{"id":611,"date":"2023-08-05T00:44:56","date_gmt":"2023-08-04T16:44:56","guid":{"rendered":"https:\/\/blog.cirno.fun\/?p=611"},"modified":"2025-03-19T00:30:35","modified_gmt":"2025-03-18T16:30:35","slug":"chap11-%e6%a0%b8%e5%87%bd%e6%95%b0","status":"publish","type":"post","link":"https:\/\/blog.sssn.tech\/?p=611","title":{"rendered":"[Chap11]-\u6838\u51fd\u6570"},"content":{"rendered":"<p>\u8003\u5bdf\u4e0b\u9762\u7684\u5206\u7c7b\u95ee\u9898<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691165310098.png\" alt=\"file\" \/><\/p>\n<p>\u4e3a\u4e86\u5f97\u5230\u4e0a\u56fe\u7684\u51b3\u7b56\u8fb9\u754c, \u4e00\u4e2a\u53ef\u80fd\u7684\u6a21\u578b\u662f<\/p>\n<pre><code class=\"language-katex\">h_\\theta(x)=\\theta_0+\\theta_1x_1+\\theta_2x_2+\\theta_3x_1x_2+\\theta_4x_1^2+...<\/code><\/pre>\n<p>\u5982\u6b64\u8fd9\u6837\u7684\u5f62\u5f0f<\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u7528\u4e00\u7cfb\u5217\u65b0\u7684\u7279\u5f81f\u6765\u66ff\u6362\u6a21\u578b\u4e2d\u7684\u6bcf\u4e00\u9879, \u4f7f\u5f97\u6a21\u578b\u4e3a<\/p>\n<pre><code class=\"language-katex\">h_\\theta(x)=\\sum \\theta_if_i<\/code><\/pre>\n<p>\u7684\u5f62\u5f0f<\/p>\n<p>\u7136\u800c, \u9664\u4e86\u5bf9\u539f\u6709\u7279\u5f81\u8fdb\u884c\u7ebf\u6027\u7ec4\u5408\u4ee5\u5916, \u6211\u4eec\u8fd8\u53ef\u4ee5\u7528<strong>\u6838\u51fd\u6570(Kernel)<\/strong>\u6765\u8ba1\u7b97\u65b0\u7684\u7279\u5f81f, \u8fd9\u4e9bf\u4f1a\u4f18\u4e8e\u4e0a\u9762\u7684\u6548\u679c<\/p>\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u5b9e\u4f8bx, \u6211\u4eec\u9009\u5b9a\u4e86\u4e09\u4e2a<strong>\u5730\u6807(Landmark)<\/strong>l1, l2, l3<\/p>\n<p>\u4e8b\u5b9e\u4e0a, \u5730\u6807\u7684\u4f4d\u7f6e\u548c\u8bad\u7ec3\u6837\u672c\u7684\u4f4d\u7f6e\u4e00\u4e00\u5bf9\u5e94, \u5177\u4f53\u7684\u7406\u7531\u4f1a\u653e\u5728\u4e0b\u9762<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691228324367.png\" alt=\"file\" \/><\/p>\n<p>\u6211\u4eec\u5229\u7528x\u7684\u5404\u4e2a\u7279\u5f81\u4e0e\u5730\u6807\u7684\u8fd1\u4f3c\u7a0b\u5ea6\u6765\u751f\u6210\u65b0\u7684\u7279\u5f81f<\/p>\n<pre><code class=\"language-katex\">f_i=similarity(x, l^{(i)})<\/code><\/pre>\n<p>\u5176\u4e2d<\/p>\n<pre><code class=\"language-katex\">\nsimilarity(x, y)=exp(-\\frac{||x-y||^2}{2\\sigma^2})\n<\/code><\/pre>\n<p>\u6ce8\u610f\u5206\u5b50\u4e0a\u9762\u662f\u5411\u91cf\u7684\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb, \u5c31\u662f\u51e0\u4f55\u8ddd\u79bb<\/p>\n<p>\u8fd9\u91cc\u7684similarity\u5c31\u662f\u6838\u51fd\u6570, \u5177\u4f53\u800c\u8a00, \u8fd9\u662f\u4e00\u4e2a<strong>\u9ad8\u65af\u6838\u51fd\u6570(Gaussian Kernel)<\/strong><\/p>\n<p>\u8fd9\u4e2a\u6838\u51fd\u6570\u548c\u6b63\u6001\u5206\u5e03\u6ca1\u4ec0\u4e48\u5173\u7cfb, \u53ea\u662f\u770b\u4e0a\u53bb\u50cf\u800c\u5df2<\/p>\n<p>\u8fd9\u4e9b\u5730\u6807\u7684\u4f5c\u7528\u662f, \u5982\u679c\u8bad\u7ec3\u5b9e\u4f8bx\u4e0e\u5730\u6807L\u4e4b\u95f4\u7684\u8ddd\u79bb\u8fd1\u4f3c\u4e0e0, \u5219\u65b0\u7279\u5f81f\u8fd1\u4f3c\u4e8eexp(0)=1, \u53cd\u4e4b\u5982\u679c\u8f83\u8fdc, \u5219f\u8fd1\u4f3c\u4e8eexp(-INF)=0<\/p>\n<p>\u5bf9\u4e8e\u9ad8\u65af\u6838\u4e2dsigma\u7684\u4f5c\u7528, \u53ef\u4ee5\u770b\u4e0b\u56fe<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691167551302.png\" alt=\"file\" \/><\/p>\n<p>\u6211\u4eec\u5728\u5b9e\u4f8b\u4e2d\u52a0\u5165\u4e00\u4e2a\u7c89\u8272\u7684\u70b9x, \u89c2\u5bdf\u4ed6\u7684\u9884\u6d4b\u51fd\u6570, \u5047\u8bbe\u6211\u4eec\u5df2\u7ecf\u5f97\u5230\u4e86theta\u7684\u503c, \u5206\u522b\u662f-0.5, 1, 1, 0<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691167628807.png\" alt=\"file\" \/><\/p>\n<p>x\u79bbl1\u6bd4\u8f83\u8fd1, \u79bbl2, l3\u8f83\u8fdc, \u6240\u4ee5f1\u63a5\u8fd11, f2, f3\u63a5\u8fd10, \u6b64\u65f6\u7ed3\u5408theta\u7684\u503c, \u53ef\u4ee5\u8ba1\u7b97\u5f97\u5230h&gt;0, \u6240\u4ee5\u6211\u4eec\u5224\u5b9ax\u5c5e\u4e8e\u8be5\u5206\u7c7b<\/p>\n<p>\u4e8b\u5b9e\u4e0a, \u89c2\u5bdftheta\u53ef\u4ee5\u53d1\u73b0, \u8fd9\u4e2a\u6a21\u578b\u7684\u610f\u601d\u662f, \u5bf9\u4e8e\u63a5\u8fd1l1\u548cl2\u7684\u70b9, \u6211\u4eec\u66f4\u6709\u53ef\u80fd\u5c06\u5176\u5224\u5b9a\u4e3a\u6b63, \u800c\u8fdc\u79bb\u4e4b\u7684\u70b9\u66f4\u6709\u53ef\u80fd\u88ab\u5224\u5b9a\u4e3a\u8d1f<\/p>\n<p>\u8fd9\u91cc\u7684\u7ea2\u8272\u66f2\u7ebf\u662f\u6211\u4eec\u4f9d\u636e\u4e00\u4e2a\u5355\u4e00\u7684\u8bad\u7ec3\u5b9e\u4f8b\u548c\u6211\u4eec\u9009\u53d6\u7684\u5730\u6807\u5f97\u5230\u7684\u5224\u5b9a\u8fb9\u754c, \u5728\u9884\u6d4b\u65f6, \u6211\u4eec\u91c7\u7528\u7684\u7279\u5f81\u4e0d\u662f\u8bad\u7ec3\u5b9e\u4f8b\u672c\u8eab\u7684\u7279\u5f81xi, \u800c\u662f\u901a\u8fc7\u6838\u51fd\u6570\u8ba1\u7b97\u5f97\u5230\u7684\u65b0\u7279\u5f81fi<\/p>\n<p>\u5982\u4f55\u9009\u62e9\u5730\u6807? \u6211\u4eec\u901a\u5e38\u6839\u636e\u8bad\u7ec3\u96c6\u7684\u6570\u91cf\u9009\u62e9\u5730\u6807\u6570\u91cf, \u5e76\u4e14\u8ba9\u5730\u6807\u4e0e\u8bad\u7ec3\u96c6\u6570\u636e\u4e00\u4e00\u5bf9\u5e94<\/p>\n<pre><code class=\"language-katex\">l^{(i)}=x^{(i)}, i \\in [1, m]<\/code><\/pre>\n<p>\u8fd9\u6837\u7684\u597d\u5904\u5728\u4e8e, \u6211\u4eec\u5f97\u5230\u7684\u65b0\u7279\u5f81\u662f\u5efa\u7acb\u5728\u539f\u6709\u7279\u5f81\u4e0e\u5de1\u793c\u90a3\u51e0\u4e2d\u6240\u6709\u5176\u4ed6\u7279\u5f81\u8ddd\u79bb\u57fa\u7840\u4e0a\u7684, \u5373<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691228610266.png\" alt=\"file\" \/><\/p>\n<p>\u5219\u652f\u6301\u5411\u91cf\u673a\u505a\u51fa\u5047\u8bbe\u7684\u8fc7\u7a0b\u5982\u4e0b<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691228882205.png\" alt=\"file\" \/><\/p>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u8f93\u5165x, \u8ba1\u7b97\u65b0\u7279\u5f81f, \u7136\u540e\u6839\u636etheta\u8ba1\u7b97z, \u5f53z&gt;=0\u65f6\u9884\u6d4b1, \u53cd\u4e4b\u9884\u6d4b0<\/p>\n<p>\u5728\u6b63\u5219\u5316\u9879\u4e2d, \u6211\u4eec\u53ef\u4ee5\u7528\u5411\u91cf\u5316\u7684\u8868\u8fbe<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/blog.sssn.tech\/wp-content\/uploads\/2023\/08\/image-1691229013313.png\" alt=\"file\" \/><\/p>\n<p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d, \u6211\u4eec\u4f1a\u8c03\u6574\u6210<\/p>\n<pre><code class=\"language-katex\">\\theta^TM\\theta<\/code><\/pre>\n<p>\u7684\u5f62\u5f0f, M\u662f\u6839\u636e\u6838\u51fd\u6570\u9009\u62e9\u7684\u4e00\u4e2a\u77e9\u9635, \u53ef\u4ee5\u7b80\u5316\u8ba1\u7b97<\/p>\n<p>\u7406\u8bba\u4e0a\u6765\u8bf4, \u903b\u8f91\u56de\u5f52\u4e2d\u4e5f\u53ef\u4ee5\u4f7f\u7528\u6838\u51fd\u6570, \u4f46\u662f\u4e0a\u9762\u7528M\u77e9\u9635\u7b80\u5316\u8fd0\u7b97\u7684\u65b9\u6cd5\u5374\u4e0d\u9002\u7528\u903b\u8f91\u56de\u5f52, \u56e0\u6b64\u8ba1\u7b97\u975e\u5e38\u8017\u65f6<\/p>\n<p>\u5728\u6b64, \u4e0d\u4ecb\u7ecd\u6700\u5c0f\u5316\u652f\u6301\u5411\u91cf\u673a\u4ee3\u4ef7\u51fd\u6570\u7684\u65b9\u6cd5<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8003\u5bdf\u4e0b\u9762\u7684\u5206\u7c7b\u95ee\u9898 \u4e3a\u4e86\u5f97\u5230\u4e0a\u56fe\u7684\u51b3\u7b56\u8fb9\u754c, \u4e00\u4e2a\u53ef\u80fd\u7684\u6a21\u578b\u662f h_\\theta [&#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-611","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\/611","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=611"}],"version-history":[{"count":2,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/611\/revisions"}],"predecessor-version":[{"id":827,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=\/wp\/v2\/posts\/611\/revisions\/827"}],"wp:attachment":[{"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=611"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=611"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.sssn.tech\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=611"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}