{"id":3061,"date":"2025-08-09T09:21:43","date_gmt":"2025-08-09T01:21:43","guid":{"rendered":"https:\/\/www.leexinghai.com\/aic\/?p=3061"},"modified":"2025-08-17T10:40:35","modified_gmt":"2025-08-17T02:40:35","slug":"2-4%e8%af%be%e5%90%8e%e6%80%9d%e8%80%83-%e7%ba%bf%e6%80%a7%e4%b8%8d%e5%8f%af%e5%88%86%e5%88%b0%e7%ba%bf%e6%80%a7%e5%8f%af%e5%88%86%e7%9a%84%e8%bd%ac%e5%8c%96","status":"publish","type":"post","link":"https:\/\/www.leexinghai.com\/aic\/2-4%e8%af%be%e5%90%8e%e6%80%9d%e8%80%83-%e7%ba%bf%e6%80%a7%e4%b8%8d%e5%8f%af%e5%88%86%e5%88%b0%e7%ba%bf%e6%80%a7%e5%8f%af%e5%88%86%e7%9a%84%e8%bd%ac%e5%8c%96\/","title":{"rendered":"2.4\u8bfe\u540e\u601d\u8003-\u7ebf\u6027\u4e0d\u53ef\u5206\u5230\u7ebf\u6027\u53ef\u5206\u7684\u8f6c\u5316"},"content":{"rendered":"\n<h2 class=\"wp-block-heading\">\u95ee\u9898\uff1a\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u8fd9\u662f\u4e00\u4e2a\u7ebf\u6027\u4e0d\u53ef\u5206\u7684\u60c5\u51b5\u3002\u56e0\u4e3ax\u628ao\u7ed9\u5305\u56f4\u8d77\u6765\u4e86\u3002\u6211\u4eec\u627e\u4e0d\u5230\u4e00\u6761\u5408\u9002\u7684\u76f4\u7ebf\u5c06x\u548co\u5b8c\u5168\u5206\u5f00\u3002\u90a3\u4e48\u6211\u4eec\u9700\u8981\u600e\u4e48\u505a\u624d\u53ef\u4ee5\u5c06\u8fd9\u4e2a\u7ebf\u6027\u4e0d\u53ef\u5206\u7684\u60c5\u51b5\u53d8\u6210\u7ebf\u6027\u53ef\u5206\u7684\u60c5\u51b5\u5462\uff1f<\/h2>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"935\" height=\"495\" src=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-4.png\" alt=\"\" class=\"wp-image-3062\" srcset=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-4.png 935w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-4-300x159.png 300w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-4-768x407.png 768w\" sizes=\"auto, (max-width: 935px) 100vw, 935px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 \u629b\u51fa\u95ee\u9898\uff1aSVM \u8be5\u600e\u4e48\u529e\uff1f<\/h3>\n\n\n\n<p>\u652f\u6301\u5411\u91cf\u673a\uff08SVM\uff09\u9ed8\u8ba4\u627e\u4e00\u6761<strong>\u7ebf\u6027\u5206\u9694\u8d85\u5e73\u9762<\/strong>\u3002\u4f46\u8fd9\u4e2a\u56fe\u4e2d\u660e\u663e\u505a\u4e0d\u5230\u3002\u600e\u4e48\u529e\u5462\uff1f<\/p>\n\n\n\n<p>\u6211\u4eec\u6709\u4e24\u4e2a\u89e3\u51b3\u65b9\u5411\uff1a<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">1\ufe0f\u20e3 \u4f7f\u7528 <strong>\u6838\u51fd\u6570 SVM\uff08Kernel SVM\uff09<\/strong><\/h4>\n\n\n\n<p>\u5c06\u539f\u59cb\u7684\u4e8c\u7ef4\u6570\u636e\uff08X<sub>1<\/sub>,X<sub>2<\/sub>\uff09\u6620\u5c04\u5230<strong>\u9ad8\u7ef4\u7a7a\u95f4<\/strong>\uff0c\u6bd4\u5982\uff1a<\/p>\n\n\n\n<p class=\"has-text-align-center\"> \u03d5(X<sub>1<\/sub>,X<sub>2<\/sub>)=(X<sub>1<\/sub>,X<sub>2<\/sub>,X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup>)<\/p>\n\n\n\n<p>\u5728\u65b0\u7a7a\u95f4\u4e2d\uff0c\u8ddd\u79bb\u539f\u70b9\u8fd1\u7684\u70b9\uff08O\uff09\u548c\u8fdc\u7684\u70b9\uff08X\uff09\u53ef\u4ee5\u7528\u4e00\u4e2a\u5e73\u9762\u5206\u5f00\u3002\u8fd9\u4e2a\u65b9\u6cd5\u5c31\u53ef\u4ee5\u5904\u7406\u8fd9\u7c7b\u201c\u5706\u73af\u7ed3\u6784\u201d\u7684\u6570\u636e\u3002<\/p>\n\n\n\n<p><strong>\u6548\u679c\u56fe\u50cf\uff1a<\/strong> \u53d8\u6362\u540e\u53ef\u4ee5\u5728\u9ad8\u7ef4\u4e2d\u753b\u4e00\u4e2a\u5e73\u9762\uff0c\u7b49\u4ef7\u4e8e\u5728\u539f\u59cb\u4e8c\u7ef4\u5e73\u9762\u4e2d\u753b\u4e00\u4e2a\u201c\u5706\u5f62\u51b3\u7b56\u8fb9\u754c\u201d\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\">2\ufe0f\u20e3 \u6216\u8005\u4f7f\u7528 <strong>RBF \u6838\uff08\u5f84\u5411\u57fa\u6838\uff09<\/strong><\/h4>\n\n\n\n<p class=\"has-text-align-center\">K(X,X\u2032)=exp(\u2212\u03b3||X\u2212X\u2032||<sup>2<\/sup>)<\/p>\n\n\n\n<p>RBF \u6838\u53ef\u4ee5\u9690\u5f0f\u5730\u628a\u6570\u636e\u6620\u5c04\u5230<strong>\u65e0\u9650\u7ef4\u7a7a\u95f4<\/strong>\uff0c\u4ece\u800c\u5b9e\u73b0\u975e\u7ebf\u6027\u5206\u5272\uff0c\u8fd9\u7c7b\u201c\u5185\u5916\u5305\u56f4\u7ed3\u6784\u201d\u5bf9 RBF \u6838\u975e\u5e38\u53cb\u597d\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83d\udfe6 \u4e8c\u3001\u60f3\u6cd5\uff1a\u53d8\u6362\u7a7a\u95f4\uff01<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p><strong>\u6838\u5fc3\u601d\u60f3\uff1a\u5728\u5f53\u524d\u7a7a\u95f4\u5206\u4e0d\u5f00\uff0c\u90a3\u6211\u4eec\u5c31\u628a\u5b83\u201c\u53d8\u5f62\u201d\u4e00\u4e0b\uff0c\u5728\u4e00\u4e2a\u65b0\u7684\u7a7a\u95f4\u4e2d\u8bd5\u8bd5\u770b\uff01<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>\u8fd9\u5c31\u5f15\u51fa\u4e86\u4e24\u4e2a\u5927\u62db\uff1a<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 \u65b9\u6cd51\uff1a\u624b\u52a8\u8bbe\u8ba1\u201c\u7279\u5f81\u6620\u5c04\u201d \u03c6(x)<\/h3>\n\n\n\n<p>\u6211\u4eec\u5148\u4e3e\u4e2a\u7ecf\u5178\u4f8b\u5b50\u3002<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">\u5047\u8bbe\u4f60\u7684\u8f93\u5165\u662f\u4e8c\u7ef4\u7684 (X<sub>1<\/sub>, X<sub>2<\/sub>)<\/h4>\n\n\n\n<p>\u53ef\u4ee5\u8bbe\u8ba1\u4e00\u4e2a\u65b0\u7684\u7b2c\u4e09\u4e2a\u7ef4\u5ea6\uff1a z=X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup><\/p>\n\n\n\n<p>\u8fd9\u6837\u6211\u4eec\u5c31\u628a\u6bcf\u4e2a\u70b9 \uff08X<sub>1<\/sub>,X<sub>2<\/sub>\uff09 \u6620\u5c04\u5230\u4e86\u4e09\u7ef4\u7a7a\u95f4\uff1a\u03d5(X<sub>1<\/sub>,X<sub>2<\/sub>)=(X<sub>1<\/sub>,X<sub>2<\/sub>,X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup>)<\/p>\n\n\n\n<p>\u5728\u8fd9\u4e2a\u65b0\u7a7a\u95f4\u91cc\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6240\u6709\u7ea2\u5708\u201cO\u201d\u70b9\u7684 X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup> \u6bd4\u8f83\u5c0f\uff08\u9760\u8fd1\u539f\u70b9\uff09<\/li>\n\n\n\n<li>\u6240\u6709\u84dd\u53c9\u201cX\u201d\u70b9\u7684 X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup>\u6bd4\u8f83\u5927\uff08\u79bb\u5f97\u8fdc\uff09<\/li>\n<\/ul>\n\n\n\n<p>\u73b0\u5728\uff0c<strong>\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u4e2a\u201c\u5e73\u9762\u201d\u6765\u5206\u5f00\u8fd9\u4e24\u7c7b\u70b9<\/strong>\uff01<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u2705 \u5728\u4e09\u7ef4\u7a7a\u95f4\u91cc\u53ef\u5206 \u21d2 \u5c31\u76f8\u5f53\u4e8e\u6211\u4eec\u201c\u975e\u7ebf\u6027\u5730\u201d\u628a\u6570\u636e\u5728\u4e8c\u7ef4\u91cc\u5206\u5f00\u4e86\u3002<\/p>\n<\/blockquote>\n\n\n\n<p>\u4e5f\u53ef\u4ee5\u653e\u677e\u9650\u5236\u6761\u4ef6--\u300b\u5bf9\u6bcf\u4e2a\u8bad\u7ec3\u6837\u672c\u548c\u6807\u7b7e\uff08X<sub>i<\/sub>+X<sub>i<\/sub>\uff09\u8bbe\u7f6e\u677e\u5f1b\u53d8\u91cf\u03b4<sub>i<\/sub>,\u5373\u6709y<sub>i<\/sub>(\u03c9<sup>T<\/sup>X<sub>i<\/sub>+b)\u22651-\u03b4<sub>i<\/sub>,\u2200i<\/p>\n\n\n\n<p>\u8bbe\u7f6e\u65b0\u7684\u7ea6\u675f\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"296\" src=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-12-1024x296.png\" alt=\"\" class=\"wp-image-3080\" srcset=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-12-1024x296.png 1024w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-12-300x87.png 300w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-12-768x222.png 768w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-12-1536x444.png 1536w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-12.png 1637w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p> <\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\u2705 \u65b9\u6cd52\uff1a\u7528\u6838\u51fd\u6570\uff08Kernel Trick\uff09<\/h3>\n\n\n\n<p>\u6838\u51fd\u6570\u7684\u672c\u8d28\u5c31\u662f\uff1a<\/p>\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\">\n<p>\u7528\u4e00\u79cd\u6570\u5b66\u65b9\u5f0f\uff0c<strong>\u8ba9\u6211\u4eec\u201c\u597d\u50cf\u201d\u628a\u6570\u636e\u6620\u5c04\u5230\u9ad8\u7ef4\u7a7a\u95f4\u53bb\u5206\u5f00\u5b83\u4eec\uff0c\u4f46\u5b9e\u9645\u4e0a\u4e0d\u7528\u771f\u7684\u7b97\u9ad8\u7ef4\u7684\u5750\u6807\u3002<\/strong><\/p>\n<\/blockquote>\n\n\n\n<p>\u6bd4\u5982\u53ef\u4ee5\u7528<strong>RBF \u6838\u51fd\u6570<\/strong>\uff1a K(X,X\u2032)=exp(\u2212\u03b3||X\u2212X\u2032||<sup>2<\/sup>)<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u6838\u80fd\u5904\u7406\u201c\u540c\u5fc3\u5706\u201d\u201c\u5305\u56f4\u7ed3\u6784\u201d\u201c\u6591\u70b9\u72b6\u201d\u7684\u6570\u636e\u3002<\/p>\n\n\n\n<p>\u4f60\u4e0d\u7528\u5199 \u03d5(X)\u6620\u5c04\uff0c\u4e5f\u4e0d\u7528\u5199 z=X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup>\uff0c\u76f4\u63a5\u8c03\u7528\u6838\u51fd\u6570\u5c31\u884c\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\udfe5 \u4e09\u3001\u56fe\u50cf\u7406\u89e3<\/h2>\n\n\n\n<p>\u5728\u56fe\u91cc\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u201cO\u201d \u662f\u5185\u5708\uff0c\u8ddd\u79bb\u539f\u70b9\u8fd1<\/li>\n\n\n\n<li>\u201cX\u201d \u662f\u5916\u5708\uff0c\u8ddd\u79bb\u539f\u70b9\u8fdc<\/li>\n<\/ul>\n\n\n\n<p>\u5982\u679c\u7528 r = X<sub>1<\/sub><sup>2<\/sup>+X<sub>2<\/sub><sup>2<\/sup> \u8fd9\u4e2a\u65b0\u7ef4\u5ea6\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u539f\u7a7a\u95f4<\/th><th>\u65b0\u7a7a\u95f4 \uff08X<sub>1<\/sub>,X<sub>2<\/sub>,r\uff09<\/th><\/tr><\/thead><tbody><tr><td>O \u70b9\u96c6\u4e2d\u5728\u5c0f r \u4f4d\u7f6e<\/td><td>\u8ddd\u79bb\u539f\u70b9\u8fd1 \u2192 \u65b0\u8f74\u65b9\u5411\u9760\u201c\u4e0b\u201d<\/td><\/tr><tr><td>X \u70b9\u96c6\u4e2d\u5728\u5927 r \u4f4d\u7f6e<\/td><td>\u79bb\u539f\u70b9\u8fdc \u2192 \u65b0\u8f74\u65b9\u5411\u9760\u201c\u4e0a\u201d<\/td><\/tr><tr><td>\u539f\u7a7a\u95f4\u4e0d\u53ef\u7ebf\u6027\u5206<\/td><td>\u65b0\u7a7a\u95f4\u53ef\u7528\u201c\u5e73\u9762\u201d\u7ebf\u6027\u5206 \u2192 \u6210\u529f\uff01<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\ud83d\udfe8 \u56db\u3001\u6700\u7ec8\u76ee\u7684\uff1a\u8ba9\u6570\u636e\u53d8\u6210\u7ebf\u6027\u53ef\u5206<\/h2>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>\u65b9\u6cd5<\/th><th>\u505a\u4e86\u4ec0\u4e48<\/th><th>\u4f18\u70b9<\/th><\/tr><\/thead><tbody><tr><td>\u7279\u5f81\u6620\u5c04<\/td><td>\u624b\u52a8\u6dfb\u52a0\u65b0\u7ef4\u5ea6\uff0c\u6bd4\u5982 X<sup>2<\/sup>+Y<sup>2<\/sup><\/td><td>\u76f4\u89c2\u597d\u7406\u89e3<\/td><\/tr><tr><td>\u6838\u51fd\u6570\uff08SVM\uff09<\/td><td>\u9690\u5f0f\u53d8\u6362\u6570\u636e\uff0c\u4e0d\u7528\u624b\u52a8\u5199\u9ad8\u7ef4\u7279\u5f81<\/td><td>\u81ea\u52a8\u5316\u3001\u9002\u7528\u66f4\u590d\u6742\u7ed3\u6784<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">\u2705 \u5c0f\u7ed3<\/h2>\n\n\n\n<p>\ud83c\udfaf \u5f53\u6570\u636e\u7ebf\u6027\u4e0d\u53ef\u5206\uff0c\u6211\u4eec\u53ef\u4ee5\u7528<strong>\u7279\u5f81\u6620\u5c04<\/strong>\u6216<strong>\u6838\u51fd\u6570<\/strong>\u628a\u6570\u636e\u201c\u62ac\u5230\u66f4\u9ad8\u7684\u7a7a\u95f4\u201d\uff0c\u8ba9\u5b83<strong>\u53d8\u6210\u7ebf\u6027\u53ef\u5206<\/strong>\uff0c\u4ece\u800c\u8ba9 SVM \u627e\u5230\u5b8c\u7f8e\u7684\u5206\u7c7b\u8d85\u5e73\u9762\u3002<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\u2705\u7528Python\u6765\u8fdb\u884c\u6f14\u793a\uff1a<\/p>\n\n\n\n<p>\ud83d\udca1\u4ee3\u7801\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1578\" height=\"1868\" src=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-5.png\" alt=\"\" class=\"wp-image-3063\" srcset=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-5.png 1578w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-5-253x300.png 253w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-5-865x1024.png 865w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-5-768x909.png 768w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-5-1298x1536.png 1298w\" sizes=\"auto, (max-width: 1578px) 100vw, 1578px\" \/><figcaption class=\"wp-element-caption\">\u56fe2.4.1-2 \u6f14\u793a\u4ee3\u7801<\/figcaption><\/figure>\n\n\n\n<p>\ud83d\udca1\u6548\u679c\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"900\" height=\"900\" src=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-6.png\" alt=\"\" class=\"wp-image-3064\" srcset=\"https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-6.png 900w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-6-300x300.png 300w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-6-150x150.png 150w, https:\/\/www.leexinghai.com\/aic\/wp-content\/uploads\/2025\/08\/image-6-768x768.png 768w\" sizes=\"auto, (max-width: 900px) 100vw, 900px\" \/><figcaption class=\"wp-element-caption\">\u56fe2.4.1-3 \u539f\u59cb\u4e8c\u7ef4\u7a7a\u95f4-\u7ebf\u6027\u4e0d\u53ef\u5206\u60c5\u51b5<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" 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