11Q129 -11 102 10T74 74Q74 91 79 106T122 220Q160 321 166 341T173 380Q173 404 156 404H154Q124 404 99 371T61 287Q60 286 59 284T58 281T56 279T53 278T49 278T41 278H27Q21 284 21 287Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><use data-c=\"1D436\" xlink:href=\"#MJX-162-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(748,-150) scale(0.707)\"><use data-c=\"1D456\" xlink:href=\"#MJX-162-TEX-I-1D456\"><\/use><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><msub><mi>C<\/mi><mi>i<\/mi><\/msub><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">C_i<\/script><span>.<\/span><\/p><h3 id='\u5f62\u5fc3-centroid-of-a-cluster'><span>\u5f62\u5fc3 centroid of a cluster<\/span><\/h3><p><span>\u5f62\u5fc3\u662f\u4e00\u4e2a\u7c07\u7684<\/span><strong><span>\u4e2d\u5fc3\u70b9<\/span><\/strong><span>\u3002<\/span><\/p><p><span>\u5f62\u5fc3\u70b9\u6709\u591a\u79cd\u5f62\u5f0f\u53ef\u4ee5\u5b9a\u4e49\uff0c\u53ef\u4ee5\u7528\u4e00\u4e2a\u7c07\u7684\u6240\u6709\u503c\u7684\u5747\u503c\u6216\u8005\u662f\u4e00\u4e2a\u7c07\u7684\u4e2d\u5fc3\u70b9\u3002<\/span><\/p><h2 id='k-mean'><span>K-mean<\/span><\/h2><p>&nbsp;<\/p><p><span>K-mean \u7b97\u6cd5\u7684\u76ee\u7684\u662f\uff1a <\/span><\/p><blockquote><p>&nbsp;<\/p><p><span>Find a clustering such that the within-cluster variation of each cluster is small and use the centroid of a cluster as a representative.<\/span><\/p><\/blockquote><p><span>\u627e\u5230\u4e00\u4e2a\u805a\u7c7b(clustering),\u4f7f\u5f97\u6bcf\u4e2a\u7c07\u7684<\/span><em><span>\u7c07\u5185\u53d8\u5dee<\/span><\/em><span>\u662f\u5f88\u5c0f\u7684\uff0c\u5e76\u4e14\u4f7f\u7528\u5f62\u5fc3\u4f5c\u4e3a\u4ee3\u8868.[1] <\/span><a href='#jump'><span>\u7c07\u5185\u53d8\u5dee<\/span><\/a><span>\u7684\u5b9a\u4e49\u89c1\u4e0b\u6587\u4e2d\u7684\u7b26\u53f7\u89c4\u5b9a\u3002<\/span><\/p><h3 id='\u7b26\u53f7\u89c4\u5b9a'><span>\u7b26\u53f7\u89c4\u5b9a<\/span><\/h3><ul><li><p><span>\u5bf9\u8c61(objects) <\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.537ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 6867.1 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-397-TEX-B-1D429\" d=\"M32 442L123 446Q214 450 215 450H221V409Q222 409 229 413T251 423T284 436T328 446T382 450Q480 450 540 388T600 223Q600 128 539 61T361 -6H354Q292 -6 236 28L227 34V-132H296V-194H287Q269 -191 163 -191Q56 -191 38 -194H29V-132H98V113V284Q98 330 97 348T93 370T83 376Q69 380 42 380H29V442H32ZM457 224Q457 303 427 349T350 395Q282 395 235 352L227 345V104L233 97Q274 45 337 45Q383 45 420 86T457 224Z\"><\/path><path id=\"MJX-397-TEX-N-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path id=\"MJX-397-TEX-N-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path id=\"MJX-397-TEX-I-1D45D\" d=\"M23 287Q24 290 25 295T30 317T40 348T55 381T75 411T101 433T134 442Q209 442 230 378L240 387Q302 442 358 442Q423 442 460 395T497 281Q497 173 421 82T249 -10Q227 -10 210 -4Q199 1 187 11T168 28L161 36Q160 35 139 -51T118 -138Q118 -144 126 -145T163 -148H188Q194 -155 194 -157T191 -175Q188 -187 185 -190T172 -194Q170 -194 161 -194T127 -193T65 -192Q-5 -192 -24 -194H-32Q-39 -187 -39 -183Q-37 -156 -26 -148H-6Q28 -147 33 -136Q36 -130 94 103T155 350Q156 355 156 364Q156 405 131 405Q109 405 94 377T71 316T59 280Q57 278 43 278H29Q23 284 23 287ZM178 102Q200 26 252 26Q282 26 310 49T356 107Q374 141 392 215T411 325V331Q411 405 350 405Q339 405 328 402T306 393T286 380T269 365T254 350T243 336T235 326L232 322Q232 321 229 308T218 264T204 212Q178 106 178 102Z\"><\/path><path id=\"MJX-397-TEX-N-31\" d=\"M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z\"><\/path><path id=\"MJX-397-TEX-N-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><path id=\"MJX-397-TEX-N-2E\" d=\"M78 60Q78 84 95 102T138 120Q162 120 180 104T199 61Q199 36 182 18T139 0T96 17T78 60Z\"><\/path><path id=\"MJX-397-TEX-I-1D451\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><path id=\"MJX-397-TEX-N-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mtext\"><use data-c=\"1D429\" xlink:href=\"#MJX-397-TEX-B-1D429\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(916.8,0)\"><use data-c=\"3D\" xlink:href=\"#MJX-397-TEX-N-3D\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(1972.6,0)\"><use data-c=\"28\" xlink:href=\"#MJX-397-TEX-N-28\"><\/use><\/g><g data-mml-node=\"msub\" transform=\"translate(2361.6,0)\"><g data-mml-node=\"mi\"><use data-c=\"1D45D\" xlink:href=\"#MJX-397-TEX-I-1D45D\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(536,-150) scale(0.707)\"><use data-c=\"31\" xlink:href=\"#MJX-397-TEX-N-31\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3301.1,0)\"><use data-c=\"2C\" xlink:href=\"#MJX-397-TEX-N-2C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3745.8,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-397-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4190.4,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-397-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4635.1,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-397-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5079.8,0)\"><use data-c=\"2C\" xlink:href=\"#MJX-397-TEX-N-2C\"><\/use><\/g><g data-mml-node=\"msub\" transform=\"translate(5524.4,0)\"><g data-mml-node=\"mi\"><use data-c=\"1D45D\" xlink:href=\"#MJX-397-TEX-I-1D45D\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(536,-150) scale(0.707)\"><use data-c=\"1D451\" xlink:href=\"#MJX-397-TEX-I-1D451\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(6478.1,0)\"><use data-c=\"29\" xlink:href=\"#MJX-397-TEX-N-29\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mtext mathvariant=\"bold\">p<\/mtext><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><msub><mi>p<\/mi><mn>1<\/mn><\/msub><mo>,<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>,<\/mo><msub><mi>p<\/mi><mi>d<\/mi><\/msub><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">\\textbf{p}=(p_1,...,p_d)<\/script><span>  \u662f\u5728\u4e00\u4e2a<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.176ex\" height=\"1.593ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 520 704\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.023ex;\"><defs><path id=\"MJX-552-TEX-I-1D451\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D451\" xlink:href=\"#MJX-552-TEX-I-1D451\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>d<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">d<\/script><span>\u7ef4\u5411\u91cf\u7a7a\u95f4\u7684\u70b9\u3002<\/span><\/p><\/li><li><p><span>\u5e73\u65b9\u8ddd\u79bb\u548c\uff08\u7528\u6765\u8861\u91cf\u4e00\u4e2a\u7c07\u7684\u7d27\u51d1\u7a0b\u5ea6(compactness))(sum of squared distances):<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n105\" cid=\"n105\" mdtype=\"math_block\" data-math-tag-before=\"0\" data-math-tag-after=\"1\" data-math-labels=\"[]\"><div class=\"md-rawblock-container md-math-container\" contenteditable=\"false\" tabindex=\"-1\"><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" width=\"full\" style=\"min-width: 36.51ex; position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"5.37ex\" role=\"img\" focusable=\"false\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -2.119ex; min-width: 36.51ex;\"><defs><path id=\"MJX-1171-TEX-I-1D446\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"><\/path><path id=\"MJX-1171-TEX-I-1D438\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><path id=\"MJX-1171-TEX-N-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path id=\"MJX-1171-TEX-I-1D436\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><path id=\"MJX-1171-TEX-I-1D457\" d=\"M297 596Q297 627 318 644T361 661Q378 661 389 651T403 623Q403 595 384 576T340 557Q322 557 310 567T297 596ZM288 376Q288 405 262 405Q240 405 220 393T185 362T161 325T144 293L137 279Q135 278 121 278H107Q101 284 101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z\"><\/path><path id=\"MJX-1171-TEX-N-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path id=\"MJX-1171-TEX-N-3D\" d=\"M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z\"><\/path><path id=\"MJX-1171-TEX-LO-2211\" d=\"M60 948Q63 950 665 950H1267L1325 815Q1384 677 1388 669H1348L1341 683Q1320 724 1285 761Q1235 809 1174 838T1033 881T882 898T699 902H574H543H251L259 891Q722 258 724 252Q725 250 724 246Q721 243 460 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xlink:href=\"#MJX-477-TEX-I-1D446\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(4493,0)\"><use data-c=\"1D446\" xlink:href=\"#MJX-477-TEX-I-1D446\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(5138,0)\"><use data-c=\"1D438\" xlink:href=\"#MJX-477-TEX-I-1D438\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5902,0)\"><use data-c=\"28\" xlink:href=\"#MJX-477-TEX-N-28\"><\/use><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(6291,0)\"><g data-mml-node=\"mi\"><use data-c=\"43\" xlink:href=\"#MJX-477-TEX-C-43\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(6818,0)\"><use data-c=\"29\" xlink:href=\"#MJX-477-TEX-N-29\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>arg<\/mi><mo data-mjx-texclass=\"NONE\">\u2061<\/mo><munder><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><\/mrow><\/munder><mi>S<\/mi><mi>S<\/mi><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">\\arg\\min_{\\mathcal{C}} SSE(\\mathcal{C})<\/script>\n<span>\u4f7f\u5f97\u6574\u4f53SSE\u6700\u5c0f\u7684\u805a\u7c7b\u3002<\/span><\/p><\/li><\/ul><h3 id='\u7b97\u6cd5'><span>\u7b97\u6cd5<\/span><\/h3><p><span>\u76ee\u524d\u5df2\u7ecf\u8bc1\u660e\uff0c\u5373\u4f7f\u662f\u6570\u636e\u7684\u7ef4\u5ea6\u53ea\u6709\u4e8c\u7ef4\uff0c\u7c07\u7684\u6570\u91cf\u4e0d\u56fa\u5b9a\uff0c\u60f3\u8981\u627e\u5230\u6700\u4f73\u5212\u5206\u4f7f\u5f97<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.6ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3359 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-603-TEX-I-1D446\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 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data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">SSE(\\mathcal{C})<\/script><span>\u503c\u6700\u5c0f\u7684\u95ee\u9898\u662fNP-hard\u7684\u3002\u5bf9\u4e8e\u7ef4\u5ea6\u4e0d\u56fa\u5b9a\uff0c\u7c07\u7684\u6570\u91cf\u56fa\u5b9a\uff0c\u627e\u5230\u6700\u4f73\u5212\u5206\u4f7f\u5f97<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.6ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3359 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-603-TEX-I-1D446\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"><\/path><path id=\"MJX-603-TEX-I-1D438\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><path id=\"MJX-603-TEX-N-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path id=\"MJX-603-TEX-C-43\" d=\"M201 -25Q167 -25 136 -14T75 23T29 94T12 202Q12 290 50 394T161 574Q227 642 303 673T433 704Q435 705 457 705Q533 701 533 640Q533 606 507 548T464 474Q431 444 396 444Q381 444 381 453Q381 459 388 473T407 513T428 563Q433 580 433 594Q433 636 381 636Q314 636 260 594T175 489T128 363T112 247Q112 157 153 101T273 44Q347 44 398 121Q413 144 437 157T481 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data-mjx-texclass=\"ORD\" transform=\"translate(2443,0)\"><g data-mml-node=\"mi\"><use data-c=\"43\" xlink:href=\"#MJX-603-TEX-C-43\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2970,0)\"><use data-c=\"29\" xlink:href=\"#MJX-603-TEX-N-29\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>S<\/mi><mi>S<\/mi><mi>E<\/mi><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">SSE(\\mathcal{C})<\/script><span>\u503c\u6700\u5c0f\u7684\u95ee\u9898\u4e5f\u662fNP-hard\u7684\u3002<\/span><\/p><p><span>\u4f46\u662f\u5982\u679c\u7c07\u548c\u6570\u636e\u7684\u7ef4\u5ea6\u90fd\u7ed9\u5b9a\uff0c\u90a3\u4e48\u95ee\u9898\u53ef\u4ee5\u5728<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" 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xlink:href=\"#MJX-550-TEX-N-28\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(389,0)\"><use data-c=\"1D451\" xlink:href=\"#MJX-550-TEX-I-1D451\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(909,0)\"><use data-c=\"1D458\" xlink:href=\"#MJX-550-TEX-I-1D458\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(1430,0)\"><use data-c=\"2B\" xlink:href=\"#MJX-550-TEX-N-2B\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(2208,0)\"><use data-c=\"31\" xlink:href=\"#MJX-550-TEX-N-31\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2708,0)\"><use data-c=\"29\" xlink:href=\"#MJX-550-TEX-N-29\"><\/use><\/g><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(4024.9,0)\"><use data-c=\"1D459\" xlink:href=\"#MJX-550-TEX-I-1D459\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(4322.9,0)\"><use data-c=\"1D45C\" xlink:href=\"#MJX-550-TEX-I-1D45C\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(4807.9,0)\"><use data-c=\"1D454\" xlink:href=\"#MJX-550-TEX-I-1D454\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(5284.9,0)\"><use data-c=\"1D45B\" xlink:href=\"#MJX-550-TEX-I-1D45B\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5884.9,0)\"><use data-c=\"29\" xlink:href=\"#MJX-550-TEX-N-29\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>n<\/mi><mrow data-mjx-texclass=\"ORD\"><mo stretchy=\"false\">(<\/mo><mi>d<\/mi><mi>k<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><\/msup><mi>l<\/mi><mi>o<\/mi><mi>g<\/mi><mi>n<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">O(n^{(dk+1)}logn)<\/script><span>\u7684\u65f6\u95f4\u5185\u6c42\u89e3\uff0c\u5176\u4e2d<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.176ex\" height=\"1.593ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 520 704\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.023ex;\"><defs><path id=\"MJX-552-TEX-I-1D451\" d=\"M366 683Q367 683 438 688T511 694Q523 694 523 686Q523 679 450 384T375 83T374 68Q374 26 402 26Q411 27 422 35Q443 55 463 131Q469 151 473 152Q475 153 483 153H487H491Q506 153 506 145Q506 140 503 129Q490 79 473 48T445 8T417 -8Q409 -10 393 -10Q359 -10 336 5T306 36L300 51Q299 52 296 50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157Q33 205 53 255T101 341Q148 398 195 420T280 442Q336 442 364 400Q369 394 369 396Q370 400 396 505T424 616Q424 629 417 632T378 637H357Q351 643 351 645T353 664Q358 683 366 683ZM352 326Q329 405 277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q233 26 290 98L298 109L352 326Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" 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xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">k<\/script><span>\u662f\u7c07\u7684\u6570\u91cf\uff0c<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.357ex\" height=\"1.025ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -442 600 453\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-572-TEX-I-1D45B\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 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width=\"1.179ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 521 705\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-602-TEX-I-1D458\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 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xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.647ex\" height=\"1.645ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 2054 727\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.05ex;\"><defs><path id=\"MJX-731-TEX-I-1D446\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 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153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D456\" xlink:href=\"#MJX-596-TEX-I-1D456\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(622.8,0)\"><use data-c=\"2208\" xlink:href=\"#MJX-596-TEX-N-2208\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(1567.6,0)\"><use data-c=\"31\" xlink:href=\"#MJX-596-TEX-N-31\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2067.6,0)\"><use data-c=\"2C\" xlink:href=\"#MJX-596-TEX-N-2C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2512.2,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-596-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2956.9,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-596-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3401.6,0)\"><use data-c=\"2E\" xlink:href=\"#MJX-596-TEX-N-2E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3846.2,0)\"><use data-c=\"2C\" xlink:href=\"#MJX-596-TEX-N-2C\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(4290.9,0)\"><use data-c=\"1D458\" xlink:href=\"#MJX-596-TEX-I-1D458\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>i<\/mi><mo>\u2208<\/mo><mn>1<\/mn><mo>,<\/mo><mo>.<\/mo><mo>.<\/mo><mo>.<\/mo><mo>,<\/mo><mi>k<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">i\\in1,...,k<\/script><span>\u3002<\/span><\/li><li><span>\u4e3a\u6bcf\u4e2a\u7c07\u91cd\u65b0\u8ba1\u7b97\u5f62\u5fc3\uff0c\u5e76\u628a\u6bcf\u4e2a\u5f62\u5fc3\u4f5c\u4e3a\u65b0\u7684\u4ee3\u8868\u5bf9\u8c61<\/span><\/li><\/ol><p><span>\t<\/span><span>\u76f4\u5230\uff1a<\/span><\/p><ol><li><span>\u4ee3\u8868\u5bf9\u8c61\u4e0d\u518d\u6539\u53d8<\/span><\/li><\/ol><hr \/><h3 id='\u5206\u6790'><span>\u5206\u6790<\/span><\/h3><p><span>k-mean\u7b97\u6cd5\u590d\u6742\u5ea6\u662f<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"6.839ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3023 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-598-TEX-I-1D442\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path id=\"MJX-598-TEX-N-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path id=\"MJX-598-TEX-I-1D45B\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 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511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z\"><\/path><path id=\"MJX-598-TEX-N-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D442\" xlink:href=\"#MJX-598-TEX-I-1D442\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(763,0)\"><use data-c=\"28\" xlink:href=\"#MJX-598-TEX-N-28\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(1152,0)\"><use data-c=\"1D45B\" xlink:href=\"#MJX-598-TEX-I-1D45B\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(1752,0)\"><use data-c=\"1D458\" xlink:href=\"#MJX-598-TEX-I-1D458\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(2273,0)\"><use data-c=\"1D461\" xlink:href=\"#MJX-598-TEX-I-1D461\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2634,0)\"><use data-c=\"29\" xlink:href=\"#MJX-598-TEX-N-29\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><mi>n<\/mi><mi>k<\/mi><mi>t<\/mi><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">O(nkt)<\/script><span>\uff0cn\u662f\u5bf9\u8c61\u603b\u6570\uff0ck\u662f\u7c07\u6570\uff0ct\u662f\u8fed\u4ee3\u6b21\u6570\u3002\u901a\u5e38\u60c5\u51b5\u4e0b\u6709<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.271ex\" height=\"2.009ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 6749.8 888\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.439ex;\"><defs><path id=\"MJX-600-TEX-I-1D458\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><path id=\"MJX-600-TEX-N-3C\" d=\"M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z\"><\/path><path id=\"MJX-600-TEX-I-1D45B\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path id=\"MJX-600-TEX-N-2C\" d=\"M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z\"><\/path><path id=\"MJX-600-TEX-I-1D461\" d=\"M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D458\" xlink:href=\"#MJX-600-TEX-I-1D458\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(798.8,0)\"><g data-mml-node=\"text\"><use data-c=\"3C\" xlink:href=\"#MJX-600-TEX-N-3C\"><\/use><\/g><g data-mml-node=\"text\" transform=\"translate(778,0)\"><use data-c=\"3C\" xlink:href=\"#MJX-600-TEX-N-3C\"><\/use><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(2632.6,0)\"><use data-c=\"1D45B\" xlink:href=\"#MJX-600-TEX-I-1D45B\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3232.6,0)\"><use data-c=\"2C\" xlink:href=\"#MJX-600-TEX-N-2C\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(3677.2,0)\"><use data-c=\"1D461\" xlink:href=\"#MJX-600-TEX-I-1D461\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4316,0)\"><g data-mml-node=\"text\"><use data-c=\"3C\" xlink:href=\"#MJX-600-TEX-N-3C\"><\/use><\/g><g data-mml-node=\"text\" transform=\"translate(778,0)\"><use data-c=\"3C\" xlink:href=\"#MJX-600-TEX-N-3C\"><\/use><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(6149.8,0)\"><use data-c=\"1D45B\" xlink:href=\"#MJX-600-TEX-I-1D45B\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><mo>&lt;&lt;<\/mo><mi>n<\/mi><mo>,<\/mo><mi>t<\/mi><mo>&lt;&lt;<\/mo><mi>n<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">k<<n,t<<n<\/script><span>.\u6240\u4ee5\u5bf9\u4e8e\u5927\u6570\u636e\u96c6\u8fd9\u79cd\u7b97\u6cd5\u975e\u5e38\u6709\u6548\u3002<\/span><\/p><p><span>\u4f18\u52bf:<\/span><\/p><ol><li><span>\u7b97\u6cd5\u590d\u6742\u5ea6\u901a\u5e38\u60c5\u51b5\u4e0b\u6bd4\u8f83\u4f4e<\/span><\/li><li><span>\u6613\u4e8e\u90e8\u7f72\u3002<\/span><\/li><\/ol><p><span>\u5c40\u9650\u6027\u5728\u4e8e\uff1a<\/span><\/p><ol><li><span>\u5fc5\u987b\u7ed9\u51fa\u7c07\u7684\u5747\u503c\u7684\u5b9a\u4e49\u3002<\/span><\/li><li><span>\u8981\u6c42\u7528\u6237\u4e8b\u524d\u7ed9\u51fa<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.179ex\" height=\"1.595ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -694 521 705\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-602-TEX-I-1D458\" d=\"M121 647Q121 657 125 670T137 683Q138 683 209 688T282 694Q294 694 294 686Q294 679 244 477Q194 279 194 272Q213 282 223 291Q247 309 292 354T362 415Q402 442 438 442Q468 442 485 423T503 369Q503 344 496 327T477 302T456 291T438 288Q418 288 406 299T394 328Q394 353 410 369T442 390L458 393Q446 405 434 405H430Q398 402 367 380T294 316T228 255Q230 254 243 252T267 246T293 238T320 224T342 206T359 180T365 147Q365 130 360 106T354 66Q354 26 381 26Q429 26 459 145Q461 153 479 153H483Q499 153 499 144Q499 139 496 130Q455 -11 378 -11Q333 -11 305 15T277 90Q277 108 280 121T283 145Q283 167 269 183T234 206T200 217T182 220H180Q168 178 159 139T145 81T136 44T129 20T122 7T111 -2Q98 -11 83 -11Q66 -11 57 -1T48 16Q48 26 85 176T158 471L195 616Q196 629 188 632T149 637H144Q134 637 131 637T124 640T121 647Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D458\" xlink:href=\"#MJX-602-TEX-I-1D458\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>k<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">k<\/script><span>\u3002<\/span><\/li><li><span>\u5bf9\u566a\u58f0\u548c\u79bb\u7fa4\u70b9\u654f\u611f\u3002\u56e0\u4e3a\u5c11\u91cf\u7684\u6781\u503c\u4f1a\u5bf9\u5747\u503c\u4ea7\u751f\u5f88\u5927\u5f71\u54cd\u3002<\/span><\/li><li><span>\u7c07\u8981\u6c42\u5f62\u72b6\u5f97\u662f\u51f8\u7684<\/span><\/li><li><span>\u6027\u80fd\u6216\u8005\u8bf4\u662f\u65f6\u95f4\u590d\u6742\u5ea6\u4e0e\u521d\u59cb\u5316\u7684\u5173\u7cfb\u5f88\u5927\u3002<\/span><\/li><\/ol><h2 id='k-median'><span>k-Median<\/span><\/h2><p><span>k-mean\u7b97\u6cd5\u5bf9\u79bb\u7fa4\u70b9\u6bd4\u8f83\u654f\u611f\u3002\u6539\u8fdb\u7684\u4e00\u79cd\u60f3\u6cd5\u662f\u4e0d\u8ba9\u5bf9\u8c61\u548c\u5747\u503c\u6bd4\u8f83\uff0c\u800c\u662f\u8ba9\u5bf9\u8c61\u548c\u5bf9\u8c61\u6bd4\u8f83\u3002<\/span><\/p><p><span>\u5177\u4f53\u6765\u8bf4\uff0c\u6211\u4eec\u4e3a\u6bcf\u4e00\u4e2a\u7c07\u6311\u9009\u4e00\u4e2a\u4ee3\u8868\u5bf9\u8c61\u3002\u7136\u540e\u8ba9\u5269\u4e0b\u7684\u5bf9\u8c61\u548c\u8fd9\u4e9b\u4ee3\u8868\u5bf9\u8c61\u6bd4\uff0c\u627e\u5230\u4e0e\u4ee3\u8868\u5bf9\u8c61\u6700\u76f8\u4f3c\u7684\uff0c\u5c06\u5bf9\u8c61\u653e\u5165\u4ee3\u8868\u5bf9\u8c61\u6240\u5bf9\u5e94\u7684\u7c07\u4e2d\u3002<\/span><\/p><p><span>\u4e0e<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"7.6ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3359 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-603-TEX-I-1D446\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"><\/path><path id=\"MJX-603-TEX-I-1D438\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 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stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">SSE(\\mathcal{C})<\/script><span>\u7c7b\u4f3c\uff0c\u8fd9\u91cc\u6211\u4eec\u53ef\u4ee5\u5b9a\u4e49\u4e00\u4e2a\u7edd\u5bf9\u8bef\u5dee\u6807\u51c6(absolute-error criterion):<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n375\" cid=\"n375\" mdtype=\"math_block\" data-math-tag-before=\"3\" data-math-labels=\"[]\" data-math-tag-after=\"4\"><div class=\"md-rawblock-container md-math-container\" contenteditable=\"false\" tabindex=\"-1\"><mjx-container class=\"MathJax\" jax=\"SVG\" display=\"true\" width=\"full\" style=\"min-width: 50.439ex; position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"100%\" height=\"5.37ex\" role=\"img\" focusable=\"false\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -2.119ex; min-width: 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displaystyle=\"true\"><mlabeledtr><mtd><mtext>(5)<\/mtext><\/mtd><mtd><mi>E<\/mi><mo>=<\/mo><munderover><mo data-mjx-texclass=\"OP\">\u2211<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>i<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><mi>k<\/mi><\/munderover><munder><mo data-mjx-texclass=\"OP\">\u2211<\/mo><mrow data-mjx-texclass=\"ORD\"><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">p<\/mi><\/mrow><mo>\u2208<\/mo><msub><mi>C<\/mi><mi>j<\/mi><\/msub><\/mrow><\/munder><mi>d<\/mi><mi>i<\/mi><mi>s<\/mi><mi>t<\/mi><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mi mathvariant=\"bold\">p<\/mi><\/mrow><mo>,<\/mo><mrow data-mjx-texclass=\"ORD\"><msub><mi mathvariant=\"bold\">o<\/mi><mi mathvariant=\"bold\">i<\/mi><\/msub><\/mrow><mo stretchy=\"false\">)<\/mo><\/mtd><\/mlabeledtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/div><\/div><p><span>\u5176\u4e2d<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.999ex\" height=\"1.362ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -452 883.6 602\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.339ex;\"><defs><path id=\"MJX-725-TEX-B-1D428\" d=\"M287 -5Q228 -5 182 10T109 48T63 102T39 161T32 219Q32 272 50 314T94 382T154 423T214 446T265 452H279Q319 452 326 451Q428 439 485 376T542 221Q542 156 514 108T442 33Q384 -5 287 -5ZM399 230V250Q399 280 398 298T391 338T372 372T338 392T282 401Q241 401 212 380Q190 363 183 334T175 230Q175 202 175 189T177 153T183 118T195 91T215 68T245 56T287 50Q348 50 374 84Q388 101 393 132T399 230Z\"><\/path><path id=\"MJX-725-TEX-B-1D422\" d=\"M72 610Q72 649 98 672T159 695Q193 693 217 670T241 610Q241 572 217 549T157 525Q120 525 96 548T72 610ZM46 442L136 446L226 450H232V62H294V0H286Q271 3 171 3Q67 3 49 0H40V62H109V209Q109 358 108 362Q103 380 55 380H43V442H46Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\"><g data-mml-node=\"msub\"><g data-mml-node=\"mi\"><use data-c=\"1D428\" xlink:href=\"#MJX-725-TEX-B-1D428\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(608,-150) scale(0.707)\"><use data-c=\"1D422\" xlink:href=\"#MJX-725-TEX-B-1D422\"><\/use><\/g><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mrow data-mjx-texclass=\"ORD\"><msub><mi mathvariant=\"bold\">o<\/mi><mi mathvariant=\"bold\">i<\/mi><\/msub><\/mrow><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">\\mathbf{o_i}<\/script><span>\u662f\u9009\u62e9\u7684\u4ee3\u8868\u5bf9\u8c61\u3002k-median\u7b97\u6cd5\u5c31\u662f\u8981\u6700\u5c0f\u5316<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"8.097ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 3579 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-727-TEX-I-1D434\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><path id=\"MJX-727-TEX-I-1D438\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><path id=\"MJX-727-TEX-I-1D436\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><path id=\"MJX-727-TEX-N-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path id=\"MJX-727-TEX-C-43\" d=\"M201 -25Q167 -25 136 -14T75 23T29 94T12 202Q12 290 50 394T161 574Q227 642 303 673T433 704Q435 705 457 705Q533 701 533 640Q533 606 507 548T464 474Q431 444 396 444Q381 444 381 453Q381 459 388 473T407 513T428 563Q433 580 433 594Q433 636 381 636Q314 636 260 594T175 489T128 363T112 247Q112 157 153 101T273 44Q347 44 398 121Q413 144 437 157T481 171Q496 171 496 160Q496 150 476 123Q426 56 350 16T201 -25Z\"><\/path><path id=\"MJX-727-TEX-N-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D434\" xlink:href=\"#MJX-727-TEX-I-1D434\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(750,0)\"><use data-c=\"1D438\" xlink:href=\"#MJX-727-TEX-I-1D438\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(1514,0)\"><use data-c=\"1D436\" xlink:href=\"#MJX-727-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2274,0)\"><use data-c=\"28\" xlink:href=\"#MJX-727-TEX-N-28\"><\/use><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(2663,0)\"><g data-mml-node=\"mi\"><use data-c=\"43\" xlink:href=\"#MJX-727-TEX-C-43\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3190,0)\"><use data-c=\"29\" xlink:href=\"#MJX-727-TEX-N-29\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>A<\/mi><mi>E<\/mi><mi>C<\/mi><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">AEC(\\mathcal{C})<\/script><span>\u7684\u503c\u3002<\/span><\/p><p><span>\u5f53k=1\u65f6\uff0c\u627e\u4e2d\u5fc3\u70b9\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.832ex\" height=\"2.452ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -833.9 2577.6 1083.9\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-730-TEX-I-1D442\" d=\"M740 435Q740 320 676 213T511 42T304 -22Q207 -22 138 35T51 201Q50 209 50 244Q50 346 98 438T227 601Q351 704 476 704Q514 704 524 703Q621 689 680 617T740 435ZM637 476Q637 565 591 615T476 665Q396 665 322 605Q242 542 200 428T157 216Q157 126 200 73T314 19Q404 19 485 98T608 313Q637 408 637 476Z\"><\/path><path id=\"MJX-730-TEX-N-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path id=\"MJX-730-TEX-I-1D45B\" d=\"M21 287Q22 293 24 303T36 341T56 388T89 425T135 442Q171 442 195 424T225 390T231 369Q231 367 232 367L243 378Q304 442 382 442Q436 442 469 415T503 336T465 179T427 52Q427 26 444 26Q450 26 453 27Q482 32 505 65T540 145Q542 153 560 153Q580 153 580 145Q580 144 576 130Q568 101 554 73T508 17T439 -10Q392 -10 371 17T350 73Q350 92 386 193T423 345Q423 404 379 404H374Q288 404 229 303L222 291L189 157Q156 26 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 112 180T152 343Q153 348 153 366Q153 405 129 405Q91 405 66 305Q60 285 60 284Q58 278 41 278H27Q21 284 21 287Z\"><\/path><path id=\"MJX-730-TEX-N-32\" d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path id=\"MJX-730-TEX-N-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D442\" xlink:href=\"#MJX-730-TEX-I-1D442\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(763,0)\"><use data-c=\"28\" xlink:href=\"#MJX-730-TEX-N-28\"><\/use><\/g><g data-mml-node=\"msup\" transform=\"translate(1152,0)\"><g data-mml-node=\"mi\"><use data-c=\"1D45B\" xlink:href=\"#MJX-730-TEX-I-1D45B\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(633,363) scale(0.707)\"><use data-c=\"32\" xlink:href=\"#MJX-730-TEX-N-32\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(2188.6,0)\"><use data-c=\"29\" xlink:href=\"#MJX-730-TEX-N-29\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>O<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>n<\/mi><mn>2<\/mn><\/msup><mo stretchy=\"false\">)<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">O(n^2)<\/script><span>\uff0c\u5982\u679ck&gt;1,\u627e\u4e2d\u5fc3\u70b9\u662fNP-hard\u7684\u3002<\/span><\/p><p><span>k-median\u7b97\u6cd5\u540c\u6837\u53ef\u4ee5\u8ba1\u7b97\u65e0\u6cd5\u53d6\u5747\u503c\u7684ordering\u6570\u636e\u3002<\/span><\/p><p><span>k-median\u7b97\u6cd5\u4e0ek-mean\u7c7b\u4f3c\uff0c\u53ea\u662f\u516c\u5f0f\u4e0d\u540c\uff0c\u5728\u6b64\u4e0d\u505a\u8d58\u8ff0\uff0c\u6709\u5174\u8da3\u53ef\u4ee5\u9605\u8bfb\u8fd9\u7bc7\u6587\u7ae0\uff0c\u4ecb\u7ecd\u4e86k-mean,k-median\uff0c\u4ee5\u53ca\u884d\u751f\u51fa\u7684<\/span><a href='https:\/\/rstudio-pubs-static.s3.amazonaws.com\/455393_f20bacf1329a49dab40eb393308b33eb.html'><span>PAM<\/span><\/a><span>\u3002<\/span><\/p><h2 id='silhouette-coefficient'><span>Silhouette-Coefficient<\/span><\/h2><p><span>\u5982\u4f55\u6311\u9009\u53c2\u6570k\u5462\uff1f\u975e\u5e38\u7b80\u5355\u7684\u60f3\u6cd5\u662f\u904d\u5386k\u7684\u5927\u5c0f\uff0c\u4ece2\u4e00\u76f4\u5230n-1\uff0cn\u662f\u6570\u636e\u7684\u89c4\u6a21\u3002\u7136\u540e\u6211\u4eec\u6311\u9009\u51fa\u6700\u597d\u7684\u805a\u7c7b\u6240\u5bf9\u5e94\u7684k\u3002<\/span><\/p><p><span>\u90a3\u4e48\u6211\u4eec\u5e94\u8be5\u5982\u4f55\u8861\u91cf\u4e00\u4e2a\u597d\u7684\u805a\u7c7b\u5462\uff1f\u5355\u7eaf\u53ea\u662f\u7528<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"4.647ex\" height=\"1.645ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -705 2054 727\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.05ex;\"><defs><path id=\"MJX-731-TEX-I-1D446\" d=\"M308 24Q367 24 416 76T466 197Q466 260 414 284Q308 311 278 321T236 341Q176 383 176 462Q176 523 208 573T273 648Q302 673 343 688T407 704H418H425Q521 704 564 640Q565 640 577 653T603 682T623 704Q624 704 627 704T632 705Q645 705 645 698T617 577T585 459T569 456Q549 456 549 465Q549 471 550 475Q550 478 551 494T553 520Q553 554 544 579T526 616T501 641Q465 662 419 662Q362 662 313 616T263 510Q263 480 278 458T319 427Q323 425 389 408T456 390Q490 379 522 342T554 242Q554 216 546 186Q541 164 528 137T492 78T426 18T332 -20Q320 -22 298 -22Q199 -22 144 33L134 44L106 13Q83 -14 78 -18T65 -22Q52 -22 52 -14Q52 -11 110 221Q112 227 130 227H143Q149 221 149 216Q149 214 148 207T144 186T142 153Q144 114 160 87T203 47T255 29T308 24Z\"><\/path><path id=\"MJX-731-TEX-I-1D438\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D446\" xlink:href=\"#MJX-731-TEX-I-1D446\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(645,0)\"><use data-c=\"1D446\" xlink:href=\"#MJX-731-TEX-I-1D446\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(1290,0)\"><use data-c=\"1D438\" xlink:href=\"#MJX-731-TEX-I-1D438\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>S<\/mi><mi>S<\/mi><mi>E<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">SSE<\/script><span>\u6216\u8005\u662f<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"5.145ex\" height=\"1.67ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -716 2274 738\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.05ex;\"><defs><path id=\"MJX-733-TEX-I-1D434\" d=\"M208 74Q208 50 254 46Q272 46 272 35Q272 34 270 22Q267 8 264 4T251 0Q249 0 239 0T205 1T141 2Q70 2 50 0H42Q35 7 35 11Q37 38 48 46H62Q132 49 164 96Q170 102 345 401T523 704Q530 716 547 716H555H572Q578 707 578 706L606 383Q634 60 636 57Q641 46 701 46Q726 46 726 36Q726 34 723 22Q720 7 718 4T704 0Q701 0 690 0T651 1T578 2Q484 2 455 0H443Q437 6 437 9T439 27Q443 40 445 43L449 46H469Q523 49 533 63L521 213H283L249 155Q208 86 208 74ZM516 260Q516 271 504 416T490 562L463 519Q447 492 400 412L310 260L413 259Q516 259 516 260Z\"><\/path><path id=\"MJX-733-TEX-I-1D438\" d=\"M492 213Q472 213 472 226Q472 230 477 250T482 285Q482 316 461 323T364 330H312Q311 328 277 192T243 52Q243 48 254 48T334 46Q428 46 458 48T518 61Q567 77 599 117T670 248Q680 270 683 272Q690 274 698 274Q718 274 718 261Q613 7 608 2Q605 0 322 0H133Q31 0 31 11Q31 13 34 25Q38 41 42 43T65 46Q92 46 125 49Q139 52 144 61Q146 66 215 342T285 622Q285 629 281 629Q273 632 228 634H197Q191 640 191 642T193 659Q197 676 203 680H757Q764 676 764 669Q764 664 751 557T737 447Q735 440 717 440H705Q698 445 698 453L701 476Q704 500 704 528Q704 558 697 578T678 609T643 625T596 632T532 634H485Q397 633 392 631Q388 629 386 622Q385 619 355 499T324 377Q347 376 372 376H398Q464 376 489 391T534 472Q538 488 540 490T557 493Q562 493 565 493T570 492T572 491T574 487T577 483L544 351Q511 218 508 216Q505 213 492 213Z\"><\/path><path id=\"MJX-733-TEX-I-1D436\" 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type=\"math\/tex\">AEC<\/script><span>\u80af\u5b9a\u662f\u4e0d\u884c\u7684\uff0c\u56e0\u4e3a\u968f\u7740k\u7684\u589e\u52a0\uff0c\u8fd9\u4e24\u4e2a\u503c\u5fc5\u7136\u4f1a\u51cf\u5c0f\u3002<\/span><\/p><p><span>Silhouette-Coefficient\u53ef\u4ee5\u8bc4\u4f30\u4e00\u4e2a\u805a\u7c7b\u7684\u8d28\u91cf\u3002\u6311\u9009\u5b83\u7684\u539f\u56e0\u4e5f\u5f88\u7b80\u5355\uff0c\u8fd9\u4e2a\u7cfb\u6570\u4e0d\u4f1a\u56e0\u4e3ak\u7684\u589e\u52a0\u800c\u5355\u8c03\u3002<\/span><\/p><p><span>Silhouette-Coefficient\u7684\u60f3\u6cd5\u662f\uff0c\u805a\u7c7b\u7684\u8d28\u91cf\u597d\u574f\uff0c\u5bf9\u5e94\u4e8e\u8fd9\u4e2a\u805a\u7c7b\u662f\u5426\u5c06\u5bf9\u8c61\u201c\u6070\u5f53\u201d\u5f97\u6620\u5c04\u5230\u4e86\u805a\u7c7b\u91cc\u3002\u6240\u8c13\u6070\u5f53\uff0c\u6b63\u5982\u6211\u4eec\u524d\u9762\u63d0\u5230\u7684\uff0c\u5c31\u662f\u60f3\u8ba9\u540c\u4e00\u4e2a\u7c07\u5185\u7684\u5bf9\u8c61\u5c3d\u53ef\u80fd\u76f8\u4f3c\uff0c\u4e0d\u540c\u7684\u7c07\u7684\u5bf9\u8c61\u5c3d\u53ef\u80fd\u76f8\u5f02\u3002\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u89c4\u5b9a<\/span><mjx-container 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transform=\"translate(889,0)\"><\/use><\/g><\/g><\/g><\/g><\/svg><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\"><mlabeledtr><mtd><mtext>(7)<\/mtext><\/mtd><mtd><mi>b<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><munder><mo data-mjx-texclass=\"OP\" movablelimits=\"true\">min<\/mo><mrow data-mjx-texclass=\"ORD\"><msub><mi>C<\/mi><mi>i<\/mi><\/msub><mo>\u2260<\/mo><mi>C<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><\/munder><mo fence=\"false\" stretchy=\"false\">{<\/mo><mfrac><mn>1<\/mn><mrow><mo stretchy=\"false\">|<\/mo><msub><mi>C<\/mi><mi>i<\/mi><\/msub><mo stretchy=\"false\">|<\/mo><\/mrow><\/mfrac><munder><mo data-mjx-texclass=\"OP\">\u2211<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>p<\/mi><mo>\u2208<\/mo><msub><mi>C<\/mi><mi>i<\/mi><\/msub><\/mrow><\/munder><mi>d<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo>,<\/mo><mi>p<\/mi><mo stretchy=\"false\">)<\/mo><mo fence=\"false\" stretchy=\"false\">}<\/mo><\/mtd><\/mlabeledtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/div><\/div><p><span>\u53ef\u4ee5\u7528\u4e0b\u9762\u7684\u56fe\u7247\u6765\u8868\u793a\u4e0a\u9762\u7684\u5b9a\u4e49\u3002<\/span><\/p><p><img decoding=\"async\" src=\"https:\/\/raw.githubusercontent.com\/Mhrooz\/pics\/master\/uPic\/image-20230104141325989_01_04_14_13.png\" alt=\"image-20230104141325989\" style=\"zoom:50%;\" \/><\/p><p><span>Silhouette Coefficient\u5b9a\u4e49\u5982\u4e0b:<\/span><\/p><div contenteditable=\"false\" spellcheck=\"false\" class=\"mathjax-block md-end-block md-math-block md-rawblock\" id=\"mathjax-n417\" cid=\"n417\" mdtype=\"math_block\" data-math-tag-before=\"7\" data-math-labels=\"[]\" data-math-tag-after=\"8\"><div 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xlink:href=\"#MJX-1098-TEX-N-31\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(1556,0)\"><use data-c=\"2C\" xlink:href=\"#MJX-1098-TEX-N-2C\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(2000.7,0)\"><use data-c=\"31\" xlink:href=\"#MJX-1098-TEX-N-31\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2500.7,0)\"><use data-c=\"5D\" xlink:href=\"#MJX-1098-TEX-N-5D\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mo stretchy=\"false\">[<\/mo><mo>\u2212<\/mo><mn>1<\/mn><mo>,<\/mo><mn>1<\/mn><mo stretchy=\"false\">]<\/mo><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">[-1,1]<\/script><span>\u3002<\/span><\/p><p><span>\u901a\u8fc7silhouette coefficient, \u6211\u4eec\u5b9a\u4e49\u4e00\u4e2a\u7c07<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"2.357ex\" 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transform=\"translate(1389,0)\"><\/use><\/g><\/g><\/g><\/g><\/svg><\/g><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"block\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><mtable displaystyle=\"true\"><mlabeledtr><mtd><mtext>(10)<\/mtext><\/mtd><mtd><mi>s<\/mi><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mrow><mo stretchy=\"false\">|<\/mo><mi>D<\/mi><mo stretchy=\"false\">|<\/mo><\/mrow><\/mfrac><munder><mo data-mjx-texclass=\"OP\">\u2211<\/mo><mrow data-mjx-texclass=\"ORD\"><mi>o<\/mi><mo>\u2208<\/mo><mi>D<\/mi><\/mrow><\/munder><mi>s<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><\/mtd><\/mlabeledtr><\/mtable><\/math><\/mjx-assistive-mml><\/mjx-container><\/div><\/div><p><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: 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xlink:href=\"#MJX-1253-TEX-I-1D44E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4332.6,0)\"><use data-c=\"28\" xlink:href=\"#MJX-1253-TEX-N-28\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(4721.6,0)\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1253-TEX-I-1D45C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5206.6,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1253-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5873.3,0)\"><use data-c=\"2192\" xlink:href=\"#MJX-1253-TEX-N-2192\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(7151.1,0)\"><use data-c=\"1D460\" xlink:href=\"#MJX-1253-TEX-I-1D460\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(7620.1,0)\"><use data-c=\"28\" xlink:href=\"#MJX-1253-TEX-N-28\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(8009.1,0)\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1253-TEX-I-1D45C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(8494.1,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1253-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(9160.9,0)\"><use data-c=\"2248\" xlink:href=\"#MJX-1253-TEX-N-2248\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(10216.7,0)\"><use data-c=\"31\" xlink:href=\"#MJX-1253-TEX-N-31\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo>&gt;&gt;<\/mo><mi>a<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">\u2192<\/mo><mi>s<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2248<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">b(o)>>a(o)\\rightarrow s(o)\\approx 1<\/script><span>\uff0c\u5219\u79f0\u8fd9\u4e2a\u7c07\u7684\u4ee3\u8868\u5bf9\u8c61<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.023ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -441 485 452\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-1275-TEX-I-1D45C\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1275-TEX-I-1D45C\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>o<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">o<\/script><span>\u5f88\u6709\u4ee3\u8868\u6027\u3002<\/span>\n<span>\u5982\u679c<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"22.486ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 9938.7 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-1276-TEX-I-1D44F\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 694Q246 694 246 685T212 542Q204 508 195 472T180 418L176 399Q176 396 182 402Q231 442 283 442Q345 442 383 396T422 280Q422 169 343 79T173 -11Q123 -11 82 27T40 150V159Q40 180 48 217T97 414Q147 611 147 623T109 637Q104 637 101 637H96Q86 637 83 637T76 640T73 647ZM336 325V331Q336 405 275 405Q258 405 240 397T207 376T181 352T163 330L157 322L136 236Q114 150 114 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50Q294 48 292 46Q233 -10 172 -10Q117 -10 75 30T33 157ZM351 328Q351 334 346 350T323 385T277 405Q242 405 210 374T160 293Q131 214 119 129Q119 126 119 118T118 106Q118 61 136 44T179 26Q217 26 254 59T298 110Q300 114 325 217T351 328Z\"><\/path><path id=\"MJX-1276-TEX-N-2192\" d=\"M56 237T56 250T70 270H835Q719 357 692 493Q692 494 692 496T691 499Q691 511 708 511H711Q720 511 723 510T729 506T732 497T735 481T743 456Q765 389 816 336T935 261Q944 258 944 250Q944 244 939 241T915 231T877 212Q836 186 806 152T761 85T740 35T732 4Q730 -6 727 -8T711 -11Q691 -11 691 0Q691 7 696 25Q728 151 835 230H70Q56 237 56 250Z\"><\/path><path id=\"MJX-1276-TEX-I-1D460\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"><\/path><path id=\"MJX-1276-TEX-N-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 16T82 83Q39 165 39 320Q39 494 96 585ZM321 597Q291 629 250 629Q208 629 178 597Q153 571 145 525T137 333Q137 175 145 125T181 46Q209 16 250 16Q290 16 318 46Q347 76 354 130T362 333Q362 478 354 524T321 597Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D44F\" xlink:href=\"#MJX-1276-TEX-I-1D44F\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(429,0)\"><use data-c=\"28\" xlink:href=\"#MJX-1276-TEX-N-28\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(818,0)\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1276-TEX-I-1D45C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(1303,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1276-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(1969.8,0)\"><use data-c=\"2248\" xlink:href=\"#MJX-1276-TEX-N-2248\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(3025.6,0)\"><use data-c=\"1D44E\" xlink:href=\"#MJX-1276-TEX-I-1D44E\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3554.6,0)\"><use data-c=\"28\" xlink:href=\"#MJX-1276-TEX-N-28\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(3943.6,0)\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1276-TEX-I-1D45C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4428.6,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1276-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5095.3,0)\"><use data-c=\"2192\" xlink:href=\"#MJX-1276-TEX-N-2192\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(6373.1,0)\"><use data-c=\"1D460\" xlink:href=\"#MJX-1276-TEX-I-1D460\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(6842.1,0)\"><use data-c=\"28\" xlink:href=\"#MJX-1276-TEX-N-28\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(7231.1,0)\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1276-TEX-I-1D45C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(7716.1,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1276-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(8382.9,0)\"><use data-c=\"2248\" xlink:href=\"#MJX-1276-TEX-N-2248\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(9438.7,0)\"><use data-c=\"30\" xlink:href=\"#MJX-1276-TEX-N-30\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2248<\/mo><mi>a<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">\u2192<\/mo><mi>s<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2248<\/mo><mn>0<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">b(o)\\approx a(o)\\rightarrow s(o)\\approx 0<\/script><span>\uff0c\u5219\u53ef\u4ee5\u8bf4\u5bf9\u8c61<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.023ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -441 485 452\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-1275-TEX-I-1D45C\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1275-TEX-I-1D45C\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>o<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">o<\/script><span>\u5728\u4e24\u4e2a\u7c07\u4e4b\u95f4\u3002<\/span>\n<span>\u5982\u679c<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"26.006ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 11494.7 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-1296-TEX-I-1D44F\" d=\"M73 647Q73 657 77 670T89 683Q90 683 161 688T234 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data-mml-node=\"mi\" transform=\"translate(8009.1,0)\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1296-TEX-I-1D45C\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(8494.1,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1296-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(9160.9,0)\"><use data-c=\"2248\" xlink:href=\"#MJX-1296-TEX-N-2248\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(10216.7,0)\"><use data-c=\"2212\" xlink:href=\"#MJX-1296-TEX-N-2212\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(10994.7,0)\"><use data-c=\"31\" xlink:href=\"#MJX-1296-TEX-N-31\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>b<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo>&lt;&lt;<\/mo><mi>a<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">\u2192<\/mo><mi>s<\/mi><mo stretchy=\"false\">(<\/mo><mi>o<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2248<\/mo><mo>\u2212<\/mo><mn>1<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">b(o) << a(o)\\rightarrow s(o)\\approx -1<\/script><span>\uff0c\u5219\u53ef\u4ee5\u8bf4\u5bf9\u8c61<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"1.097ex\" height=\"1.023ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -441 485 452\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.025ex;\"><defs><path id=\"MJX-1275-TEX-I-1D45C\" d=\"M201 -11Q126 -11 80 38T34 156Q34 221 64 279T146 380Q222 441 301 441Q333 441 341 440Q354 437 367 433T402 417T438 387T464 338T476 268Q476 161 390 75T201 -11ZM121 120Q121 70 147 48T206 26Q250 26 289 58T351 142Q360 163 374 216T388 308Q388 352 370 375Q346 405 306 405Q243 405 195 347Q158 303 140 230T121 120Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D45C\" xlink:href=\"#MJX-1275-TEX-I-1D45C\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>o<\/mi><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">o<\/script><span>\u8ddd\u79bb\u53e6\u4e00\u4e2a\u7c07\u66f4\u8fd1\u3002<\/span><\/p><p><span>\u5bf9\u4e8e\u4e00\u4e2a\u805a\u7c7b\u6765\u8bf4\uff0c<\/span><\/p><p><span>\u5982\u679c<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.831ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 6997.1 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-1309-TEX-N-30\" d=\"M96 585Q152 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xlink:href=\"#MJX-1309-TEX-I-1D460\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3080.6,0)\"><use data-c=\"28\" xlink:href=\"#MJX-1309-TEX-N-28\"><\/use><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3469.6,0)\"><g data-mml-node=\"mi\"><use data-c=\"43\" xlink:href=\"#MJX-1309-TEX-C-43\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3996.6,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1309-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4663.3,0)\"><use data-c=\"2264\" xlink:href=\"#MJX-1309-TEX-N-2264\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(5719.1,0)\"><use data-c=\"31\" xlink:href=\"#MJX-1309-TEX-N-31\"><\/use><use data-c=\"2E\" xlink:href=\"#MJX-1309-TEX-N-2E\" transform=\"translate(500,0)\"><\/use><use data-c=\"30\" xlink:href=\"#MJX-1309-TEX-N-30\" transform=\"translate(778,0)\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>0.7<\/mn><mo>&lt;<\/mo><mi>s<\/mi><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><mo>\u2264<\/mo><mn>1.0<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">0.7<s(\\mathcal{C})\\leq 1.0<\/script><span>\uff0c\u5219\u662f\u4e00\u4e2a\u597d\u805a\u7c7b\u3002<\/span>\n<span>\u5982\u679c<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"15.831ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 6997.1 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-1308-TEX-N-30\" d=\"M96 585Q152 666 249 666Q297 666 345 640T423 548Q460 465 460 320Q460 165 417 83Q397 41 362 16T301 -15T250 -22Q224 -22 198 -16T137 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250Z\"><\/path><path id=\"MJX-1308-TEX-C-43\" d=\"M201 -25Q167 -25 136 -14T75 23T29 94T12 202Q12 290 50 394T161 574Q227 642 303 673T433 704Q435 705 457 705Q533 701 533 640Q533 606 507 548T464 474Q431 444 396 444Q381 444 381 453Q381 459 388 473T407 513T428 563Q433 580 433 594Q433 636 381 636Q314 636 260 594T175 489T128 363T112 247Q112 157 153 101T273 44Q347 44 398 121Q413 144 437 157T481 171Q496 171 496 160Q496 150 476 123Q426 56 350 16T201 -25Z\"><\/path><path id=\"MJX-1308-TEX-N-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path id=\"MJX-1308-TEX-N-2264\" d=\"M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 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xlink:href=\"#MJX-1308-TEX-N-3C\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(2611.6,0)\"><use data-c=\"1D460\" xlink:href=\"#MJX-1308-TEX-I-1D460\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3080.6,0)\"><use data-c=\"28\" xlink:href=\"#MJX-1308-TEX-N-28\"><\/use><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3469.6,0)\"><g data-mml-node=\"mi\"><use data-c=\"43\" xlink:href=\"#MJX-1308-TEX-C-43\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(3996.6,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1308-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(4663.3,0)\"><use data-c=\"2264\" xlink:href=\"#MJX-1308-TEX-N-2264\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(5719.1,0)\"><use data-c=\"30\" xlink:href=\"#MJX-1308-TEX-N-30\"><\/use><use data-c=\"2E\" xlink:href=\"#MJX-1308-TEX-N-2E\" transform=\"translate(500,0)\"><\/use><use data-c=\"37\" xlink:href=\"#MJX-1308-TEX-N-37\" transform=\"translate(778,0)\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>0.5<\/mn><mo>&lt;<\/mo><mi>s<\/mi><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><mo>\u2264<\/mo><mn>0.7<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">0.5<s(\\mathcal{C})\\leq 0.7<\/script><span>\uff0c\u5219\u662f\u4e00\u4e2a\u4e2d\u805a\u7c7b\uff08\u4e0d\u597d\u4e0d\u574f\u3002<\/span>\n<span>\u5982\u679c<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"16.962ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 7497.1 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path 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429Z\"><\/path><path id=\"MJX-1322-TEX-N-35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><path id=\"MJX-1322-TEX-N-3C\" d=\"M694 -11T694 -19T688 -33T678 -40Q671 -40 524 29T234 166L90 235Q83 240 83 250Q83 261 91 266Q664 540 678 540Q681 540 687 534T694 519T687 505Q686 504 417 376L151 250L417 124Q686 -4 687 -5Q694 -11 694 -19Z\"><\/path><path id=\"MJX-1322-TEX-I-1D460\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"><\/path><path id=\"MJX-1322-TEX-N-28\" d=\"M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z\"><\/path><path id=\"MJX-1322-TEX-C-43\" d=\"M201 -25Q167 -25 136 -14T75 23T29 94T12 202Q12 290 50 394T161 574Q227 642 303 673T433 704Q435 705 457 705Q533 701 533 640Q533 606 507 548T464 474Q431 444 396 444Q381 444 381 453Q381 459 388 473T407 513T428 563Q433 580 433 594Q433 636 381 636Q314 636 260 594T175 489T128 363T112 247Q112 157 153 101T273 44Q347 44 398 121Q413 144 437 157T481 171Q496 171 496 160Q496 150 476 123Q426 56 350 16T201 -25Z\"><\/path><path id=\"MJX-1322-TEX-N-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z\"><\/path><path id=\"MJX-1322-TEX-N-2264\" d=\"M674 636Q682 636 688 630T694 615T687 601Q686 600 417 472L151 346L399 228Q687 92 691 87Q694 81 694 76Q694 58 676 56H670L382 192Q92 329 90 331Q83 336 83 348Q84 359 96 365Q104 369 382 500T665 634Q669 636 674 636ZM84 -118Q84 -108 99 -98H678Q694 -104 694 -118Q694 -130 679 -138H98Q84 -131 84 -118Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mn\"><use data-c=\"30\" xlink:href=\"#MJX-1322-TEX-N-30\"><\/use><use data-c=\"2E\" xlink:href=\"#MJX-1322-TEX-N-2E\" transform=\"translate(500,0)\"><\/use><use data-c=\"32\" xlink:href=\"#MJX-1322-TEX-N-32\" transform=\"translate(778,0)\"><\/use><use data-c=\"35\" xlink:href=\"#MJX-1322-TEX-N-35\" transform=\"translate(1278,0)\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2055.8,0)\"><use data-c=\"3C\" xlink:href=\"#MJX-1322-TEX-N-3C\"><\/use><\/g><g data-mml-node=\"mi\" transform=\"translate(3111.6,0)\"><use data-c=\"1D460\" xlink:href=\"#MJX-1322-TEX-I-1D460\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(3580.6,0)\"><use data-c=\"28\" xlink:href=\"#MJX-1322-TEX-N-28\"><\/use><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(3969.6,0)\"><g data-mml-node=\"mi\"><use data-c=\"43\" xlink:href=\"#MJX-1322-TEX-C-43\"><\/use><\/g><\/g><g data-mml-node=\"mo\" transform=\"translate(4496.6,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1322-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(5163.3,0)\"><use data-c=\"2264\" xlink:href=\"#MJX-1322-TEX-N-2264\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(6219.1,0)\"><use data-c=\"30\" xlink:href=\"#MJX-1322-TEX-N-30\"><\/use><use data-c=\"2E\" xlink:href=\"#MJX-1322-TEX-N-2E\" transform=\"translate(500,0)\"><\/use><use data-c=\"35\" xlink:href=\"#MJX-1322-TEX-N-35\" transform=\"translate(778,0)\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mn>0.25<\/mn><mo>&lt;<\/mo><mi>s<\/mi><mo stretchy=\"false\">(<\/mo><mrow data-mjx-texclass=\"ORD\"><mi data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\">C<\/mi><\/mrow><mo stretchy=\"false\">)<\/mo><mo>\u2264<\/mo><mn>0.5<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">0.25<s(\\mathcal{C})\\leq 0.5<\/script><span>\uff0c\u5219\u662f\u4e00\u4e2a\u574f\u805a\u7c7b\u3002<\/span>\n<span>\u5982\u679c<\/span><mjx-container class=\"MathJax\" jax=\"SVG\" style=\"position: relative;\"><svg xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"11.87ex\" height=\"2.262ex\" role=\"img\" focusable=\"false\" viewBox=\"0 -750 5246.6 1000\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" aria-hidden=\"true\" style=\"vertical-align: -0.566ex;\"><defs><path id=\"MJX-1338-TEX-I-1D460\" d=\"M131 289Q131 321 147 354T203 415T300 442Q362 442 390 415T419 355Q419 323 402 308T364 292Q351 292 340 300T328 326Q328 342 337 354T354 372T367 378Q368 378 368 379Q368 382 361 388T336 399T297 405Q249 405 227 379T204 326Q204 301 223 291T278 274T330 259Q396 230 396 163Q396 135 385 107T352 51T289 7T195 -10Q118 -10 86 19T53 87Q53 126 74 143T118 160Q133 160 146 151T160 120Q160 94 142 76T111 58Q109 57 108 57T107 55Q108 52 115 47T146 34T201 27Q237 27 263 38T301 66T318 97T323 122Q323 150 302 164T254 181T195 196T148 231Q131 256 131 289Z\"><\/path><path id=\"MJX-1338-TEX-C-28\" d=\"M241 -250Q203 -212 174 -140T144 39Q144 158 180 288T296 544T481 746L487 750H499Q517 750 517 740Q517 736 495 716Q399 630 331 491T236 228T208 3Q208 -73 224 -130T255 -214T271 -244Q271 -250 252 -250H241Z\"><\/path><path id=\"MJX-1338-TEX-I-1D436\" d=\"M50 252Q50 367 117 473T286 641T490 704Q580 704 633 653Q642 643 648 636T656 626L657 623Q660 623 684 649Q691 655 699 663T715 679T725 690L740 705H746Q760 705 760 698Q760 694 728 561Q692 422 692 421Q690 416 687 415T669 413H653Q647 419 647 422Q647 423 648 429T650 449T651 481Q651 552 619 605T510 659Q484 659 454 652T382 628T299 572T226 479Q194 422 175 346T156 222Q156 108 232 58Q280 24 350 24Q441 24 512 92T606 240Q610 253 612 255T628 257Q648 257 648 248Q648 243 647 239Q618 132 523 55T319 -22Q206 -22 128 53T50 252Z\"><\/path><path id=\"MJX-1338-TEX-N-29\" d=\"M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 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d=\"M109 429Q82 429 66 447T50 491Q50 562 103 614T235 666Q326 666 387 610T449 465Q449 422 429 383T381 315T301 241Q265 210 201 149L142 93L218 92Q375 92 385 97Q392 99 409 186V189H449V186Q448 183 436 95T421 3V0H50V19V31Q50 38 56 46T86 81Q115 113 136 137Q145 147 170 174T204 211T233 244T261 278T284 308T305 340T320 369T333 401T340 431T343 464Q343 527 309 573T212 619Q179 619 154 602T119 569T109 550Q109 549 114 549Q132 549 151 535T170 489Q170 464 154 447T109 429Z\"><\/path><path id=\"MJX-1338-TEX-N-35\" d=\"M164 157Q164 133 148 117T109 101H102Q148 22 224 22Q294 22 326 82Q345 115 345 210Q345 313 318 349Q292 382 260 382H254Q176 382 136 314Q132 307 129 306T114 304Q97 304 95 310Q93 314 93 485V614Q93 664 98 664Q100 666 102 666Q103 666 123 658T178 642T253 634Q324 634 389 662Q397 666 402 666Q410 666 410 648V635Q328 538 205 538Q174 538 149 544L139 546V374Q158 388 169 396T205 412T256 420Q337 420 393 355T449 201Q449 109 385 44T229 -22Q148 -22 99 32T50 154Q50 178 61 192T84 210T107 214Q132 214 148 197T164 157Z\"><\/path><\/defs><g stroke=\"currentColor\" fill=\"currentColor\" stroke-width=\"0\" transform=\"scale(1,-1)\"><g data-mml-node=\"math\"><g data-mml-node=\"mi\"><use data-c=\"1D460\" xlink:href=\"#MJX-1338-TEX-I-1D460\"><\/use><\/g><g data-mml-node=\"TeXAtom\" data-mjx-texclass=\"ORD\" transform=\"translate(469,0)\"><g data-mml-node=\"mo\"><use data-c=\"28\" xlink:href=\"#MJX-1338-TEX-C-28\"><\/use><\/g><\/g><g data-mml-node=\"mi\" transform=\"translate(986,0)\"><use data-c=\"1D436\" xlink:href=\"#MJX-1338-TEX-I-1D436\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(1746,0)\"><use data-c=\"29\" xlink:href=\"#MJX-1338-TEX-N-29\"><\/use><\/g><g data-mml-node=\"mo\" transform=\"translate(2412.8,0)\"><use data-c=\"2264\" xlink:href=\"#MJX-1338-TEX-N-2264\"><\/use><\/g><g data-mml-node=\"mn\" transform=\"translate(3468.6,0)\"><use data-c=\"30\" xlink:href=\"#MJX-1338-TEX-N-30\"><\/use><use data-c=\"2E\" xlink:href=\"#MJX-1338-TEX-N-2E\" transform=\"translate(500,0)\"><\/use><use data-c=\"32\" xlink:href=\"#MJX-1338-TEX-N-32\" transform=\"translate(778,0)\"><\/use><use data-c=\"35\" xlink:href=\"#MJX-1338-TEX-N-35\" transform=\"translate(1278,0)\"><\/use><\/g><\/g><\/g><\/svg><mjx-assistive-mml unselectable=\"on\" display=\"inline\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mi>s<\/mi><mrow data-mjx-texclass=\"ORD\"><mo data-mjx-variant=\"-tex-calligraphic\" mathvariant=\"script\" stretchy=\"false\">(<\/mo><\/mrow><mi>C<\/mi><mo stretchy=\"false\">)<\/mo><mo>\u2264<\/mo><mn>0.25<\/mn><\/math><\/mjx-assistive-mml><\/mjx-container><script type=\"math\/tex\">s\\mathcal(C)\\leq 0.25<\/script><span>\uff0c\u5219\u5c31\u6ca1\u6709\u4e00\u4e2a\u805a\u7c7b\u7ed3\u6784\u3002<\/span><\/p><h2 id='reference'><span>Reference<\/span><\/h2><p><span>[1] S.P. Lloyd: Least squares quantization in PCM. In IEEE Information Theory, 1982<\/span><\/p><\/div><\/div>\n<\/body>\n<\/html>\n","protected":false},"excerpt":{"rendered":"<p>4_1_Partitioning_Methods Clustering &#8211; Partitionin<a class=\"more-link\" href=\"https:\/\/blog.mhrooz.xyz\/index.php\/2023\/01\/03\/clustering_-_partitioning_methods\/\">\u7ee7\u7eed\u9605\u8bfb<span class=\"screen-reader-text\">&#8220;Clustering &#8211; Partitioning Methods&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[61,38,55,12],"tags":[57,58,64],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2567"}],"collection":[{"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/comments?post=2567"}],"version-history":[{"count":3,"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2567\/revisions"}],"predecessor-version":[{"id":2578,"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/posts\/2567\/revisions\/2578"}],"wp:attachment":[{"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/media?parent=2567"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/categories?post=2567"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.mhrooz.xyz\/index.php\/wp-json\/wp\/v2\/tags?post=2567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}