{"id":2964,"date":"2022-02-20T20:34:57","date_gmt":"2022-02-20T12:34:57","guid":{"rendered":"https:\/\/egonlin.com\/?p=2964"},"modified":"2023-02-01T11:23:58","modified_gmt":"2023-02-01T03:23:58","slug":"%e7%ac%ac%e4%b8%80%e8%8a%82%ef%bc%9a%e6%84%9f%e7%9f%a5%e6%9c%ba%e5%bc%95%e5%85%a5","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=2964","title":{"rendered":"\u7b2c\u4e00\u8282\uff1a\u611f\u77e5\u673a\u5f15\u5165"},"content":{"rendered":"

\u611f\u77e5\u673a<\/h1>\n

  \u611f\u77e5\u673a\u57281957\u5e74\u88ab\u63d0\u51fa\uff0c\u7b97\u662f\u6700\u53e4\u8001\u7684\u5206\u7c7b\u65b9\u6cd5\u4e4b\u4e00\u3002<\/p>\n

  \u867d\u7136\u611f\u77e5\u673a\u6cdb\u5316\u80fd\u529b\u4e0d\u53ca\u5176\u4ed6\u7684\u5206\u7c7b\u6a21\u578b\uff0c\u4f46\u662f\u5982\u679c\u80fd\u591f\u5bf9\u611f\u77e5\u673a\u7684\u539f\u7406\u6709\u4e00\u5b9a\u7684\u8ba4\u8bc6\uff0c\u5728\u4e4b\u540e\u5b66\u4e60\u652f\u6301\u5411\u91cf\u673a\u3001\u795e\u7ecf\u7f51\u7edc\u7b49\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u7684\u65f6\u5019\u4f1a\u8f7b\u677e\u5f88\u591a\u3002<\/p>\n

1,\u611f\u77e5\u673a\u5b66\u4e60\u76ee\u6807<\/h1>\n
    \n
  1. \u611f\u77e5\u673a\u6a21\u578b<\/li>\n
  2. \u611f\u77e5\u673a\u7684\u635f\u5931\u51fd\u6570\u548c\u76ee\u6807\u51fd\u6570<\/li>\n
  3. \u611f\u77e5\u673a\u539f\u59cb\u5f62\u5f0f\u548c\u5bf9\u5076\u5f62\u5f0f<\/li>\n
  4. \u611f\u77e5\u673a\u6d41\u7a0b<\/li>\n
  5. \u611f\u77e5\u673a\u4f18\u7f3a\u70b9<\/li>\n<\/ol>\n

    2,\u611f\u77e5\u673a\u5f15\u5165<\/h1>\n

    2.1\u7ebf\u6027\u53ef\u5206\u548c\u7ebf\u6027\u4e0d\u53ef\u5206<\/h2>\n

    \"\"<\/div><\/p>\n

      \u6bcf\u9022\u4e0b\u5348\u6709\u4f53\u80b2\u8bfe\uff0c\u603b\u4f1a\u6709\u7537\u5b69\u548c\u5973\u5b69\u5728\u5b66\u6821\u7684\u64cd\u573a\u4e0a\u73a9\u800d\u3002<\/p>\n

      \u5047\u8bbe\u7531\u4e8e\u4f20\u7edf\u601d\u60f3\u7684\u5f71\u54cd\uff0c\u7537\u5b69\u603b\u4f1a\u548c\u7537\u5b69\u4e00\u8d77\u6253\u6253\u7bee\u7403\uff0c\u5973\u5b69\u603b\u4f1a\u548c\u5973\u5b69\u4e00\u8d77\u8e22\u6bfd\u5b50\u3001\u8df3\u8df3\u7ef3\uff0c\u5982\u4e0b\u56fe\u6240\u793a\u3002<\/p>\n

    # \u611f\u77e5\u673a\u5f15\u5165\u56fe\u4f8b\nimport numpy as np\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n\nnp.random.seed(1)\nx1 = np.random.random(20)+1.5\ny1 = np.random.random(20)+0.5\nx2 = np.random.random(20)+3\ny2 = np.random.random(20)+0.5\n\n# \u4e00\u884c\u4e8c\u5217\u7b2c\u4e00\u4e2a\nplt.subplot(121)\nplt.scatter(x1, y1, s=50, color='b', label='\u7537\u5b69(+1)')\nplt.scatter(x2, y2, s=50, color='r', label='\u5973\u5b69(-1)')\nplt.vlines(2.8, 0, 2, colors="r", linestyles="-", label='$wx+b=0$')\nplt.title('\u7ebf\u6027\u53ef\u5206', fontproperties=font, fontsize=20)\nplt.xlabel('x')\nplt.legend(prop=font)\n\n# \u4e00\u884c\u4e8c\u5217\u7b2c\u4e8c\u4e2a\nplt.subplot(122)\nplt.scatter(x1, y1, s=50, color='b', label='\u7537\u5b69(+1)')\nplt.scatter(x2, y2, s=50, color='r', label='\u5973\u5b69(-1)')\nplt.scatter(3.5, 1, s=50, color='b')\nplt.title('\u7ebf\u6027\u4e0d\u53ef\u5206', fontproperties=font, fontsize=20)\nplt.xlabel('x')\nplt.legend(prop=font, loc='upper right')\nplt.show()<\/code><\/pre>\n
    \"\"<\/div><\/p>\n
      \u4ece\u5de6\u56fe\u4e2d\u4e5f\u53ef\u4ee5\u770b\u51fa\u603b\u80fd\u627e\u5230\u4e00\u6761\u76f4\u7ebf\u5c06\u7537\u5b69\u548c\u5973\u5b69\u5206\u5f00\uff0c\u5373\u7537\u5b69\u548c\u5973\u5b69\u5728\u64cd\u573a\u4e0a\u7684\u5206\u5e03\u662f\u7ebf\u6027\u53ef\u5206\u7684\uff0c\u6b64\u65f6\u8be5\u5206\u9694\u76f4\u7ebf\u4e3a
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d$\\omega,b$\u662f\u53c2\u6570\uff0c$x$\u662f\u7537\u5b69\u548c\u5973\u5b69\u5171\u6709\u7684\u67d0\u79cd\u7279\u5f81\u3002<\/p>\n
      \u5982\u679c\u67d0\u4e2a\u7537\u5b69\u4e0d\u542c\u8bdd\u8dd1\u5230\u5973\u5b69\u90a3\u8fb9\u53bb\u4e86\uff0c\u5982\u4e0b\u56fe\u53f3\u56fe\u6240\u793a\uff0c\u5219\u65e0\u6cd5\u901a\u8fc7\u4e00\u6761\u76f4\u7ebf\u80fd\u591f\u628a\u6240\u6709\u7684\u7537\u5b69\u548c\u5973\u5b69\u5206\u5f00\uff0c\u5219\u79f0\u7537\u5b69\u548c\u5973\u5b69\u5728\u64cd\u573a\u4e0a\u7684\u5206\u5e03\u662f\u7ebf\u6027\u4e0d\u53ef\u5206\u7684\uff0c\u5373\u65e0\u6cd5\u4f7f\u7528\u611f\u77e5\u673a\u7b97\u6cd5\u5b8c\u6210\u8be5\u5206\u7c7b\u8fc7\u7a0b\u3002<\/p>\n
      \u4e0a\u8ff0\u6574\u4e2a\u8fc7\u7a0b\u5176\u5b9e\u5c31\u662f\u611f\u77e5\u673a\u5b9e\u73b0\u7684\u4e00\u4e2a\u8fc7\u7a0b\u3002<\/p>\n
    3,\u611f\u77e5\u673a\u8be6\u89e3<\/h1>\n
    3.1\u611f\u77e5\u673a\u6a21\u578b<\/h2>\n
      \u611f\u77e5\u673a\u662f\u4e00\u4e2a\u4e8c\u5206\u7c7b\u7ebf\u6027\u6a21\u578b\uff0c\u5373\u8f93\u51fa\u4e3a\u5b9e\u4f8b\u7684\u7c7b\u522b\uff0c\u4e00\u822c\u4e3a\u5176\u4e2d\u4e00\u7c7b\u79f0\u4e3a\u6b63\u7c7b$(+1)$\uff0c\u53e6\u4e00\u7c7b\u79f0\u4e3a\u8d1f\u7c7b$(-1)$\u3002\u53ef\u4ee5\u628a\u4e0a\u56fe\u6240\u793a\u7684\u7537\u5b69$(+1)$\u79f0\u4e3a\u6b63\u7c7b\uff0c\u5973\u5b69$(-1)$\u79f0\u4e3a\u8d1f\u7c7b\u3002<\/p>\n
      \u5047\u8bbe\u6709$m$\u4e2a\u5b9e\u4f8b$n$\u7ef4\u7279\u5f81\u5e76\u4e14\u6570\u636e\u7ebf\u6027\u53ef\u5206\u7684\u6570\u636e\u96c6
    \n
    \"file\"<\/div>
    \n\u5b83\u7684\u8f93\u51fa\u7a7a\u95f4\u5373$y$\u7684\u53d6\u503c\u662f$y={+1,-1}$\u3002<\/p>\n
      \u7531\u4e8e\u6570\u636e\u7ebf\u6027\u53ef\u5206\uff0c\u5982\u679c\u662f\u4e8c\u7ef4\u7a7a\u95f4\uff0c\u5219\u603b\u80fd\u627e\u5230\u4e00\u6761\u76f4\u7ebf\u5c06\u4e8c\u7ef4\u7a7a\u95f4\u4e2d\u7684\u6570\u636e\u96c6\u5206\u4e3a\u4e24\u7c7b\uff0c\u5982\u4e0a\u56fe\u6240\u793a\u7684$\\omega{x}+b=0$\uff0c\u5982\u679c\u662f\u4e09\u7ef4\u7a7a\u95f4\uff0c\u5219\u80fd\u627e\u5230\u4e00\u4e2a\u5e73\u9762\u628a\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u6570\u636e\u96c6\u5206\u4e3a\u4e24\u7c7b\u3002\u5bf9\u4e8e\u4e0a\u8ff0\u7684\u5047\u8bbe\u7684\u6570\u636e\u96c6$T$\uff0c\u5219\u603b\u80fd\u627e\u5230\u4e00\u4e2a\u8d85\u5e73\u9762$S$\u5c06\u8be5\u6570\u636e\u96c6\u5206\u6210\u4e24\u7c7b\uff0c\u8be5\u8d85\u5e73\u9762$S$\u53ef\u4ee5\u8bb0\u4f5c
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d\u5982\u679c\u5047\u8bbe$\\omega_0=b,x_0=1$\uff0c\u5219\u8d85\u5e73\u9762\u4e3a
    \n
    \"file\"<\/div>
    \n\u5982\u679c\u628a\u4e0a\u8ff0\u516c\u5f0f\u4f7f\u7528\u5411\u91cf\u6765\u8868\u793a\uff0c\u5219\u8d85\u5e73\u9762\u4e3a
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d$\\omega,x$\u90fd\u4e3a$n+1$\u7ef4\u7684\u5411\u91cf\u3002<\/p>\n
      \u5982\u679c\u628a$\\omega^Tx > 0$\u5185\u7684\u6570\u636e\u96c6\u770b\u6210\u4e00\u7c7b\uff1b\u628a$\\omega^Tx < 0$\u5185\u7684\u6570\u636e\u96c6\u770b\u6210\u53e6\u4e00\u7c7b\uff0c\u5373\u901a\u8fc7$\\omega^Tx=0$\u6210\u529f\u5c06\u6570\u636e\u96c6\u5206\u4e3a\u4e24\u7c7b\u3002\u4e3a\u4e86\u5c06\u4e24\u4e2a\u7c7b\u522b\u7b26\u53f7\u5316\uff0c\u6211\u4eec\u53ef\u4ee5\u4f7f\u7528$sign$\u51fd\u6570\uff0c\u7531\u6b64\u5373\u53ef\u5f97\u5230\u611f\u77e5\u673a\u7684\u6a21\u578b\u4e3a
    \n
    \"file\"<\/div><\/p>\n
    3.2\u611f\u77e5\u673a\u635f\u5931\u51fd\u6570<\/h2>\n
      \u5047\u8bbe\u6709\u4e00\u4e2a\u7ebf\u6027\u53ef\u5206\u7684\u6570\u636e\u96c6
    \n
    \"file\"<\/div>
    \n\u5219\u6570\u636e\u96c6\u4e2d\u7684\u6837\u672c$x_i$\u5230\u8d85\u5e73\u9762$S$\u7684\u8ddd\u79bb\u4e3a
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d$||\\omega||$\u4e3aL2\u8303\u6570\u3002<\/p>\n
      \u8be5\u8ddd\u79bb\u516c\u5f0f\u6e90\u81ea\u4e8e\u6570\u5b66\u4e2d\u70b9$(x_0,y_0)$\u5230\u9762$Ax+By+C=0$\u7684\u516c\u5f0f
    \n
    \"file\"<\/div>
    \n  \u5047\u8bbe\u5b58\u5728\u4e00\u4e2a\u8bef\u5206\u7c7b\u7684\u6837\u672c$(x_i,y_i)$\uff0c\u5bf9\u6709\u8bef\u5206\u7c7b\u7684\u6837\u672c\u90fd\u5b58\u5728$- y_i(\\omega^Tx_i) > 0$\u3002\u56e0\u4e3a\u8bef\u5206\u7c7b\u65f6\u5f53$\\omega^Tx_i = 1$\u65f6$y_i = -1$\uff1b\u5f53$\\omega^Tx_i = -1$\u65f6$y_i = 1$\u3002\u56e0\u6b64$|\\omega^Tx_i| = -y_i(\\omega^Tx_i)$\uff0c\u5219\u8bef\u5206\u7c7b\u70b9\u5230\u8d85\u5e73\u9762$S$\u7684\u8ddd\u79bb\u5373\u635f\u5931\u51fd\u6570\u4e3a
    \n
    \"file\"<\/div><\/p>\n
    3.3\u611f\u77e5\u673a\u76ee\u6807\u51fd\u6570<\/h2>\n
      \u5047\u8bbe\u8bef\u5206\u7c7b\u70b9\u7684\u96c6\u5408\u4e3a$M$\uff0c\u90a3\u4e48\u6240\u6709\u8bef\u5206\u7c7b\u70b9\u5230\u8d85\u5e73\u9762$S$\u7684\u8ddd\u79bb\u5373\u611f\u77e5\u673a\u7684\u76ee\u6807\u51fd\u6570\u4e3a
    \n
    \"file\"<\/div>
    \n  \u7ed9\u5b9a\u4e86\u6240\u6709\u8bef\u5206\u7c7b\u70b9\u5230\u8d85\u5e73\u9762\u7684\u8ddd\u79bb\uff0c\u6211\u4eec\u7684\u76ee\u7684\u5c31\u662f\u4f18\u5316\u4e0a\u8ff0\u516c\u5f0f\uff0c\u5373\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570\u3002<\/p>\n
      \u7531\u4e8e$\\omega^Tx_i=\\omega_1x_1 + \\omega_2x_2 + \\cdots + \\omega_nx_n + b$\uff0c\u5982\u679c$\\omega$\u548c$b$\u6210\u6bd4\u4f8b\u7684\u589e\u52a0\uff0c\u5373\u5206\u5b50\u7684$\\omega$\u548c$b$\u6269\u5927$n$\u500d\u65f6\uff0c\u5206\u6bcd\u7684L2\u8303\u6570\u4e5f\u5c06\u6269\u5927$n$\u500d\uff0c\u4e5f\u5c31\u662f\u8bf4\u5206\u5b50\u548c\u5206\u6bcd\u6709\u56fa\u5b9a\u7684\u500d\u6570\u5173\u7cfb\uff0c\u5373\u53ef\u4ee5\u5c06\u5206\u5b50\u6216\u5206\u6bcd\u56fa\u5b9a\u4e3a$1$\uff0c\u7136\u540e\u6c42\u5206\u5b50\u81ea\u5df1\u6216\u5206\u6bcd\u7684\u5012\u6570\u7684\u6700\u5c0f\u5316\u4f5c\u4e3a\u65b0\u7684\u76ee\u6807\u51fd\u6570\u3002(\u6b64\u5904\u8bb2\u89e3\u62ff\u51fa$b$\uff0c\u4e8b\u5b9e\u4e0a$b$\u5bf9\u7ed3\u679c\u7684\u5f71\u54cd\u5f88\u5c0f\uff0c\u540e\u7eed\u4f1a\u7ee7\u7eed\u7528\u5411\u91cf\u7684\u65b9\u5f0f\uff0c\u5e76\u4e14\u5ffd\u7565$b$)\u3002<\/p>\n
      \u611f\u77e5\u673a\u5c06\u5206\u6bcd$||\\omega||$\u56fa\u5b9a\u4e3a$1$\uff0c\u7136\u540e\u5c06\u5206\u5b50\u7684\u6700\u5c0f\u5316\u4f5c\u4e3a\u76ee\u6807\u51fd\u6570\uff0c\u56e0\u6b64\u611f\u77e5\u673a\u7684\u76ee\u6807\u51fd\u6570\u66f4\u65b0\u4e3a
    \n
    \"file\"<\/div>
    \n  \u591a\u8bf4\u4e00\u5634\uff0c\u652f\u6301\u5411\u91cf\u673a\u5219\u662f\u5c06\u5206\u5b50\u56fa\u5b9a\u4f4d$1$\uff0c\u7136\u540e\u5c06\u5206\u6bcd\u7684\u5012\u6570\u6700\u5c0f\u5316\u4f5c\u4e3a\u76ee\u6807\u51fd\u6570\u3002<\/p>\n
      \u5bf9\u4e8e\u7ed9\u5b9a\u7684\u76ee\u6807\u51fd\u6570$J(\\omega)$\uff0c\u5982\u679c\u6ca1\u6709\u8bef\u5206\u7c7b\u70b9\uff0c\u76ee\u6807\u51fd\u6570\u503c\u4e3a0\uff1b\u5982\u679c\u8bef\u5206\u7c7b\u70b9\u8d8a\u5c11\uff0c\u5219\u76ee\u6807\u51fd\u6570\u503c\u8d8a\u5c0f\uff1b\u5982\u679c\u8bef\u5206\u7c7b\u70b9\u8d8a\u591a\uff0c\u5219\u76ee\u6807\u51fd\u6570\u503c\u8d8a\u5927\u3002<\/p>\n
      \u6c42\u51fa\u76ee\u6807\u51fd\u6570\u7684\u6700\u5c0f\u503c\u4fbf\u53ef\u5f97\u5230\u8bef\u5206\u7c7b\u70b9\u5c11\u7684\u611f\u77e5\u673a\u6a21\u578b\uff0c\u5e76\u4e14\u4ece\u76ee\u6807\u51fd\u6570\u4e2d\u4e5f\u53ef\u4ee5\u770b\u51fa\u76ee\u6807\u51fd\u6570\u4e2d\u672a\u77e5\u7684\u53d8\u91cf\u53ea\u6709$\\omega$\uff0c\u56e0\u6b64\u9700\u8981\u6c42\u51fa\u80fd\u4f7f\u76ee\u6807\u51fd\u6570\u503c\u6700\u5c0f\u7684$\\omega$\u3002<\/p>\n
    3.4\u611f\u77e5\u673a\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570\u539f\u59cb\u5f62\u5f0f<\/h2>\n
      \u5047\u8bbe\u611f\u77e5\u673a\u7684\u76ee\u6807\u51fd\u6570\u4e3a
    \n
    \"file\"<\/div>
    \n  \u4e3a\u4e86\u6c42\u8be5\u51fd\u6570\u7684\u6700\u5c0f\u503c\u4e00\u822c\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\uff0c\u9996\u5148\u901a\u8fc7\u8be5\u76ee\u6807\u51fd\u6570\u53ef\u4ee5\u6c42\u51fa\u76ee\u6807\u51fd\u6570\u5bf9$\\omega$\u7684\u504f\u5bfc\u4e3a
    \n
    \"file\"<\/div>
    \n  \u5728\u8bad\u7ec3\u96c6\u4e2d\u9009\u53d6\u4e00\u4e2a\u6570\u636e$(x_i, y_i)$\uff0c\u8bbe\u5b9a$\\omega=0$\uff0c\u5982\u679c$-y_i(\\omega^Tx_i)>0$\uff0c\u5219\u5bf9$\\omega$\u4f7f\u7528\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u8fed\u4ee3\u66f4\u65b0
    \n
    \"file\"<\/div>
    \n  \u5176\u4e2d$\\alpha(0<\\alpha\\leq1)$\u662f\u81ea\u5b9a\u4e49\u7684\u8d85\u53c2\u6570\u79f0\u4e3a\u5b66\u4e60\u7387(learning rate)<\/code>\u3002<\/p>\n
      \u901a\u8fc7\u5bf9$\\omega$\u4e0d\u65ad\u5730\u66f4\u65b0\u76f4\u5230\u8bad\u7ec3\u96c6\u4e2d\u6ca1\u6709\u8bef\u5206\u7c7b\u7684\u70b9\u65f6\u66f4\u65b0\u505c\u6b62\u3002\u5373\u53ef\u6c42\u51fa\u76ee\u6807\u51fd\u6570$J(\\omega)$\u7684\u6700\u5c0f\u503c\uff0c\u5219\u8be5$\\omega$\u5373\u6700\u540e\u611f\u77e5\u673a\u6a21\u578b\u7684\u6700\u4f18$\\omega$\u3002<\/p>\n
      \u8fd9\u79cd\u5b66\u4e60\u7b97\u6cd5\u53ef\u4ee5\u7406\u89e3\u6210\uff0c\u5f53\u5b9e\u4f8b\u70b9\u88ab\u8bef\u5206\u7c7b\u540e\uff0c\u5219\u8c03\u6574$\\omega$\u7684\u503c\uff0c\u4f7f\u8d85\u5e73\u9762\u5411\u9760\u8bef\u5206\u7c7b\u70b9\u7684\u4e00\u4fa7\u79fb\u52a8\uff0c\u56e0\u6b64\u51cf\u5c11\u8be5\u8bef\u5206\u7c7b\u70b9\u4e0e\u8d85\u5e73\u9762\u95f4\u7684\u8ddd\u79bb\uff0c\u76f4\u81f3\u8d85\u5e73\u9762\u8d8a\u8fc7\u8be5\u8bef\u5206\u7c7b\u70b9\u5c06\u5176\u5206\u7c7b\u6b63\u786e\uff1b\u5f53\u5b9e\u4f8b\u70b9\u5206\u7c7b\u6b63\u786e\uff0c\u5219\u4e0d\u4f1a\u66f4\u65b0$\\omega$\u3002<\/p>\n
    3.5\u611f\u77e5\u673a\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570\u5bf9\u5076\u5f62\u5f0f<\/h2>\n
      \u901a\u8fc7\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u53ef\u4ee5\u5f97\u5230\u4e86\u4e00\u4e2a\u8f83\u597d\u7684\u611f\u77e5\u673a\u6a21\u578b\uff0c\u4f46\u662f\u5982\u679c\u6837\u672c\u7279\u5f81\u8f83\u591a\u6216\u8005\u8bef\u5206\u7c7b\u7684\u6570\u636e\u8f83\u591a\uff0c\u8ba1\u7b97\u5c06\u6210\u4e3a\u8be5\u7b97\u6cd5\u7684\u6700\u5927\u7684\u4e00\u4e2a\u9ebb\u70e6\uff0c\u63a5\u4e0b\u6765\u5c06\u4ecb\u7ecd\u8ba1\u7b97\u91cf\u8f83\u5c11\u7684\u611f\u77e5\u673a\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570\u7684\u5bf9\u5076\u5f62\u5f0f\uff0c\u901a\u8fc7\u8be5\u65b9\u6cd5\uff0c\u5c06\u6781\u5927\u5730\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002<\/p>\n
      \u5047\u8bbe\u8bef\u5206\u7c7b\u70b9$(x_i,y_i)$\u901a\u8fc7\u68af\u5ea6\u4e0b\u964d\u7b97\u6cd5\u4fee\u6539$\\omega$\u5171$n_i$\u6b21\uff0c\u8bef\u5206\u7c7b\u70b9\u6bcf\u6b21\u589e\u91cf$\\alpha{x_i}y_i$\uff0c\u5219$\\omega$\u7684\u589e\u91cf\u662f$\\alpha{n_i}x_iy_i$\uff0c\u800c\u6b63\u786e\u5206\u7c7b\u70b9\u7684$n_i$\u5219\u521d\u59cb\u5316\u4e3a$0$\uff0c\u56e0\u6b64\u6240\u6709\u5b9e\u4f8b\u7684\u603b\u589e\u91cf\u4e3a
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d$n_i$\u521d\u59cb\u503c\u4e3a$0$\uff0c\u6bcf\u5f53\u8bef\u5206\u7c7b\u70b9\u56e0\u8bef\u5206\u7c7b\u800c\u68af\u5ea6\u66f4\u65b0\u65f6\u5219$n_i+1$\u3002<\/p>\n
      \u901a\u8fc7\u8bef\u5206\u7c7b\u70b9\u7684\u603b\u589e\u91cf\u516c\u5f0f\u5373\u53ef\u5f97\u5230\u4e00\u4e2a\u65b0\u7684\u611f\u77e5\u673a\u76ee\u6807\u51fd\u6570\u4e3a
    \n
    \"file\"<\/div>
    \n  \u5bf9\u76ee\u6807\u51fd\u6570\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u6cd5\u6c42\u6700\u5c0f\u5316\u76ee\u6807\u51fd\u6570\uff0c\u5373\u5bf9$\\alpha{n_i}$\u6c42\u504f\u5bfc\u5f97
    \n
    \"file\"<\/div>
    \n  \u5728\u8bad\u7ec3\u96c6\u4e2d\u9009\u53d6\u4e00\u4e2a\u70b9$(x_j, y_j)$\uff0c\u8bbe\u5b9a$\\alpha=0, n_i=0, \\quad (i=1,2,\\cdots,m)$\uff0c\u5982\u679c$-y_i(\\alpha{n_i}x_ix_j)>0$\uff0c\u5219\u5bf9$\\alpha{n_i}$\u4f7f\u7528\u968f\u673a\u68af\u5ea6\u4e0b\u964d\u7684\u8fed\u4ee3\u66f4\u65b0
    \n
    \"file\"<\/div>
    \n  \u901a\u8fc7\u5bf9$\\alpha{n_i}$\u4e0d\u65ad\u5730\u66f4\u65b0\u76f4\u5230\u8bad\u7ec3\u96c6\u4e2d\u6ca1\u6709\u8bef\u5206\u7c7b\u7684\u70b9\u65f6\u66f4\u65b0\u505c\u6b62\u3002\u5373\u53ef\u6c42\u51fa\u76ee\u6807\u51fd\u6570$J(\\alpha{ni})$\u7684\u6700\u5c0f\u503c\uff0c\u540c\u65f6\u53ef\u4ee5\u5f97\u5230\u6700\u4f18\u7684$\\sum<\/em>{i=1}^m\\alpha{n_i}x_iyi$\uff0c\u7531\u4e8e$\\omega = \\sum<\/em>{i=1}^m\\alpha{n_i}x_iy_i$\u5373\u4e5f\u53ef\u4ee5\u5f97\u5230\u611f\u77e5\u673a\u6a21\u578b\u7684\u6700\u4f18$\\omega$\u3002<\/p>\n
      \u5bf9\u5076\u5f62\u5f0f\u4e2d\u5728\u5224\u65ad\u8bef\u5206\u7c7b\u70b9\u7684\u65f6\u5019\u662f\u8ba1\u7b97$x_i,x_j$\u4e24\u4e2a\u6837\u672c\u7684\u5185\u79ef\uff0c\u56e0\u6b64\u4e3a\u4e86\u65b9\u4fbf\u53ef\u4ee5\u9884\u5148\u5c06\u8bad\u7ec3\u96c6\u4e2d\u6837\u672c\u4e4b\u95f4\u7684\u5185\u79ef\u8ba1\u7b97\u51fa\u6765\u5e76\u4ee5\u77e9\u9635\u7684\u5f62\u5f0f\u5b58\u50a8\uff0c\u8fd9\u4e2a\u77e9\u9635\u5c31\u662f\u6240\u8c13\u7684Gram\u77e9\u9635(Gram matrix)<\/code>\uff0c\u8fd9\u4e5f\u6b63\u662f\u5bf9\u5076\u5f62\u5f0f\u6bd4\u539f\u59cb\u5f62\u5f0f\u8ba1\u7b97\u901f\u5ea6\u66f4\u5feb\u7684\u539f\u56e0\u4e4b\u4e00\u3002<\/p>\n
    3.6\u611f\u77e5\u673a\u7b97\u6cd5\u7684\u6536\u655b\u6027<\/h2>\n
    \"\"<\/div><\/p>\n
      \u611f\u77e5\u673a\u7b97\u6cd5\u4e2d\u6240\u6709\u8bef\u5206\u7c7b\u70b9\u5230\u8d85\u5e73\u9762\u7684\u603b\u8ddd\u79bb\u4e3a
    \n
    \"file\"<\/div>
    \n  \u901a\u5e38\u60c5\u51b5\u4e0b\u9ed8\u8ba4$||w||2$\u4e3a1(\u6ce8\uff1a\u652f\u6301\u5411\u91cf\u673a\u4f1a\u8bb2\u5230\u4e3a\u4ec0\u4e48\u4e3a1)\uff0c\u5373\u5b58\u5728\u6ee1\u8db3\u6761\u4ef6$||\\hat{w}<\/em>{opt}||=1$\u7684\u8d85\u5e73\u9762$\\hat{w}{opt}^T\\hat{x}=0$\u5c06\u6570\u636e\u96c6\u5b8c\u5168\u6b63\u786e\u5206\u5f00\uff0c\u5373\u5f53$\\hat{w}<\/em>{opt}^T\\hat{x}>0$\uff0c\u5219$yi>0$\uff1b\u5f53$\\hat{w}<\/em>{opt}^T\\hat{x}<0$\uff0c\u5219$y_i<0$\u3002\u56e0\u6b64\u4e00\u5b9a\u5b58\u5728$\\gamma>0$\uff0c\u5bf9\u4efb\u4f55\u4e00\u4e2a\u6837\u672c$(x_i,y_i)$\u90fd\u6709
    \n
    \"file\"<\/div>
    \n  \u5f53$1\\geq{i}\\leq{n}$\u65f6$R=max||\\hat{x_i}||$\uff0c\u5219\u611f\u77e5\u673a\u7b97\u6cd5\u5728\u8bad\u7ec3\u96c6\u4e0a\u7684\u8bef\u5206\u7c7b\u6b21\u6570$k$\u6ee1\u8db3
    \n
    \"file\"<\/div><\/p>\n
    4\u611f\u77e5\u673a\u6d41\u7a0b<\/h1>\n
    4.1\u8f93\u5165<\/h2>\n
      \u6709$m$\u4e2a\u5b9e\u4f8b$n$\u7ef4\u7279\u5f81\u7684\u6570\u636e\u96c6
    \n
    \"file\"<\/div>
    \n\u5176\u4e2d$x_i$\u662f\u5b9e\u4f8b\u7684\u7279\u5f81\u5411\u91cf\u5373$({x_i}^{(1)},{x_i}^{(2)},\\cdots,{x_i}^{(n)})$\u3002<\/p>\n
    4.2\u8f93\u51fa<\/h2>\n
      $\\omega$\u548c\u611f\u77e5\u673a\u6a21\u578b$f(x)=sign(\\omega^Tx)$\u3002<\/p>\n
    4.3\u539f\u59cb\u5f62\u5f0f\u6d41\u7a0b<\/h2>\n
      \n
    1. \u9009\u53d6\u521d\u503c$\\omega=0$<\/li>\n
    2. \u8bad\u7ec3\u96c6\u4e2d\u9009\u53d6\u6570\u636e$(x_i,y_i)$\uff0c\u5982\u679c$-y_i(\\omega^Tx_i)>0$\uff0c\u5219\u5bf9$\\omega$\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u66f4\u65b0<\/li>\n<\/ol>\n
      \"file\"<\/div><\/p>\n
        \n
      1. \u91cd\u590d\u6b65\u9aa42\uff0c\u76f4\u81f3\u8bad\u7ec3\u96c6\u4e2d\u6ca1\u6709\u8bef\u5206\u7c7b\u70b9<\/li>\n
      2. \u5f97\u5230\u6700\u5c0f\u5316\u7684\u76ee\u6807\u51fd\u6570$J(\\omega)$\uff0c\u540c\u65f6\u53ef\u4ee5\u5f97\u5230\u6700\u4f18\u7684$\\omega^$\uff0c\u611f\u77e5\u673a\u6a21\u578b\u4e3a$f(x)=sign({w^<\/em>}^Tx)$<\/li>\n<\/ol>\n
        4.4\u5bf9\u5076\u5f62\u5f0f\u6d41\u7a0b<\/h2>\n
          \n
        1. \u9009\u53d6\u521d\u503c$\\alpha=0, n_i=0, \\quad (i=1,2,\\cdots,m)$<\/li>\n
        2. \u8bad\u7ec3\u96c6\u4e2d\u9009\u53d6\u6570\u636e$(x_j,y_j)$\uff0c\u5982\u679c$-y_j(\\alpha{n_i}x_ix_j)>0$\uff0c\u5219\u5bf9$\\alpha{n_i}$\u4f7f\u7528\u68af\u5ea6\u4e0b\u964d\u66f4\u65b0\u5e76\u66f4\u65b0\u8be5\u5b9e\u4f8b\u5206\u7c7b\u9519\u8bef\u7684\u6b21\u6570$n_i$<\/li>\n<\/ol>\n
          \"file\"<\/div><\/p>\n
            \n
          1. \u91cd\u590d\u6b65\u9aa42\uff0c\u76f4\u81f3\u8bad\u7ec3\u96c6\u4e2d\u6ca1\u6709\u8bef\u5206\u7c7b\u70b9<\/li>\n
          2. \u5f97\u5230\u6700\u5c0f\u5316\u7684\u76ee\u6807\u51fd\u6570$J(\\alpha{ni})$\uff0c\u540c\u65f6\u53ef\u4ee5\u5f97\u5230\u6700\u4f18\u7684$\\sum<\/em>{i=1}^m\\alpha{n_i}x_iyi$\uff0c\u7531\u4e8e$\\omega = \\sum<\/em>{i=1}^m\\alpha{n_i}x_iy_i$\u5373\u4e5f\u53ef\u4ee5\u5f97\u5230\u611f\u77e5\u673a\u6a21\u578b\u7684\u6700\u4f18$\\omega^$\uff0c\u611f\u77e5\u673a\u6a21\u578b\u4e3a$f(x)=sign({w^<\/em>}^Tx)$\u3002<\/li>\n<\/ol>\n
            5\u611f\u77e5\u673a\u4f18\u7f3a\u70b9<\/h1>\n
            5.1\u4f18\u70b9<\/h2>\n
              \n
            1. \u7b80\u5355\u6613\u61c2\uff0c\u7f16\u7a0b\u5b9e\u73b0\u5bb9\u6613<\/li>\n
            2. \u7531\u4e8e\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u548c\u795e\u7ecf\u7f51\u7edc\u7b49\u7b97\u6cd5\u5728\u6b64\u57fa\u7840\u4e0a\u6539\u8fdb\u7684\uff0c\u611f\u77e5\u673a\u5728\u4e00\u5b9a\u7a0b\u5ea6\u4e0a\u503c\u5f97\u7ec6\u7ec6\u4f53\u4f1a<\/li>\n<\/ol>\n
              5.2\u7f3a\u70b9<\/h2>\n
                \n
              1. \u76ee\u524d\u5728\u5de5\u4e1a\u4e0a\u4f7f\u7528\u7684\u8f83\u5c11(\u592a\u53e4\u8001\u4e86\uff0c\u6ca1\u8f99\uff01)<\/li>\n
              2. \u53ea\u80fd\u5904\u7406\u7ebf\u6027\u53ef\u5206\u7684\u6570\u636e(\u5b83\u7684\u540e\u4ee3\u652f\u6301\u5411\u91cf\u673a\u548c\u795e\u7ecf\u7f51\u7edc\u5b8c\u7f8e\u7684\u89e3\u51b3\u4e86\u8fd9\u4e2a\u7f3a\u70b9)<\/li>\n
              3. \u65e0\u6cd5\u89e3\u51b3\u56de\u5f52\u95ee\u9898(\u8bd5\u7740\u4f7f\u7528\u56de\u5f52\u652f\u6301\u5411\u91cf\u673a\uff1f)<\/li>\n<\/ol>\n
                6\u5c0f\u7ed3<\/h1>\n
                  \u611f\u77e5\u673a\u7b97\u6cd5\u6700\u5927\u7684\u524d\u63d0\u5219\u662f\u6570\u636e\u96c6\u9700\u8981\u7ebf\u6027\u53ef\u5206\uff0c\u8fd9\u4e5f\u6b63\u662f\u611f\u77e5\u673a\u7b97\u6cd5\u6700\u5927\u7684\u5c40\u9650\u6027\u3002\u4e3a\u4e86\u89e3\u51b3\u7ebf\u6027\u4e0d\u53ef\u5206\u6570\u636e\u7684\u5206\u7c7b\u95ee\u9898\uff0c\u56e0\u6b64\u5728\u6b64\u611f\u77e5\u673a\u7b97\u6cd5\u7684\u57fa\u7840\u4e0a\u53d1\u660e\u4e86\u975e\u7ebf\u6027\u652f\u6301\u5411\u91cf\u673a\u3001\u795e\u7ecf\u7f51\u7edc\u7b49\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u3002<\/p>\n
                  \u611f\u77e5\u673a\u7b97\u6cd5\u867d\u7136\u73b0\u5728\u7528\u7684\u5f88\u5c11\u4e86\uff0c\u4f46\u662f\u5982\u679c\u80fd\u6df1\u523b\u4e86\u89e3\u611f\u77e5\u673a\u7b97\u6cd5\u7684\u5bf9\u5076\u5f62\u5f0f\u4e3a\u4ec0\u4e48\u6bd4\u539f\u59cb\u5f62\u5f0f\u66f4\u5feb\u7684\u505a\u5230\u7b97\u6cd5\u6536\u655b\u4f1a\u8ba9\u4f60\u672a\u6765\u5b66\u4e60\u5176\u4ed6\u7684\u673a\u5668\u5b66\u4e60\u7b97\u6cd5\u8f7b\u677e\u4e0d\u5c11\u3002<\/p>\n
                  \u611f\u77e5\u673a\u5176\u5b9e\u7528\u5230\u4e86\u90e8\u5206\u7ebf\u6027\u6a21\u578b\u77e5\u8bc6\uff0c\u81f3\u4e8e\u7ebf\u6027\u6a21\u578b\u662f\u4ec0\u4e48\uff0c\u4e0b\u4e00\u7bc7\u5373\u4f1a\u63ed\u6653\u2014\u2014\u7ebf\u6027\u56de\u5f52\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
                \u611f\u77e5\u673a   \u611f\u77e5\u673a\u57281957\u5e74\u88ab\u63d0\u51fa\uff0c\u7b97\u662f\u6700\u53e4\u8001\u7684\u5206\u7c7b\u65b9\u6cd5\u4e4b\u4e00\u3002    […]<\/p>\n","protected":false},"author":3,"featured_media":2946,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,285],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/2964"}],"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=2964"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/2964\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/media\/2946"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2964"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2964"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2964"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}