{"id":599,"date":"2023-08-04T01:11:57","date_gmt":"2023-08-03T17:11:57","guid":{"rendered":"https:\/\/blog.cirno.fun\/?p=599"},"modified":"2025-03-19T00:30:53","modified_gmt":"2025-03-18T16:30:53","slug":"chap10-%e6%94%af%e6%8c%81%e5%90%91%e9%87%8f%e6%9c%basvm","status":"publish","type":"post","link":"https:\/\/blog.sssn.tech\/?p=599","title":{"rendered":"[Chap10]-\u652f\u6301\u5411\u91cf\u673aSVM\u521d\u6b65"},"content":{"rendered":"<p>\u8fd8\u6709\u4e00\u4e2a\u66f4\u52a0\u5f3a\u5927\u7684\u7b97\u6cd5\u5e7f\u6cdb\u7684\u5e94\u7528\u4e8e\u5de5\u4e1a\u754c\u548c\u5b66\u672f\u754c\uff0c\u5b83\u88ab\u79f0\u4e3a<strong>\u652f\u6301\u5411\u91cf\u673a(Support Vector Machine)<\/strong>\u3002<\/p>\n<p>\u4e0e\u903b\u8f91\u56de\u5f52\u548c\u795e\u7ecf\u7f51\u7edc\u76f8\u6bd4\uff0c\u652f\u6301\u5411\u91cf\u673a\uff0c\u6216\u8005\u7b80\u79f0 SVM\uff0c\u5728\u5b66\u4e60\u590d\u6742\u7684\u975e\u7ebf\u6027\u65b9\u7a0b\u65f6\u63d0\u4f9b\u4e86\u4e00\u79cd\u66f4\u4e3a\u6e05\u6670\uff0c\u66f4\u52a0\u5f3a\u5927\u7684\u65b9\u5f0f\u3002<\/p>\n<h2>\u4f18\u5316\u76ee\u6807<\/h2>\n<p>\u8fd9\u91cc\u6211\u4eec\u4ece\u903b\u8f91\u56de\u5f52\u5f00\u59cb, \u4e00\u70b9\u70b9\u4fee\u6539\u5f97\u5230\u652f\u6301\u5411\u91cf\u673a<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691080729116.png\" alt=\"file\" \/><\/p>\n<p>\u5728\u903b\u8f91\u56de\u5f52\u4e2d, \u5bf9\u4e8e\u4e00\u4e2ay=1\u7684\u6837\u672c, \u6211\u4eec\u5e0c\u671bh(x)\u8d8b\u8fd1\u4e8e1, \u90a3\u5c31\u8981\u4ee4 z = thetaX\u8fdc\u5927\u4e8e0, \u76f8\u5bf9\u7684, \u5982\u679c\u5bf9\u4e8ey=0\u7684\u6837\u672c, \u6211\u4eec\u5e0c\u671bz\u8fdc\u5c0f\u4e8e0<\/p>\n<p>\u652f\u6301\u5411\u91cf\u673a\u7684\u635f\u5931\u51fd\u6570\u53ef\u4ee5\u5728\u903b\u8f91\u56de\u5f52\u7684\u635f\u5931\u51fd\u6570\u4e0a\u505a\u5982\u4e0b\u4fee\u6539:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691081274446.png\" alt=\"file\" \/><\/p>\n<p>\u9ed1\u8272\u7684\u662f\u903b\u8f91\u56de\u5f52\u7684, \u7d2b\u8272\u7684\u662f\u652f\u6301\u5411\u91cf\u673a\u7684<\/p>\n<p>\u548c\u903b\u8f91\u56de\u5f52\u4e00\u6837, \u9700\u8981\u5bf9\u6837\u672cy\u503c\u505a\u5206\u7c7b\u8ba8\u8bba, \u7d2b\u8272\u56fe\u50cf\u662f\u5206\u6bb5\u7684\u76f4\u7ebf, \u4e14\u8fc7(1, 0) \u6216\u8005(-1, 0)<\/p>\n<p>\u6211\u4eec\u7ed9\u4e24\u4e2a\u65b0\u51fd\u6570\u8d77\u540d<code>cost_0(z)<\/code>\u548c<code>cost_1(z)<\/code>, \u5206\u522b\u5bf9\u5e94y=0\u548c1\u7684\u60c5\u51b5<\/p>\n<p>\u652f\u6301\u5411\u91cf\u673a\u7684\u6574\u4f53\u635f\u5931\u51fd\u6570\u53ef\u4ee5\u7531\u903b\u8f91\u56de\u5f52\u7684\u51fd\u6570\u5982\u6b64\u4fee\u6539\u5f97\u5230<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691081592623.png\" alt=\"file\" \/><\/p>\n<p>\u9996\u5148\u6211\u4eec\u53bb\u6389\u4e86\u5f00\u5934\u7684\u5e38\u65701\/m, \u5728\u903b\u8f91\u56de\u5f52\u4e2d, \u8fd9\u4ee3\u8868\u7740\u635f\u5931\u5bf9\u6bcf\u4e2a\u6837\u672c\u7684\u5e73\u5747, \u4ed6\u662f\u5e38\u6570, \u5bf9\u6574\u4f53\u7684\u53c2\u6570\u6700\u5c0f\u503c\u53d6\u503c\u6ca1\u6709\u5f71\u54cd, \u53bb\u6389\u4ed6\u662f\u652f\u6301\u5411\u91cf\u673a\u7684\u4e60\u60ef, \u6ca1\u6709\u7edd\u5bf9\u5bf9\u9519<\/p>\n<p>\u7136\u540e\u7528\u65b0\u7684\u635f\u5931\u51fd\u6570\u66ff\u4ee3\u903b\u8f91\u56de\u5f52\u7684<\/p>\n<p>\u5728\u652f\u6301\u5411\u91cf\u673a\u4e2d, \u7528\u4e8e\u5e73\u8861\u635f\u5931\u51fd\u6570\u548c\u6b63\u5219\u5316\u9879\u7684\u53c2\u6570\u662fC, \u5378\u8f7d\u635f\u5931\u51fd\u6570\u524d, \u4e8b\u5b9e\u4e0a\u53ef\u4ee5\u770b\u4f5c\u626e\u6f14\u7c7b\u4f3c<code>\\frac{1}{\\lambda}<\/code>\u7684\u89d2\u8272<\/p>\n<p>\u652f\u6301\u5411\u91cf\u673a\u7684\u9884\u6d4b\u89c4\u5219\u5982\u4e0b <img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691082044086.png\" alt=\"file\" \/><\/p>\n<p>\u6709\u522b\u4e8e\u903b\u8f91\u56de\u5f52\u8f93\u51fa\u6982\u7387, \u652f\u6301\u5411\u91cf\u673a\u76f4\u63a5\u8f93\u51fa\u9884\u6d4b\u7684\u7ed3\u679c<\/p>\n<h2>\u5927\u8fb9\u754c(Large Margin)\u7684\u76f4\u89c2\u7406\u89e3<\/h2>\n<p>\u652f\u6301\u5411\u91cf\u673a\u4e5f\u88ab\u79f0\u4f5c\u5927\u95f4\u8ddd\u5206\u7c7b\u5668, \u901a\u8fc7\u7406\u89e3&quot;\u5927\u95f4\u8ddd&quot;\u7684\u7531\u6765, \u6709\u52a9\u4e8e\u6211\u4eec\u7406\u89e3\u5176\u601d\u60f3<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691082199911.png\" alt=\"file\" \/><\/p>\n<p>\u8fd9\u91cc\u5c060\u66ff\u6362\u6210\u00b11\u662f\u4e3a\u4e86\u5e2e\u52a9\u6a21\u578b\u66f4\u597d\u7684\u8bad\u7ec3, \u4e5f\u53ef\u4ee5\u53eb\u505a\u5b89\u5168\u56e0\u5b50, \u5f15\u5bfc\u4ed6\u505a\u51fa\u660e\u786e\u7684\u51b3\u5b9a, \u800c\u975e\u6a21\u68f1\u4e24\u53ef\u7684<\/p>\n<p>\u6211\u4eec\u770b\u4e00\u4e0b\u8fd9\u4e2a\u56e0\u5b50\u5bfc\u81f4\u4e86\u4ec0\u4e48\u7ed3\u679c: \u5177\u4f53\u800c\u8a00, \u8003\u8651\u4e00\u4e2a\u7279\u4f8b: \u6211\u4eec\u5c06C\u8bbe\u7f6e\u4e3a\u4e00\u4e2a\u975e\u5e38\u5927\u7684\u6570, \u6bd4\u59821e5, \u6765\u89c2\u5bdfSVM\u7684\u53cd\u5e94<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691082381217.png\" alt=\"file\" \/><\/p>\n<p>\u56e0\u4e3aC\u975e\u5e38\u5927, SVM\u4f1a\u8feb\u5207\u7684\u5e0c\u671b\u4f18\u5316\u635f\u5931\u51fd\u6570, \u800c\u975e\u540e\u9762\u7684\u6b63\u5219\u5316\u9879, \u6211\u4eec\u5047\u8bbe\u53ef\u4ee5\u4f18\u5316\u5176\u4e3a0, \u5219, \u5bf9\u4e8e\u4e00\u4e2ay=1\u7684\u6837\u672c, \u6211\u4eec\u9700\u8981z&gt;=1, \u53cd\u4e4b\u5219\u9700\u8981z&lt;=-1<\/p>\n<p>\u6b64\u65f6\u95ee\u9898\u53d8\u6210\u4e86, \u4ee4z\u5728\u6ee1\u8db3\u4e0a\u8ff0\u6761\u4ef6\u4e0b, \u4f18\u5316\u6b63\u5219\u9879\u81f3\u6700\u5c0f(\u6761\u4ef6\u6781\u503c\u95ee\u9898)<\/p>\n<p>\u8003\u5bdf\u4e0b\u9762\u7684\u4e8c\u5206\u7c7b\u6570\u636e\u96c6:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691163075612.png\" alt=\"file\" \/><\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u770b\u5230, \u6709\u5f88\u591a\u51b3\u7b56\u8fb9\u754c\u53ef\u4ee5\u5c06\u6570\u636e\u96c6\u5206\u4e3a\u4e24\u7c7b, \u4f46\u662fSVM\u4f1a\u9009\u62e9\u9ed1\u8272\u7684\u4e00\u6761, \u770b\u4e0a\u53bb\u66f4\u52a0\u5408\u7406, \u8fd9\u662f\u56e0\u4e3a\u9ed1\u8272\u76f4\u7ebf\u79bb\u4e24\u4fa7\u6570\u636e\u90fd\u8f83\u8fdc, \u800c\u51b3\u7b56\u8fb9\u754c\u5230\u6570\u636e\u7684\u8ddd\u79bb\u5c31\u53eb\u505a<strong>\u95f4\u8ddd(Margin)<\/strong>, \u4e0b\u56fe\u4e2d\u753b\u51fa\u7684\u90e8\u5206<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691163210873.png\" alt=\"file\" \/><\/p>\n<p>\u4e8b\u5b9e\u4e0a\u6211\u4eec\u7684\u4f18\u5316\u95ee\u9898\u662f<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691163391967.png\" alt=\"file\" \/><\/p>\n<p>\u4e0a\u56fe\u4e2ds.t.\u662fsubject to\u7684\u7f29\u5199, \u610f\u4e3a\u53d7\u9650\u4e8e<\/p>\n<p>\u8fd9\u91cc\u9700\u8981\u6ce8\u610f\u4e00\u70b9, \u5e38\u6570C\u5e76\u4e0d\u662f\u8d8a\u5927\u8d8a\u597d, \u8003\u5bdf\u4e0b\u9762\u7684\u6570\u636e\u96c6, \u6ce8\u610f\u6570\u636e\u96c6\u4e2d\u7684<strong>\u5f02\u5e38\u70b9(Outlier)<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691163351883.png\" alt=\"file\" \/><\/p>\n<p>\u5982\u679c\u6211\u4eec\u5c06C\u8bbe\u7f6e\u7684\u8fc7\u5927, \u6bd4\u59821e5, \u56e0\u4e3a\u7b97\u6cd5\u8feb\u5207\u7684\u9700\u8981\u8ba9\u7b2c\u4e00\u9879\u4e3a0, \u6240\u4ee5\u4f1a\u753b\u51fa\u7c89\u8272\u7684\u51b3\u7b56\u8fb9\u754c, \u8fd9\u663e\u7136\u662f\u4e0d\u7406\u667a\u7684<\/p>\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d, \u663e\u7136\u5e94\u8be5\u8c03\u6574C\u7684\u5927\u5c0f\u5230\u5408\u9002, \u4ee5\u83b7\u5f97\u9ed1\u8272\u7684\u51b3\u7b56\u8fb9\u754c, \u5373, \u5f53C\u4e0d\u662f\u975e\u5e38\u5927\u7684\u65f6\u5019, \u7b97\u6cd5\u53ef\u4ee5\u5ffd\u7565\u6389\u4e00\u4e9b\u5f02\u5e38\u70b9\u7684\u5f71\u54cd, \u5f97\u5230\u66f4\u597d\u7684\u51b3\u7b56\u8fb9\u754c<\/p>\n<p>\u56de\u987eC = 1\/lambda, \u56e0\u6b64<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691164812819.png\" alt=\"file\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8fd8\u6709\u4e00\u4e2a\u66f4\u52a0\u5f3a\u5927\u7684\u7b97\u6cd5\u5e7f\u6cdb\u7684\u5e94\u7528\u4e8e\u5de5\u4e1a\u754c\u548c\u5b66\u672f\u754c\uff0c\u5b83\u88ab\u79f0\u4e3a\u652f\u6301\u5411\u91cf\u673a(Suppo [&#8230;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11,18],"tags":[],"class_list":["post-599","post","type-post","status-publish","format-standard","hentry","category-11","category-18"],"_links":{"self":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/599","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=599"}],"version-history":[{"count":2,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/599\/revisions"}],"predecessor-version":[{"id":828,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/599\/revisions\/828"}],"wp:attachment":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=599"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=599"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=599"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}