{"id":359,"date":"2024-10-03T08:24:19","date_gmt":"2024-10-03T00:24:19","guid":{"rendered":"https:\/\/www.xuzhe.tj.cn\/?p=359"},"modified":"2025-05-03T00:51:31","modified_gmt":"2025-05-02T16:51:31","slug":"cart","status":"publish","type":"post","link":"https:\/\/www.xuzhe.tj.cn\/index.php\/2024\/10\/03\/cart\/","title":{"rendered":"CART\u51b3\u7b56\u6811\u7b97\u6cd5\uff1a\u5982\u4f55\u5904\u7406\u6570\u503c\u578b\u4e0e\u5206\u7c7b\u578b\u7279\u5f81"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">CART\u7b97\u6cd5<\/h2>\n\n\n<p>\u51b3\u7b56\u6811\u662f\u4e00\u79cd\u975e\u53c2\u6570\u7684\u76d1\u7763\u5b66\u4e60\u65b9\u6cd5\uff0c\u5b83\u4e0d\u5bf9\u6570\u636e\u96c6\u7684\u5206\u5e03\u5f62\u5f0f\u505a\u4efb\u4f55\u5177\u4f53\u5047\u8bbe\uff0c\u4f46\u4f1a\u6839\u636e\u6570\u636e\u4e2d\u7684\u7279\u5f81\u7c7b\u578b\u548c\u6807\u7b7e\u503c\u52a8\u6001\u5730\u751f\u6210\u6a21\u578b\u7ed3\u6784\u53ef\u4ee5\u7528\u4e8e\u5206\u7c7b\u548c\u56de\u5f52\u95ee\u9898\u3002\u51b3\u7b56\u6811\u7684\u6838\u5fc3\u601d\u60f3\u662f\u9012\u5f52\u5730\u5c06\u7279\u5f81\u7a7a\u95f4\u5212\u5206\u4e3a\u82e5\u5e72\u4e2a\u5355\u5143\uff0c\u4f7f\u5f97\u6bcf\u4e2a\u5355\u5143\u5185\u7684\u6837\u672c\u5c3d\u53ef\u80fd\u540c\u8d28\uff08\u5373\u5c5e\u4e8e\u540c\u4e00\u7c7b\u522b\u6216\u5177\u6709\u76f8\u4f3c\u7684\u76ee\u6807\u503c\uff09\u3002<\/p>\n\n<!--more-->\n\n<p>CART\uff08Classification and Regression Trees\uff09\u7b97\u6cd5\u662f\u4e00\u79cd\u5e38\u7528\u7684\u51b3\u7b56\u6811\u7b97\u6cd5\uff0c\u7531Leo Breiman\u7b49\u4eba\u57281984\u5e74\u63d0\u51fa\u3002CART\u7b97\u6cd5\u7684\u4e3b\u8981\u7279\u70b9\u5305\u62ec\uff1a<\/p>\n\n\n<ul class=\"wp-block-list\">\n    <li>\u4e8c\u53c9\u6811\u7ed3\u6784\uff1aCART\u751f\u6210\u7684\u662f\u4e8c\u53c9\u51b3\u7b56\u6811\uff0c\u6bcf\u4e2a\u5185\u90e8\u8282\u70b9\u90fd\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002<\/li>\n    <li>\u9002\u7528\u4e8e\u5206\u7c7b\u548c\u56de\u5f52\uff1aCART\u53ef\u4ee5\u5904\u7406\u5206\u7c7b\u4efb\u52a1\u548c\u56de\u5f52\u4efb\u52a1\u3002<\/li>\n    <li>\u5904\u7406\u591a\u79cd\u7279\u5f81\u7c7b\u578b\uff1a\u80fd\u591f\u540c\u65f6\u5904\u7406\u6570\u503c\u578b\u548c\u7c7b\u522b\u578b\u7279\u5f81\u3002<\/li>\n    <li>\u57fa\u4e8e\u4e0d\u7eaf\u5ea6\u5ea6\u91cf\uff1a\u4f7f\u7528\u57fa\u5c3c\u6307\u6570\uff08\u5206\u7c7b\uff09\u6216\u5747\u65b9\u8bef\u5dee\uff08\u56de\u5f52\uff09\u6765\u9009\u62e9\u6700\u4f73\u5206\u5272\u70b9\u3002<\/li>\n    <li>\u81ea\u52a8\u7279\u5f81\u9009\u62e9\uff1a\u5728\u6784\u5efa\u6811\u7684\u8fc7\u7a0b\u4e2d\uff0c\u7b97\u6cd5\u4f1a\u81ea\u52a8\u9009\u62e9\u6700\u5177\u533a\u5206\u6027\u7684\u7279\u5f81\u3002<\/li>\n    <li>\u5904\u7406\u7f3a\u5931\u503c\uff1a\u7406\u8bba\u4e0a\u63d0\u4f9b\u4e86\u5904\u7406\u7f3a\u5931\u6570\u636e\u7684\u7b56\u7565\uff0c\u5982\u4f7f\u7528\u66ff\u4ee3\u5206\u88c2\uff08Surrogate Splits\uff09\u6765\u5e94\u5bf9\u7f3a\u5931\u503c\u3002\u4f46\u5728\u4e0d\u540c\u7684\u5b9e\u73b0\u4e2d\uff08\u4f8b\u5982Scikit-learn\uff09\uff0c\u8fd9\u4e9b\u673a\u5236\u5e76\u4e0d\u4e00\u5b9a\u5185\u7f6e\u3002\u56e0\u6b64\uff0c\u7528\u6237\u901a\u5e38\u9700\u8981\u5728\u6570\u636e\u9884\u5904\u7406\u9636\u6bb5\u624b\u52a8\u5904\u7406\u7f3a\u5931\u6570\u636e\u3002<br><\/li>\n<\/ul>\n\n\n<h2 class=\"wp-block-heading\">CART\u4e0e\u5176\u5b83\u6811\u65b9\u6cd5\u7684\u533a\u522b<\/h2>\n\n\n<p>CART\u4e0e\u5176\u4ed6\u77e5\u540d\u7684\u51b3\u7b56\u6811\u7b97\u6cd5\uff0c\u5982\uff1aID3\u548cC4.5\u7b97\u6cd5\u5728\u5206\u5272\u65b9\u6cd5\u3001\u9002\u7528\u7684\u7279\u5f81\u548c\u4efb\u52a1\u7c7b\u578b\u65b9\u9762\u5b58\u5728\u4ee5\u4e0b\u533a\u522b\uff1a<\/p>\n\n\n<figure class=\"wp-block-table\">\n<table>\n    <thead>\n        <tr>\n            <th>\n                <strong>\u533a\u522b\u9879<\/strong>\n            <\/th>\n            <th>\n                <strong>CART<\/strong>\n            <\/th>\n            <th>\n                <strong>ID3<\/strong>\n            <\/th>\n            <th>\n                <strong>C4.5<\/strong>\n            <\/th>\n        <\/tr>\n    <\/thead>\n    <tbody>\n        <tr>\n            <td>\n                <strong>\u5206\u5272\u65b9\u6cd5<\/strong>\n            <\/td>\n            <td>\n                \u57fa\u5c3c\u6307\u6570\uff08\u5206\u7c7b\uff09\u3001\u5747\u65b9\u8bef\u5dee\uff08\u56de\u5f52\uff09\u4f5c\u4e3a\u5206\u5272\u6807\u51c6\uff0c\u6bcf\u6b21\u5206\u5272\u751f\u6210\u4e8c\u53c9\u6811\u3002\n            <\/td>\n            <td>\n                \u4f7f\u7528\u4fe1\u606f\u589e\u76ca\u4f5c\u4e3a\u5206\u5272\u6807\u51c6\uff0c\u53ef\u4ee5\u751f\u6210\u591a\u53c9\u6811\uff0c\u6bcf\u4e2a\u7279\u5f81\u53d6\u503c\u4e00\u4e2a\u5206\u652f\u3002\n            <\/td>\n            <td>\n                \u4f7f\u7528\u4fe1\u606f\u589e\u76ca\u6bd4\u4f5c\u4e3a\u5206\u5272\u6807\u51c6\uff0c\u53ef\u4ee5\u751f\u6210\u591a\u53c9\u6811\uff0c\u51cf\u5c11\u591a\u503c\u504f\u597d\u3002\n            <\/td>\n        <\/tr>\n        <tr>\n            <td>\n                <strong>\u9002\u7528\u7684\u7279\u5f81<\/strong>\n            <\/td>\n            <td>\n                \u540c\u65f6\u5904\u7406\u6570\u503c\u578b\u548c\u7c7b\u522b\u578b\u7279\u5f81\u3002\u5bf9\u4e8e\u6570\u503c\u578b\u7279\u5f81\uff0c\u5bfb\u627e\u6700\u4f73\u5206\u5272\u70b9\u8fdb\u884c\u4e8c\u5206\u3002\n            <\/td>\n            <td>\n                \u4e3b\u8981\u5904\u7406\u7c7b\u522b\u578b\u7279\u5f81\u3002\u5bf9\u4e8e\u6570\u503c\u578b\u7279\u5f81\uff0c\u9700\u8981\u5148\u8fdb\u884c\u79bb\u6563\u5316\u5904\u7406\u3002\n            <\/td>\n            <td>\n                \u5904\u7406\u6570\u503c\u578b\u548c\u7c7b\u522b\u578b\u7279\u5f81\uff0c\u80fd\u81ea\u52a8\u5bfb\u627e\u6700\u4f73\u5206\u5272\u70b9\uff0c\u65e0\u9700\u9884\u5904\u7406\u3002\n            <\/td>\n        <\/tr>\n        <tr>\n            <td>\n                <strong>\u4efb\u52a1\u7c7b\u578b<\/strong>\n            <\/td>\n            <td>\n                \u9002\u7528\u4e8e\u5206\u7c7b\u548c\u56de\u5f52\u4efb\u52a1\u3002\u5728\u5206\u7c7b\u4efb\u52a1\u4e2d\u4f7f\u7528\u57fa\u5c3c\u6307\u6570\uff0c\u5728\u56de\u5f52\u4efb\u52a1\u4e2d\u4f7f\u7528\u5747\u65b9\u8bef\u5dee\u3002\n            <\/td>\n            <td>\n                \u4e3b\u8981\u7528\u4e8e\u5206\u7c7b\u4efb\u52a1\uff0c\u4e0d\u9002\u7528\u4e8e\u56de\u5f52\u95ee\u9898\u3002\n            <\/td>\n            <td>\n                \u4e3b\u8981\u7528\u4e8e\u5206\u7c7b\u4efb\u52a1\uff0c\u4e5f\u53ef\u901a\u8fc7\u4fee\u6539\u5904\u7406\u56de\u5f52\u95ee\u9898\u3002\n            <\/td>\n        <\/tr>\n    <\/tbody>\n<\/table>\n<figcaption>CART\u4e0eID3\u3001C4.5\u7684\u4e3b\u8981\u533a\u522b<\/figcaption>\n<\/figure>\n\n\n<h2 class=\"wp-block-heading\">\u6570\u503c\u578b\u7279\u5f81\u4e0e\u7c7b\u522b\u7279\u5f81<\/h2>\n\n\n<p>\u6570\u503c\u7279\u5f81\u548c\u7c7b\u522b\u7279\u5f81\u662f\u4e24\u79cd\u6700\u5e38\u89c1\u7684\u7279\u5f81\u7c7b\u578b\u3002\u6570\u503c\u7279\u5f81\u662f\u53ef\u4ee5\u7528\u6570\u5b57\u8868\u793a\u5e76\u4e14\u5177\u6709\u8fde\u7eed\u6027\u7684\u7279\u5f81\uff0c\u5982\u5e74\u9f84\u3001\u8eab\u9ad8\u3001\u6536\u5165\u548c\u6e29\u5ea6\u7b49\u3002\u8fd9\u7c7b\u7279\u5f81\u53ef\u4ee5\u8fdb\u884c\u6570\u5b66\u8fd0\u7b97\uff0c\u5982\u52a0\u51cf\u4e58\u9664\uff0c\u5e76\u4e14\u901a\u5e38\u5177\u6709\u987a\u5e8f\u5173\u7cfb\u3002\u6570\u503c\u7279\u5f81\u7684\u8fd9\u4e9b\u7279\u6027\u4f7f\u5f97\u5b83\u4eec\u5728\u8bb8\u591a\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u4e2d\u6613\u4e8e\u5904\u7406\u548c\u89e3\u91ca\u3002\u7c7b\u522b\u7279\u5f81\u662f\u79bb\u6563\u7684\u3001\u4e0d\u5177\u6709\u6570\u503c\u610f\u4e49\u7684\u7279\u5f81\u3002\u5e38\u89c1\u7684\u7c7b\u522b\u7279\u5f81\u5305\u62ec\u6027\u522b\uff08\u5982\u7537\/\u5973\uff09\u3001\u989c\u8272\uff08\u5982\u7ea2\/\u7eff\/\u84dd\uff09\u3001\u804c\u4e1a\uff08\u5982\u6559\u5e08\/\u533b\u751f\/\u5de5\u7a0b\u5e08\uff09\u548c\u57ce\u5e02\uff08\u5982\u5317\u4eac\/\u4e0a\u6d77\/\u5e7f\u5dde\uff09\u7b49\u3002\u8fd9\u4e9b\u7279\u5f81\u901a\u5e38\u4e0d\u80fd\u8fdb\u884c\u6570\u5b66\u8fd0\u7b97\u3002<\/p>\n\n\n<p>\u6709\u5173\u7279\u5f81\u7c7b\u578b\u7684\u8be6\u7ec6\u8bf4\u660e\uff0c\u60a8\u4e5f\u53ef\u4ee5\u67e5\u770b\u6211\u4e4b\u524d\u64b0\u5199\u7684\u4e00\u7bc7\u535a\u5ba2\u6587\u7ae0\uff0c\u5176\u4e2d\u63d0\u4f9b\u4e86\u66f4\u5168\u9762\u7684\u4ecb\u7ecd\u3002   <a href=\"https:\/\/www.xuzhe.tj.cn\/index.php\/2024\/10\/02\/%e7%89%b9%e5%be%81%e6%98%af%e4%bb%80%e4%b9%88\/\">\u300a\u7279\u5f81\u662f\u4ec0\u4e48\u300b<\/a><\/p>\n\n\n<h2 class=\"wp-block-heading\">CART\u2014\u2014\u6570\u503c\u578b\u7279\u5f81\u7684\u5904\u7406\u65b9\u6cd5<\/h2>\n\n\n<p>CART\u7b97\u6cd5\u5904\u7406\u6570\u503c\u578b\u7279\u5f81\u65f6\uff0c\u9009\u62e9\u6700\u4f73<strong>\u5206\u5272\u70b9<\/strong>\u5c06\u6570\u636e\u96c6\u5206\u4e3a\u4e24\u90e8\u5206\u3002CART\u7b97\u6cd5\u53ef\u4ee5\u76f4\u63a5\u5904\u7406\u8fde\u7eed\u578b\u7279\u5f81\uff0c\u65e0\u9700\u9884\u5148\u79bb\u6563\u5316\u3002\u8fd9\u79cd\u65b9\u6cd5\u4fdd\u7559\u4e86\u6570\u503c\u7279\u5f81\u7684\u539f\u59cb\u4fe1\u606f\uff0c\u907f\u514d\u4e86\u79bb\u6563\u5316\u53ef\u80fd\u5bfc\u81f4\u7684\u4fe1\u606f\u635f\u5931\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u4e00\u4e9b\u65e9\u671f\u7684\u51b3\u7b56\u6811\u7b97\u6cd5\uff08\u5982ID3\uff09\u53ea\u80fd\u5904\u7406\u79bb\u6563\u503c\uff0c\u9700\u8981\u4e8b\u5148\u5bf9\u8fde\u7eed\u7279\u5f81\u8fdb\u884c\u79bb\u6563\u5316\u5904\u7406\u3002\u5b83\u901a\u8fc7\u8ba1\u7b97\u4e0d\u540c\u5206\u5272\u70b9\u7684\u57fa\u5c3c\u6307\u6570\uff08\u5206\u7c7b\u4efb\u52a1\uff09\u6216\u5747\u65b9\u8bef\u5dee\uff08\u56de\u5f52\u4efb\u52a1\uff09\uff0c\u627e\u51fa\u80fd\u6700\u5c0f\u5316\u635f\u5931\u51fd\u6570\u7684\u6700\u4f18\u5206\u5272\u70b9\u3002CART\u7b97\u6cd5\u5728\u5904\u7406\u6570\u503c\u578b\u7279\u5f81\u65f6\uff0c\u4f1a\u8003\u8651\u6570\u503c\u578b\u7279\u5f81\u7684\u5927\u5c0f\u5173\u7cfb\u548c\u8fde\u7eed\u6027\u7279\u70b9\uff0c\u4e3b\u8981\u4f53\u73b0\u5728\u4ee5\u4e0b\u51e0\u4e2a\u65b9\u9762\uff1a<\/p>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u6709\u5e8f\u6027\u8003\u8651<\/strong>\uff1aCART\u7b97\u6cd5\u4f1a\u5bf9\u6570\u503c\u578b\u7279\u5f81\u7684\u6240\u6709\u53d6\u503c\u8fdb\u884c\u6392\u5e8f\uff0c\u8fd9\u4e00\u6b65\u9aa4\u5145\u5206\u5229\u7528\u4e86\u6570\u503c\u578b\u7279\u5f81\u7684\u6709\u5e8f\u6027\u8d28\u3002\u6392\u5e8f\u540e\uff0c\u7b97\u6cd5\u53ea\u9700\u8003\u8651\u76f8\u90bb\u503c\u4e4b\u95f4\u7684\u4e2d\u70b9\u4f5c\u4e3a\u5019\u9009\u5206\u5272\u70b9\uff0c\u800c\u4e0d\u662f\u968f\u673a\u9009\u62e9\u5206\u5272\u70b9\u3002<\/li>\n    <li><strong>\u8fde\u7eed\u6027\u5904\u7406<\/strong>\uff1a\u901a\u8fc7\u9009\u62e9\u76f8\u90bb\u503c\u7684\u4e2d\u70b9\u4f5c\u4e3a\u5019\u9009\u5206\u5272\u70b9\uff0cCART\u7b97\u6cd5\u80fd\u591f\u66f4\u597d\u5730\u6355\u6349\u6570\u503c\u578b\u7279\u5f81\u7684\u8fde\u7eed\u6027\u3002\u8fd9\u79cd\u65b9\u6cd5\u53ef\u4ee5\u5728\u4fdd\u6301\u6570\u636e\u8fde\u7eed\u6027\u7684\u540c\u65f6\uff0c\u627e\u5230\u6700\u4f18\u7684\u5206\u5272\u70b9\u3002<\/li>\n    <li><strong>\u4e8c\u5206\u6cd5\u5206\u5272<\/strong>\uff1a\u5bf9\u4e8e\u6570\u503c\u578b\u7279\u5f81\uff0cCART\u7b97\u6cd5\u91c7\u7528\u4e8c\u5206\u6cd5\u8fdb\u884c\u5206\u5272\uff0c\u5373\u5c06\u6570\u636e\u5206\u4e3a&#8221;\u5c0f\u4e8e\u7b49\u4e8e&#8221;\u548c&#8221;\u5927\u4e8e&#8221;\u4e24\u90e8\u5206\u3002\u8fd9\u79cd\u65b9\u6cd5\u65e2\u4fdd\u6301\u4e86\u6570\u503c\u7684\u987a\u5e8f\u5173\u7cfb\uff0c\u53c8\u80fd\u591f\u6709\u6548\u5730\u533a\u5206\u4e0d\u540c\u7684\u6570\u503c\u8303\u56f4\u3002<br><\/li>\n<\/ol>\n\n\n<h3 class=\"wp-block-heading\">\u5177\u4f53\u6b65\u9aa4<\/h3>\n\n\n<ol class=\"wp-block-list\">\n    <li><strong>\u5bfb\u627e\u5206\u5272\u70b9<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n<p>\u5bf9\u4e8e\u6570\u503c\u578b\u7279\u5f81\uff0c\u5047\u8bbe\u7279\u5f81 \\(X\\)  \u7684\u53d6\u503c\u4e3a \\({x_1, x_2, &#8230;, x_n}\\)\uff0c\u5219CART\u4f1a\u5c06\u8fd9\u4e9b\u53d6\u503c\u8fdb\u884c\u6392\u5e8f\uff0c\u5e76\u5c1d\u8bd5\u5c06\u6bcf\u4e2a\u503c\u4f5c\u4e3a\u5019\u9009\u5206\u5272\u70b9\u3002\u5019\u9009\u5206\u5272\u70b9\u7684\u6570\u91cf\u901a\u5e38\u4e3a  \\(n-1\\)\uff0c\u5373\u6bcf\u4e2a\u76f8\u90bb\u503c\u7684\u4e2d\u70b9\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"2\">\n    <li><strong>\u8ba1\u7b97\u5206\u5272\u70b9\u7684\u57fa\u5c3c\u6307\u6570\uff08\u5206\u7c7b\u4efb\u52a1\uff09\u6216\u5747\u65b9\u8bef\u5dee\uff08\u56de\u5f52\u4efb\u52a1\uff09<\/strong>\uff1a<br><ul>\n            <li><strong>\u5206\u7c7b\u4efb\u52a1<\/strong>\uff1aCART\u4f1a\u8ba1\u7b97\u6bcf\u4e2a\u5206\u5272\u70b9\u5728\u5f53\u524d\u8282\u70b9\u4e0a\u7684\u57fa\u5c3c\u6307\u6570\uff08Gini Index\uff09\u3002\u57fa\u5c3c\u6307\u6570\u7684\u8ba1\u7b97\u65b9\u5f0f\u5982\u4e0b\uff1a<\/li>\n        <\/ul>\n\n        \n        <p class=\"has-text-align-center\">\\(\\displaystyle Gini(D) = 1 &#8211; \\sum_{i=1}^{k} p_i^2\\)<\/p>\n        \n        \u5176\u4e2d\uff0c \\(D\\)  \u662f\u6570\u636e\u96c6\uff0c \\(p_i\\)  \u662f\u7b2c \\(i\\) \u7c7b\u7684\u6837\u672c\u5360\u6bd4\uff0c \\(k\\)  \u662f\u7c7b\u522b\u6570\u3002\u57fa\u5c3c\u6307\u6570\u8d8a\u5c0f\uff0c\u8868\u793a\u8282\u70b9\u4e2d\u7684\u6837\u672c\u8d8a\u7eaf\uff08\u5373\u8282\u70b9\u4e2d\u6837\u672c\u7684\u7c7b\u522b\u8d8a\u4e00\u81f4\uff09\u3002<br><ul>\n            <li><strong>\u56de\u5f52\u4efb\u52a1<\/strong>\uff1aCART\u4f1a\u8ba1\u7b97\u6bcf\u4e2a\u5206\u5272\u70b9\u7684\u5747\u65b9\u8bef\u5dee\uff08MSE\uff09\uff0c\u5373\uff1a<\/li>\n        <\/ul>\n\n        \n        <p class=\"has-text-align-center\">\\(\\displaystyle MSE = \\frac{1}{N} \\sum_{i=1}^{N} (y_i &#8211; \\bar{y})^2\\)<\/p>\n        \n        \u5176\u4e2d\uff0c \\(N\\) \u662f\u6837\u672c\u6570\uff0c \\(y_i\\)  \u662f\u7b2c  \\(i\\) \u4e2a\u6837\u672c\u7684\u771f\u5b9e\u503c\uff0c \\(\\bar{y}\\)  \u662f\u6240\u6709\u6837\u672c\u7684\u5747\u503c\u3002MSE\u8d8a\u5c0f\uff0c\u8868\u793a\u5206\u5272\u540e\u7684\u5b50\u8282\u70b9\u4e2d\u7684\u6837\u672c\u503c\u8d8a\u63a5\u8fd1\u5e73\u5747\u503c\uff0c\u6ce2\u52a8\u6027\u8d8a\u5c0f\u3002<\/li>\n    <li><strong>\u9009\u62e9\u6700\u4f18\u5206\u5272\u70b9<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n<p>\u901a\u8fc7\u8ba1\u7b97\u6bcf\u4e2a\u5019\u9009\u5206\u5272\u70b9\u7684\u57fa\u5c3c\u6307\u6570\u6216\u5747\u65b9\u8bef\u5dee\uff0cCART\u4f1a\u9009\u62e9\u80fd\u591f\u6700\u5c0f\u5316\u57fa\u5c3c\u6307\u6570\uff08\u5206\u7c7b\u4efb\u52a1\uff09\u6216\u5747\u65b9\u8bef\u5dee\uff08\u56de\u5f52\u4efb\u52a1\uff09\u7684\u90a3\u4e2a\u5206\u5272\u70b9\u4f5c\u4e3a\u5f53\u524d\u8282\u70b9\u7684\u6700\u4f18\u5206\u5272\u70b9\u3002\u8fd9\u6837\uff0c\u6570\u503c\u578b\u7279\u5f81\u7684\u5904\u7406\u7ed3\u679c\u901a\u5e38\u662f\u7c7b\u4f3c\u4e8e\u201c\u7279\u5f81\u503c\u5c0f\u4e8e\u67d0\u4e2a\u9608\u503c\u65f6\u5411\u5de6\u5206\u652f\uff0c\u5927\u4e8e\u8be5\u9608\u503c\u65f6\u5411\u53f3\u5206\u652f\u201d\u8fd9\u6837\u7684\u5206\u5272\u89c4\u5219\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li><strong>\u751f\u6210\u5206\u652f<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n<p>\u4f7f\u7528\u6700\u4f18\u5206\u5272\u70b9\uff0c\u5c06\u5f53\u524d\u8282\u70b9\u7684\u6570\u636e\u96c6\u5206\u5272\u4e3a\u4e24\u4e2a\u5b50\u96c6\uff0c\u5e76\u7ee7\u7eed\u5bf9\u6bcf\u4e2a\u5b50\u96c6\u91cd\u590d\u4e0a\u8ff0\u8fc7\u7a0b\uff0c\u76f4\u5230\u8fbe\u5230\u505c\u6b62\u6761\u4ef6\uff08\u5982\u8282\u70b9\u7eaf\u5ea6\u8db3\u591f\u9ad8\u6216\u8282\u70b9\u6837\u672c\u6570\u4f4e\u4e8e\u67d0\u4e2a\u9608\u503c\uff09\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u793a\u4f8b<\/h3>\n\n\n<p>\u5047\u8bbe\u6709\u4e00\u4e2a\u6570\u503c\u578b\u7279\u5f81\u201c\u5e74\u9f84\u201d\uff0c\u53d6\u503c\u4e3a[25, 32, 37, 45, 50, 55]\u3002CART\u7b97\u6cd5\u4f1a\u5c1d\u8bd5\u4ee5\u4e0b\u5206\u5272\u70b9\uff1a28.5\u300134.5\u300141\u300147.5\u300152.5\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u5206\u5272\u70b9\uff0c\u7b97\u6cd5\u8ba1\u7b97\u5176\u57fa\u5c3c\u6307\u6570\u6216\u5747\u65b9\u8bef\u5dee\uff0c\u5e76\u9009\u62e9\u6700\u4f18\u7684\u5206\u5272\u70b9\u8fdb\u884c\u5206\u5272\uff0c\u4f8b\u5982\u201c\u5e74\u9f84 &lt; 47.5 \u5411\u5de6\uff0c\u5e74\u9f84 \u2265 47.5 \u5411\u53f3\u201d\u3002<\/p>\n\n\n<h2 class=\"wp-block-heading\">CART\u2014\u2014\u7c7b\u522b\u578b\u7279\u5f81\u7684\u5904\u7406\u65b9\u6cd5<\/h2>\n\n\n<p>CART\u7b97\u6cd5\u5bf9\u5206\u7c7b\u578b\u7279\u5f81\u7684\u5904\u7406\u7b56\u7565\u4e0e\u6570\u503c\u578b\u4e0d\u540c\uff0c\u8fd9\u662f\u56e0\u4e3a\u7c7b\u522b\u7279\u5f81\u7684\u79bb\u6563\u6027\u548c\u4e0d\u53ef\u6392\u5e8f\u6027\u3002CART\u7b97\u6cd5\u4f1a\u7cfb\u7edf\u5730\u8bc4\u4f30\u7c7b\u522b\u578b\u7279\u5f81\u7684\u5404\u79cd\u53d6\u503c\u7ec4\u5408\uff0c\u5f62\u6210\u4e0d\u540c\u7684\u5206\u7ec4\u65b9\u6848\u3002\u5bf9\u6bcf\u4e2a\u6f5c\u5728\u5206\u7ec4\uff0cCART\u8ba1\u7b97\u76f8\u5e94\u7684\u57fa\u5c3c\u6307\u6570\uff08\u5206\u7c7b\u4efb\u52a1\uff09\u6216\u5747\u65b9\u8bef\u5dee\uff08\u56de\u5f52\u4efb\u52a1\uff09\u3002\u901a\u8fc7\u8fd9\u79cd\u5168\u9762\u8bc4\u4f30\uff0c\u7b97\u6cd5\u80fd\u8bc6\u522b\u51fa\u6700\u4f73\u5206\u7ec4\u65b9\u5f0f\u2014\u2014\u5373\u6700\u5927\u7a0b\u5ea6\u51cf\u5c11\u4e0d\u7eaf\u5ea6\u6216\u8bef\u5dee\u7684\u65b9\u6848\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u4ec5\u9ad8\u6548\u5904\u7406\u9ad8\u7ef4\u5ea6\u7c7b\u522b\u7279\u5f81\uff0c\u8fd8\u80fd\u6355\u6349\u7c7b\u522b\u95f4\u7684\u590d\u6742\u5173\u7cfb\uff0c\u4ece\u800c\u63d0\u5347\u6a21\u578b\u7684\u9884\u6d4b\u51c6\u786e\u6027\u548c\u6cdb\u5316\u80fd\u529b\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u5177\u4f53\u6b65\u9aa4<\/h3>\n\n\n<ol class=\"wp-block-list\">\n    <li>\u7c7b\u522b\u7684\u4e8c\u5206\u5212\u5206\uff1a<\/li>\n    <li>\u5047\u8bbe\u7c7b\u522b\u578b\u7279\u5f81 \\(X\\) \u6709  \\(k\\) \u4e2a\u53d6\u503c \\(\\{A, B, C, \\ldots, K\\}\\) \uff0cCART\u4f1a\u5c1d\u8bd5\u5c06\u8fd9\u4e9b\u53d6\u503c\u8fdb\u884c\u4e8c\u5206\u7ec4\u5408\u3002\u4f8b\u5982\uff0c\u5982\u679c  \\(k = 3\\) \uff0c\u5373  \\(X\\) \u7684\u53d6\u503c\u4e3a  \\(\\{A, B, C\\}\\) \uff0c\u90a3\u4e48CART\u4f1a\u5c1d\u8bd5\u4ee5\u4e0b\u51e0\u79cd\u5206\u7ec4\u65b9\u5f0f\uff1a\\(\\{A\\}\\)  \u548c  \\(\\{B, C\\}\\) \uff1b \\(\\{B\\}\\)  \u548c  \\(\\{A, C\\}\\) \uff1b\\(\\{C\\}\\)  \u548c  \\(\\{A, B\\}\\) \u3002<br>\u5f53  \\(k\\)  \u8f83\u5927\u65f6\uff0c\u53ef\u80fd\u4f1a\u4ea7\u751f\u591a\u79cd\u5206\u7ec4\u65b9\u5f0f\uff0c\u56e0\u6b64CART\u901a\u5e38\u4ec5\u5c1d\u8bd5\u4e8c\u5206\u7b56\u7565\uff0c\u4ee5\u964d\u4f4e\u8ba1\u7b97\u590d\u6742\u5ea6\u3002<br><\/li>\n    <li>\u8ba1\u7b97\u6bcf\u79cd\u7ec4\u5408\u7684\u57fa\u5c3c\u6307\u6570\uff08\u5206\u7c7b\u4efb\u52a1\uff09\u6216\u5747\u65b9\u8bef\u5dee\uff08\u56de\u5f52\u4efb\u52a1\uff09\uff1a<\/li>\n<\/ol>\n\n\n<p>CART\u4f1a\u8ba1\u7b97\u6bcf\u79cd\u7ec4\u5408\u65b9\u5f0f\u4e0b\u7684\u57fa\u5c3c\u6307\u6570\uff08\u5bf9\u4e8e\u5206\u7c7b\u4efb\u52a1\uff09\u6216\u5747\u65b9\u8bef\u5dee\uff08\u5bf9\u4e8e\u56de\u5f52\u4efb\u52a1\uff09\uff0c\u4ee5\u8bc4\u4f30\u8be5\u5206\u7ec4\u65b9\u5f0f\u662f\u5426\u80fd\u591f\u4f7f\u5f97\u5b50\u8282\u70b9\u4e2d\u7684\u6837\u672c\u66f4\u52a0\u7eaf\u51c0\uff08\u5373\u540c\u4e00\u8282\u70b9\u4e2d\u6837\u672c\u7684\u7c7b\u522b\u66f4\u52a0\u4e00\u81f4\uff09\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"3\">\n    <li><strong>\u9009\u62e9\u6700\u4f18\u5206\u7ec4\u65b9\u5f0f<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n<p>\u5728\u6240\u6709\u5019\u9009\u5206\u7ec4\u65b9\u5f0f\u4e2d\uff0c\u9009\u62e9\u80fd\u591f\u6700\u5c0f\u5316\u57fa\u5c3c\u6307\u6570\u6216\u5747\u65b9\u8bef\u5dee\u7684\u5206\u7ec4\u65b9\u5f0f\u3002\u8fd9\u6837\uff0c\u5206\u7c7b\u578b\u7279\u5f81\u7684\u5904\u7406\u7ed3\u679c\u901a\u5e38\u662f\u7c7b\u4f3c\u4e8e\u201c\u7c7b\u522b\u5728 {A, B} \u4e2d\u7684\u6837\u672c\u5411\u5de6\u5206\u652f\uff0c\u5176\u4ed6\u7c7b\u522b\u7684\u6837\u672c\u5411\u53f3\u5206\u652f\u201d\u8fd9\u6837\u7684\u5206\u5272\u89c4\u5219\u3002<\/p>\n\n\n<ol class=\"wp-block-list\" start=\"4\">\n    <li><strong>\u751f\u6210\u5206\u652f<\/strong>\uff1a<\/li>\n<\/ol>\n\n\n<p>\u4f7f\u7528\u6700\u4f18\u5206\u7ec4\u65b9\u5f0f\uff0c\u5c06\u5f53\u524d\u8282\u70b9\u7684\u6570\u636e\u96c6\u5206\u5272\u4e3a\u4e24\u4e2a\u5b50\u96c6\uff0c\u5e76\u7ee7\u7eed\u5bf9\u6bcf\u4e2a\u5b50\u96c6\u91cd\u590d\u4e0a\u8ff0\u8fc7\u7a0b\uff0c\u76f4\u5230\u8fbe\u5230\u505c\u6b62\u6761\u4ef6\u3002<\/p>\n\n\n<h3 class=\"wp-block-heading\">\u793a\u4f8b<\/h3>\n\n\n<p>\u5047\u8bbe\u6709\u4e00\u4e2a\u7c7b\u522b\u578b\u7279\u5f81\u201c\u804c\u4e1a\u201d\uff0c\u53d6\u503c\u4e3a\u201c\u6559\u5e08\u201d\u3001\u201c\u533b\u751f\u201d\u3001\u201c\u5de5\u7a0b\u5e08\u201d\u3002CART\u4f1a\u5c1d\u8bd5\u4ee5\u4e0b\u51e0\u79cd\u5206\u5272\u65b9\u5f0f\uff1a<\/p>\n\n\n<ul class=\"wp-block-list\">\n    <li>\u201c\u6559\u5e08\u201d\u4e0e\u201c\u533b\u751f\u6216\u5de5\u7a0b\u5e08\u201d\u4f5c\u4e3a\u4e24\u4e2a\u5206\u652f\u3002<\/li>\n    <li>\u201c\u533b\u751f\u201d\u4e0e\u201c\u6559\u5e08\u6216\u5de5\u7a0b\u5e08\u201d\u4f5c\u4e3a\u4e24\u4e2a\u5206\u652f\u3002<\/li>\n    <li>\u201c\u5de5\u7a0b\u5e08\u201d\u4e0e\u201c\u6559\u5e08\u6216\u533b\u751f\u201d\u4f5c\u4e3a\u4e24\u4e2a\u5206\u652f\u3002<br><\/li>\n<\/ul>\n\n\n<p>CART\u4f1a\u8ba1\u7b97\u8fd9\u4e9b\u5206\u5272\u65b9\u5f0f\u7684\u57fa\u5c3c\u6307\u6570\uff0c\u5e76\u9009\u62e9\u6700\u4f18\u7684\u5206\u5272\u65b9\u5f0f\u8fdb\u884c\u5206\u652f\uff0c\u4f8b\u5982\u201c\u6559\u5e08\u201d\u4f5c\u4e3a\u4e00\u4e2a\u5206\u652f\uff0c\u5176\u4ed6\u804c\u4e1a\u4f5c\u4e3a\u53e6\u4e00\u4e2a\u5206\u652f\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CART\u7b97\u6cd5 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