{"id":3109,"date":"2022-02-27T11:39:06","date_gmt":"2022-02-27T03:39:06","guid":{"rendered":"https:\/\/egonlin.com\/?p=3109"},"modified":"2022-02-27T11:40:11","modified_gmt":"2022-02-27T03:40:11","slug":"%e7%ac%ac%e5%9b%9b%e8%8a%82%ef%bc%9a%e9%9d%9e%e7%ba%bf%e6%80%a7%e6%94%af%e6%8c%81%e5%90%91%e9%87%8f%e6%9c%ba","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3109","title":{"rendered":"\u7b2c\u56db\u8282\uff1a\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a"},"content":{"rendered":"

\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a<\/h1>\n

  \u652f\u6301\u5411\u91cf\u673a\u5206\u4e3a\u4e09\u79cd\uff0c\u7ebf\u6027\u53ef\u5206\u652f\u6301\u5411\u91cf\u673a\u548c\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u90fd\u662f\u5bf9\u7ebf\u6027\u53ef\u5206\u7684\u6570\u636e\u505a\u5904\u7406\uff0c\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u4e5f\u4ec5\u4ec5\u662f\u5bf9\u5f02\u5e38\u503c\u505a\u5904\u7406\uff0c\u5e76\u4e0d\u662f\u771f\u6b63\u7684\u5bf9\u975e\u7ebf\u6027\u53ef\u5206\u6570\u636e\u505a\u5904\u7406\uff0c\u63a5\u4e0b\u6765\u5c06\u4f1a\u4ecb\u7ecd\u652f\u6301\u5411\u91cf\u673a\u7684\u7b2c\u4e09\u79cd\u65b9\u6cd5\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\uff08non-linear support vector machine\uff09\u3002<\/p>\n

\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u5b66\u4e60\u76ee\u6807<\/h1>\n
    \n
  1. \u6838\u6280\u5de7<\/li>\n
  2. \u6b63\u5b9a\u6838\u51fd\u6570<\/li>\n
  3. \u5e38\u7528\u76844\u4e2a\u6838\u51fd\u6570<\/li>\n
  4. \u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u7684\u6b65\u9aa4<\/li>\n<\/ol>\n

    \u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u8be6\u89e3<\/h1>\n

    \u591a\u9879\u5f0f\u56de\u5f52\u548c\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a<\/h2>\n

      \u66fe\u5728\u7ebf\u6027\u56de\u5f52\u4e2d\u8bb2\u5230\u8fc7\u591a\u9879\u5f0f\u56de\u5f52\uff0c\u6b64\u5904\u53ea\u505a\u7b80\u5355\u56de\u987e\u3002<\/p>\n

        \u5047\u8bbe\u4e00\u4e2a\u6b63\u65b9\u4f53\u7684\u623f\u5b50\u7684\u4ef7\u683c\u4e0e\u623f\u5b50\u7684\u8fb9\u957f\u3001\u623f\u5b50\u7684\u5360\u5730\u9762\u79ef\u548c\u623f\u5b50\u7684\u4f53\u79ef\u6709\u5173\u7cfb\uff0c\u7136\u800c\u73b0\u5728\u53ea\u6709\u623f\u5b50\u7684\u8fb9\u957f$x_1$\u4e00\u4e2a\u7279\u5f81\uff0c\u5982\u679c\u53ea\u62ff\u7279\u5f81\u53bb\u9884\u6d4b\u623f\u5b50\u7684\u4ef7\u683c\uff0c\u5219\u6709\u5f88\u5927\u53ef\u80fd\u4f1a\u6b20\u62df\u5408\uff0c\u56e0\u6b64\u9700\u8981\u589e\u52a0\u623f\u5b50\u7684\u5360\u5730\u9762\u79ef\u548c\u4f53\u79ef\u8fd9\u4e24\u4e2a\u7279\u5f81\uff0c\u5373
    \n$$
    \n\\hat{y} = \\omega_1x_1 + \\omega_2{x_1}^2 + \\omega_3{x_1}^3 + b
    \n$$
    \n\u4ee4$x_1=x_1,x_2={x_1}^2,x_3={x_1}^3$\uff0c\u5219\u591a\u9879\u5f0f\u7684\u7ebf\u6027\u6a21\u578b\u53d8\u6210
    \n$$
    \n\\hat{y} = \\omega_1x_1 + \\omega_2x_2 + \\omega_3x_3 + b
    \n$$
    \n  \u901a\u8fc7\u4e0a\u8ff0\u8f6c\u53d8\u53ef\u4ee5\u770b\u5230\u628a\u7ebf\u6027\u56de\u5f52\u8f6c\u6362\u6210\u591a\u9879\u5f0f\u56de\u5f52\u4e4b\u540e\u53c8\u53d8\u56de\u4e86\u7ebf\u6027\u56de\u5f52\uff0c\u5373\u5bf9\u4e8e\u4e00\u7ef4\u4e0d\u662f\u7ebf\u6027\u7684\u6570\u636e\uff0c\u628a\u5b83\u6620\u5c04\u5230\u4e86\u4e09\u7ef4\u4e4b\u540e\uff0c\u6570\u636e\u5219\u53d8\u6210\u4e86\u7ebf\u6027\u7684\u6570\u636e\u3002<\/p>\n

      \u5176\u5b9e\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u5373\u8fd0\u7528\u4e86\u8fd9\u4e2a\u601d\u60f3\uff0c\u5373\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u628a\u4f4e\u7ef4\u7279\u5f81\u6570\u636e\u6620\u5c04\u5230\u9ad8\u7ef4\uff0c\u8ba9\u6570\u636e\u53d8\u5f97\u7ebf\u6027\u53ef\u5206\uff0c\u6b64\u65f6\u95ee\u9898\u5c31\u53d8\u6210\u4e86\u7ebf\u6027\u53ef\u5206\u7684\u6570\u636e\u5206\u7c7b\u95ee\u9898\u3002<\/p>\n

    \u6838\u6280\u5de7<\/h2>\n

    \u6838\u51fd\u6570\u5f15\u5165<\/h3>\n

      \u9996\u5148\u56de\u987e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u7684\u76ee\u6807\u51fd\u6570\u7684\u4f18\u5316\u95ee\u9898\u4e3a
    \n$$
    \n\\begin{align}
    \n& \\underbrace{\\min}{\\alpha} {{\\frac{1}{2}}\\sum<\/em>{i=1}^m\\sum_{j=1}^m\\alpha_i\\alpha_jy_iy_j(x_ixj)-\\sum<\/em>{i=1}^m\\alphai} \\
    \n& s.t. \\quad \\sum<\/em>{i=1}^m\\alpha_iy_i=0 \\
    \n& \\quad\\quad 0\\leq\\alpha_i\\geq{C}
    \n\\end{align}
    \n$$
    \n  \u4ece\u4e0a\u5f0f\u53ef\u4ee5\u53d1\u73b0\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u7684\u76ee\u6807\u51fd\u6570\u5bf9\u4e8e\u7279\u5f81\u7684\u5904\u7406\u662f\u4ee5$x_ixj$\u7684\u5f62\u5f0f\u51fa\u73b0\u7684\uff0c\u6b64\u65f6\u5982\u679c\u5b9a\u4e49\u4e00\u4e2a\u4f4e\u7ef4\u7279\u5f81\u7a7a\u95f4\u5230\u9ad8\u7ef4\u7279\u5f81\u7a7a\u95f4\u7684\u6620\u5c04\u51fd\u6570$\\phi(x)$\uff0c\u8ba9\u6240\u6709\u7279\u5f81\u6620\u5c04\u5230\u4e00\u4e2a\u66f4\u9ad8\u7684\u7ef4\u5ea6\uff0c\u8ba9\u6570\u636e\u7ebf\u6027\u53ef\u5206\uff0c\u56e0\u6b64\u5219\u53ef\u4ee5\u7ee7\u7eed\u6309\u7167\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u7684\u65b9\u6cd5\u4f18\u5316\u76ee\u6807\u51fd\u6570\uff0c\u8fdb\u800c\u6c42\u51fa\u5206\u79bb\u8d85\u5e73\u9762\u548c\u5206\u7c7b\u51b3\u7b56\u51fd\u6570\uff0c\u5373\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u7684\u76ee\u6807\u51fd\u6570\u7684\u4f18\u5316\u95ee\u9898\u53d8\u6210\u4e86
    \n$$
    \n\\begin{align}
    \n& \\underbrace{\\min}<\/em>{\\alpha} {{\\frac{1}{2}}\\sum{i=1}^m\\sum<\/em>{j=1}^m\\alpha_i\\alpha_jy_iy_j(\\phi(x_i)\\phi(xj))-\\sum<\/em>{i=1}^m\\alphai} \\
    \n& s.t. \\quad \\sum<\/em>{i=1}^m\\alpha_iy_i=0 \\
    \n& \\quad\\quad 0\\leq\\alpha_i\\geq{C}
    \n\\end{align}
    \n$$
    \n  \u53ef\u4ee5\u53d1\u73b0\u4f7f\u7528\u8be5\u65b9\u6cd5\u8c8c\u4f3c\u5b8c\u7f8e\u7684\u89e3\u51b3\u4e86\u8be5\u95ee\u9898\uff0c\u5e76\u4e14\u7531\u4e8e\u53ea\u662f\u6539\u52a8\u4e86\u6570\u636e\u7684\u7279\u5f81\u7ef4\u5ea6\uff0c\u4f46\u662f\u4e4b\u524d\u4e00\u76f4\u4f7f\u7528\u7684\u6570\u636e\u90fd\u662f\u6d4b\u8bd5\u6570\u636e\uff0c\u5982\u679c\u771f\u7684\u5230\u4e86\u751f\u4ea7\u4e0a\uff0c\u90a3\u4e48\u7279\u5f81\u53ef\u80fd\u4e0d\u4ec5\u4ec5\u5c31\u662f1\u4e2a\u30012\u4e2a\uff0c\u800c\u662f\u6210\u5343\u4e0a\u4e07\u4e2a\uff0c\u5982\u679c\u518d\u5bf9\u7279\u5f81\u8fdb\u884c\u6620\u5c04\u5904\u7406\uff0c\u90a3\u4e48\u7279\u5f81\u7684\u7ef4\u5ea6\u7684\u5feb\u901f\u589e\u52a0\uff0c\u8ba1\u7b97\u5f3a\u5ea6\u4e5f\u968f\u4e4b\u589e\u52a0\uff0c\u800c\u4e14\u9047\u5230\u65e0\u7a77\u7ef4\u7684\u7279\u5f81\uff0c\u90a3\u4e48\u6839\u672c\u65e0\u6cd5\u8ba1\u7b97\uff0c\u6240\u4ee5\u8fd9\u5e76\u4e0d\u662f\u5f88\u5408\u7406\u7684\u3002\u800c\u6838\u51fd\u6570\u5219\u5f88\u597d\u7684\u89e3\u51b3\u4e86\u8ba1\u7b97\u91cf\u5927\u7684\u95ee\u9898\u3002<\/p>\n

    \u6838\u51fd\u6570<\/h3>\n

      \u8bbe$X$\u662f\u4f4e\u7ef4\u8f93\u5165\u7a7a\u95f4\uff08\u6b27\u5f0f\u7a7a\u95f4$R^n$\u7684\u5b50\u96c6\u6216\u79bb\u6563\u96c6\u5408\uff09\uff0c$H$\u4e3a\u9ad8\u7ef4\u7279\u5f81\u7a7a\u95f4\uff08\u5e0c\u5c14\u4f2f\u7279\u7a7a\u95f4\uff09\uff0c\u82e5\u679c\u5b58\u5728\u4e00\u4e2a\u4ece$X$\u5230$H$\u7684\u6620\u5c04$\\phi(x):X \\rightarrow H$\u4f7f\u5f97\u5bf9\u6240\u6709\u7684$x,z\\in{X}$\uff0c\u51fd\u6570$K(x,z)$\u6ee1\u8db3\u6761\u4ef6
    \n$$
    \nK(x,z)=\\phi(x)\\phi(z)
    \n$$
    \n\u5219\u79f0$K(x,z)$\u4e3a\u6838\u51fd\u6570\uff0c$\\phi(x)$\u4e3a\u6620\u5c04\u51fd\u6570\uff0c\u5f0f\u4e2d\u7684$\\phi(x)\\phi(z)$\u4e3a$\\phi(x)$\u548c$\\phi(z)$\u7684\u5185\u79ef\u3002<\/p>\n

      \u7531\u4e8e$x,z\\in{X}$\uff0c\u5728\u8ba1\u7b97$K(x,z)$\u7684\u65f6\u5019\u662f\u5728\u4f4e\u7ef4\u8f93\u5165\u7a7a\u95f4$R^n$\u4e2d\u76f4\u63a5\u8ba1\u7b97\u7684\uff0c\u800c\u4e0d\u662f\u901a\u8fc7$\\phi(x)\\phi(z)$\u8ba1\u7b97\u51fa$K(x,z)$\uff0c\u56e0\u4e3a$\\phi$\u662f\u8f93\u5165\u7a7a\u95f4$R^n$\u5230\u7279\u5f81\u7a7a\u95f4$H$\u7684\u6620\u5c04\uff0c\u7279\u5f81\u7a7a\u95f4$H$\u4e00\u822c\u662f\u9ad8\u7ef4\u7684\uff0c\u751a\u81f3\u662f\u65e0\u7a77\u7ef4\u7684\uff0c\u5e76\u4e14\u5c31\u7b97\u7ed9\u5b9a\u4e86\u6838$K(x,z)$\uff0c\u7279\u5f81\u7a7a\u95f4\u548c\u6620\u5c04\u51fd\u6570\u4e5f\u4e0d\u662f\u552f\u4e00\u7684\uff0c\u53ef\u4ee5\u6709\u591a\u79cd\u4e0d\u540c\u7684\u6620\u5c04\u5173\u7cfb\u5373\u4e0d\u540c\u7684\u7279\u5f81\u7a7a\u95f4\uff0c\u5373\u4f7f\u662f\u5728\u540c\u4e00\u7279\u5f81\u7a7a\u95f4\u91cc\u4e5f\u53ef\u4ee5\u53d6\u4e0d\u540c\u7684\u6620\u5c04\u5173\u7cfb\u3002<\/p>\n

      \u603b\u800c\u8a00\u4e4b\u6838\u51fd\u6570\u7684\u597d\u5904\u5728\u4e8e\u5b83\u5728\u4f4e\u7ef4\u7a7a\u95f4\u4e0a\u8ba1\u7b97\uff0c\u800c\u5c06\u5b9e\u8d28\u4e0a\u7684\u5206\u7c7b\u6548\u679c\u5373\u5185\u53ca\u8ba1\u7b97\u8868\u73b0\u5728\u4e86\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u56e0\u6b64\u907f\u514d\u4e86\u76f4\u63a5\u5728\u9ad8\u7ef4\u4e2d\u7684\u590d\u6742\u8ba1\u7b97\u3002<\/p>\n

      \u901a\u8fc7\u4f7f\u7528\u6838\u51fd\u6570$K(x,z)$\u540e\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u7684\u5206\u79bb\u8d85\u5e73\u9762\u4e3a
    \n$$
    \n\\sum{i=1}^m \\sum<\/em>{i=1}^m{\\alpha_i}^y_iK(x,x_i)+b^<\/em> = 0
    \n$$
    \n\u5206\u7c7b\u51b3\u7b56\u51fd\u6570\u4e3a
    \n$$
    \nf(x) = sign(\\sum_{i=1}^m{\\alpha_i}^y_iK(x,x_i)+b^<\/em>)
    \n$$<\/p>\n

    \u6838\u51fd\u6570\u4e3e\u4f8b<\/h3>\n

    <\/p>

    <\/div>

    \u67e5\u770b\u66f4\u591a<\/h2>

    \u8054\u7cfb\u7ba1\u7406\u5458\u5fae\u4fe1tutu19192010\uff0c\u6ce8\u518c\u8d26\u53f7<\/p>\n<\/div>

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    \u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a   \u652f\u6301\u5411\u91cf\u673a\u5206\u4e3a\u4e09\u79cd\uff0c\u7ebf\u6027\u53ef\u5206\u652f\u6301\u5411\u91cf\u673a\u548c\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u90fd\u662f\u5bf9\u7ebf\u6027\u53ef\u5206 […]<\/p>\n","protected":false},"author":3,"featured_media":3094,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,291],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3109"}],"collection":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3109"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3109\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/media\/3094"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3109"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}