{"id":3058,"date":"2025-08-09T09:02:02","date_gmt":"2025-08-09T01:02:02","guid":{"rendered":"https:\/\/www.leexinghai.com\/aic\/?p=3058"},"modified":"2025-08-17T10:40:25","modified_gmt":"2025-08-17T02:40:25","slug":"2-3%e8%af%be%e5%90%8e%e6%80%9d%e8%80%83-%e6%94%af%e6%8c%81%e5%90%91%e9%87%8f%e6%9c%ba%e7%9a%84%e9%99%90%e5%88%b6%e6%9d%a1%e4%bb%b6","status":"publish","type":"post","link":"https:\/\/www.leexinghai.com\/aic\/2-3%e8%af%be%e5%90%8e%e6%80%9d%e8%80%83-%e6%94%af%e6%8c%81%e5%90%91%e9%87%8f%e6%9c%ba%e7%9a%84%e9%99%90%e5%88%b6%e6%9d%a1%e4%bb%b6\/","title":{"rendered":"2.3\u8bfe\u540e\u601d\u8003-\u652f\u6301\u5411\u91cf\u673a\u7684\u9650\u5236\u6761\u4ef6"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u95ee\u9898\uff1a\u652f\u6301\u5411\u91cf\u673a\u7684\u9650\u5236\u6761\u4ef6\u5982\u679c\u4ece\u22651\u53d8\u6210\u22652\uff0c\u5219\uff08\u03c9,b\uff09\u4f1a\u53d8\u6210\uff08a\u03c9,ab\uff09\u3002\u5982\u679cX<sub>i<\/sub>\u548c\u03c9\u662fM\u7ef4\u5411\u91cf\uff0ca\u4e3a\u591a\u5c11\uff1f<\/h2>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udfe8\u4e00\u3001\u539f\u59cb\u95ee\u9898\u56de\u987e\uff08\u6807\u51c6 Hard-Margin SVM\uff09<\/h2>\n\n\n\n<p>\u6211\u4eec\u60f3\u6c42\u89e3\u8fd9\u4e2a\u6700\u4f18\u5316\u95ee\u9898\uff1a<\/p>\n\n\n\n<p><strong>\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570\uff1a<\/strong><\/p>\n\n\n\n<p>min(\u03c9,b) 1\/2 ||\u03c9||<sup>2<\/sup><\/p>\n\n\n\n<p><strong>\u5728\u6ee1\u8db3\u7ea6\u675f\uff1a<\/strong><\/p>\n\n\n\n<p>y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u22651,\u2200i<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udfe6 \u4e8c\u3001\u73b0\u5728\u6211\u4eec\u628a\u7ea6\u675f\u6539\u6210 \u22652\uff0c\u4f1a\u53d1\u751f\u4ec0\u4e48\uff1f<\/h2>\n\n\n\n<p>\u73b0\u5728\u53d8\u6210\u4e86\uff1a y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u22652<\/p>\n\n\n\n<p>\u4f46\u6ce8\u610f\uff01\u8fd9\u4e2a\u65f6\u5019\u6211\u4eec<strong>\u5e76\u6ca1\u6709\u6539\u53d8\u6570\u636e\u7684\u5206\u5e03<\/strong>\uff0c\u6211\u4eec\u53ea\u662f<strong>\u4eba\u4e3a\u5730\u628a\u95f4\u9694\u8981\u6c42\u63d0\u9ad8\u4e86<\/strong>\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udfe8 \u4e09\u3001\u7f29\u653e\u4e0d\u53d8\u6027\uff08SVM \u4e2d\u7684\u5173\u952e\u6027\u8d28\uff09<\/h2>\n\n\n\n<p>\u652f\u6301\u5411\u91cf\u673a\u7684\u7ed3\u679c<strong>\u5bf9 \u03c9 \u548c b \u7684\u7f29\u653e\u662f\u4e0d\u53d8\u7684<\/strong>\u3002\u4e5f\u5c31\u662f\u8bf4\uff1a<\/p>\n\n\n\n<p>\u5982\u679c\u4e00\u7ec4 (\u03c9,b) \u6ee1\u8db3\u7ea6\u675f\uff1a y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u22651<\/p>\n\n\n\n<p>\u90a3\u4e48\u5bf9\u4e8e\u4efb\u610f\u6b63\u6570 a > 0\uff0c(a\u03c9,ab) \u4f1a\u6ee1\u8db3\uff1a y<sub>i<\/sub>((a\u03c9)<sup>T<\/sup>X<sub>i<\/sub>+ab)=a\u22c5y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u2265a<\/p>\n\n\n\n<p>\u6240\u4ee5\u5982\u679c\u6211\u4eec\u8981\u6c42\u7ea6\u675f\u662f\uff1a y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u22652<\/p>\n\n\n\n<p>\u5c31\u53ef\u4ee5\u4ece\u539f\u6765\u7684\u89e3  (\u03c9,b) \u4e58\u4ee5 a = 2 \u5f97\u5230\u4e00\u4e2a\u65b0\u89e3\uff1a (\u03c9\u2032,b\u2032)=(2\u03c9,2b)<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u2705 \u56db\u3001\u7ed3\u8bba\uff1aa = 2<\/h2>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u5f53\u652f\u6301\u5411\u91cf\u673a\u7684\u95f4\u9694\u7ea6\u675f\u4ece \u22651 \u53d8\u4e3a \u22652 \u65f6\uff0c\u6700\u4f18\u89e3 (\u03c9,b) \u4f1a\u53d8\u6210\uff1a(\u03c9\u2032,b\u2032)=(2\u03c9,2b)<\/p>\n<\/blockquote>\n\n\n\n<p>\u5373\uff1a<br><strong>\u7f29\u653e\u56e0\u5b50 a = 2<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83e\udde0 \u8865\u5145\u8bf4\u660e\uff08\u66f4\u901a\u7528\u7406\u89e3\uff09<\/h2>\n\n\n\n<p>\u5176\u5b9e\u6211\u4eec\u53ef\u4ee5\u8bf4\uff1a<br>\u5f53\u4f60\u628a\u539f\u6765\u7684\u7ea6\u675f y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u2265C \u4ece C \u6539\u4e3a\u4efb\u610f\u6b63\u6570 k\uff0c\u90a3\u4e48\u89e3\u4f1a\u53d8\u4e3a\uff1a (\u03c9\u2032,b\u2032)=(k\u03c9,kb)<\/p>\n\n\n\n<p>\u6240\u4ee5\u4f60\u53ef\u4ee5\u901a\u7528\u8bb0\u5fc6\u4e3a\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u82e5\u7ea6\u675f\u4ece \u22651 \u53d8\u4e3a \u2265k\uff0c\u5219\u89e3 (\u03c9,b) 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