{"id":3333,"date":"2022-02-27T15:10:46","date_gmt":"2022-02-27T07:10:46","guid":{"rendered":"https:\/\/egonlin.com\/?p=3333"},"modified":"2022-02-27T15:10:46","modified_gmt":"2022-02-27T07:10:46","slug":"%e7%ac%ac%e4%ba%94%e7%af%87%ef%bc%9a%e5%89%8d%e5%90%91%e9%80%89%e6%8b%a9%e6%b3%95%e5%92%8c%e5%89%8d%e5%90%91%e6%a2%af%e5%ba%a6%e6%b3%95","status":"publish","type":"post","link":"https:\/\/egonlin.com\/?p=3333","title":{"rendered":"\u7b2c\u4e94\u7bc7\uff1a\u524d\u5411\u9009\u62e9\u6cd5\u548c\u524d\u5411\u68af\u5ea6\u6cd5"},"content":{"rendered":"

\u524d\u5411\u9009\u62e9\u6cd5\u548c\u524d\u5411\u68af\u5ea6\u6cd5<\/h1>\n

  \u7531\u4e8e\u524d\u5411\u9009\u62e9\u6cd5\u548c\u524d\u5411\u68af\u5ea6\u6cd5\u7684\u5b9e\u73b0\u539f\u7406\u6d89\u53ca\u8fc7\u591a\u7684\u77e9\u9635\u8fd0\u7b97\uff0c\u672c\u6587\u53ea\u7ed9\u51fa\u4e24\u79cd\u7b97\u6cd5\u7684\u601d\u8def\u3002\u4e24\u8005\u5b9e\u73b0\u90fd\u662f\u628a\u77e9\u9635\u4e2d\u7684\u5411\u91cf\u8fd0\u7b97\u5177\u4f53\u5316\u6210\u5e73\u9762\u51e0\u4f55\u4e2d\u7684\u5411\u91cf\u8fd0\u7b97\u3002<\/p>\n

\u524d\u5411\u9009\u62e9\u6cd5<\/h1>\n

  \u524d\u5411\u9009\u62e9\u6cd5\u662f\u4e00\u79cd\u5178\u578b\u7684\u8d2a\u5fc3\u7b97\u6cd5\u3002<\/p>\n

  \u901a\u5e38\u7528\u524d\u5411\u9009\u62e9\u6cd5\u89e3\u51b3\u7ebf\u6027\u6a21\u578b\u7684\u56de\u5f52\u7cfb\u6570\u3002\u5bf9\u4e8e\u4e00\u4e2a\u6709$m$\u4e2a\u6837\u672c\uff0c\u6bcf\u4e2a\u6837\u672c\u6709$n$\u4e2a\u7279\u5f81\u7684\u8bad\u7ec3\u96c6\u800c\u8a00\uff0c\u5047\u8bbe\u53ef\u4ee5\u62df\u5408\u4e00\u4e2a\u7ebf\u6027\u6a21\u578b$Y=\\omega^TX$\uff0c\u5176\u4e2d$Y$\u662f$m1$\u7684\u5411\u91cf\uff0c$X$\u662f$m<\/em>n$\u7684\u77e9\u9635\uff0c$\\omega$\u662f$n*1$\u7684\u5411\u91cf\u3002\u5373\u53ef\u901a\u8fc7\u524d\u5411\u9009\u62e9\u6cd5\u6c42\u5f97\u6700\u5c0f\u5316\u8be5\u6a21\u578b\u7684\u53c2\u6570$\\omega$\u3002<\/p>\n

\u4f59\u5f26\u76f8\u4f3c\u5ea6\u6c42\u6295\u5f71<\/h2>\n

  \u9996\u5148\u628a\u77e9\u9635$X$\u770b\u6210$n$\u4e2a$m1$\u7684\u5411\u91cf$X_i \\quad(i=1,2,\\cdots,n)$\uff0c\u4e4b\u540e\u9009\u62e9\u4e0e\u5411\u91cf$Y$\u4f59\u5f26\u76f8\u4f3c\u5ea6\u6700\u5927\uff0c\u5373\u4e0e$Y$\u6700\u4e3a\u63a5\u8fd1\u7684\u4e00\u4e2a\u53d8\u91cf$X_i$\uff0c\u7136\u540e\u7528$X_i$\u903c\u8fd1$Y$\uff0c\u5373\u53ef\u5f97\u5230
\n$$
\n\\hat{Y}=X_i\\omega_i
\n$$
\n\u5176\u4e2d$\\omega_i={\\frac{<X_i,Y>}{{||X_i||}^2}}\\quad\\text{\u4f59\u5f26\u76f8\u4f3c\u5ea6}$\uff0c\u5176\u4e2d$<X_i,Y>=|Y|<\/em>\\cos\\alpha$\uff0c$\\alpha$\u662f$X_i$\u548c$Y$\u7684\u5939\u89d2\u3002<\/p>\n

\u4e0a\u8ff0\u516c\u5f0f\u56e0\u6b64\u53ef\u4ee5\u8ba4\u4e3a$\\hat{Y}$\u662f$Y$\u5728$X_i$\u4e0a\u7684\u6295\u5f71\u3002<\/p>\n

  \u5f97\u5230$Y$\u7684\u63a5\u8fd1\u503c$\\hat{Y}$\u540e\u65e2\u53ef\u4ee5\u5f97\u5230\u6b8b\u5dee\u503c\u4e3a$Y_{err}=Y-\\hat{Y}$\uff0c\u7531\u4e8e$\\hat{Y}$\u662f\u6295\u5f71\uff0c\u5219$\\hat{Y}$\u548c$Xi$\u662f\u6b63\u4ea4\u7684\uff0c\u56e0\u6b64\u53ef\u4ee5\u4ee5$Y<\/em>{err}$\u4e3a\u65b0\u7684\u53d8\u91cf\uff0c\u4ece\u5269\u4e0b\u7684$Xi\\quad(i=1,2,i-1,i+2,\\cdots,n)$\u4e2d\uff0c\u9009\u62e9\u4e00\u4e2a\u65b0\u7684\u6700\u63a5\u8fd1\u6b8b\u5dee$Y<\/em>{err}$\u7684$X_i$\u91cd\u590d\u4e0a\u8ff0\u6295\u5f71\u548c\u8ba1\u7b97\u6b8b\u5dee\u7684\u6d41\u7a0b\uff0c\u76f4\u81f3\u6b8b\u5dee\u4e3a0\uff0c\u505c\u6b62\u7b97\u6cd5\u3002\u5373\u53ef\u5f97\u5230$\\omega$\u3002<\/p>\n

\u4e3e\u4f8b<\/h2>\n
# \u4e3e\u4f8b\u56fe\u4f8b\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n\n# X1*w1\nplt.annotate(xytext=(2, 5), xy=(8, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(6, 4.5, s='$X_1*\\omega_1$', color='g')\n# X2*w2\nplt.annotate(xytext=(8, 5), xy=(9.3, 7.5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(9.3, 7, s='$X_2*\\omega_2$', color='g')\n# X1\nplt.annotate(xytext=(2, 5), xy=(4, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(2.5, 4.5, s='$X_1$', color='g')\n# X2\nplt.annotate(xytext=(2, 5), xy=(3, 7), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(2, 6, s='$X_2$', color='g')\n# X2\nplt.annotate(xytext=(8, 5), xy=(9, 7), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(8.2, 6.5, s='$X_2$', color='g')\n# Y\nplt.annotate(xytext=(2, 5), xy=(8, 8), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(5, 7.5, s='$Y$', color='g')\n#\nplt.annotate(xytext=(8, 5), xy=(8, 8), s='', color='r',\n             arrowprops=dict(arrowstyle="-", color='gray'))\nplt.text(7.5, 6.5, s='$Y_1$', color='g')\n#\nplt.annotate(xytext=(8, 8), xy=(9.3, 7.5), s='',\n             arrowprops=dict(arrowstyle="-", color='gray'))\nplt.text(8.5, 8, s='$Y_2$', color='g')\n\nplt.xlim(0, 11)\nplt.ylim(2, 10)\nplt.title('\u524d\u5411\u9009\u62e9\u6cd5\u4e3e\u4f8b', fontproperties=font, fontsize=20)\nplt.show()<\/code><\/pre>\n
\"\"<\/div><\/p>\n
  \u4e0a\u56fe\u5047\u8bbe$X$\u4e3a$2$\u7ef4\uff0c\u9996\u5148\u53ef\u4ee5\u770b\u51fa\uff0c\u79bb$Y$\u6700\u63a5\u8fd1\u7684\u662f$X_1$\uff0c\u56e0\u6b64\u753b\u51fa$Y$\u5728$X_1$\u4e0a\u7684\u6295\u5f71\u7ea2\u7ebf$X_1\\omega_1$\uff0c\u6b64\u65f6\u6b8b\u5dee\u4e3a\u7070\u7ebf$Y_1$\u3002\u7531\u4e8e\u76ee\u524d\u53ea\u5269\u4e0b$X_2$\uff0c\u6240\u4ee5\u63a5\u7740\u7528\u6b8b\u5dee$Y_1$\u5728$X_2$\u4e0a\u6295\u5f71\u5f97\u5230\u7ea2\u7ebf$X_2<\/em>\\omega_2$\uff0c\u5982\u679c\u4e0d\u53ea\u662f$X_2$\uff0c\u5219\u9009\u62e9\u6700\u63a5\u8fd1$Y_1$\u7684$X_i$\u3002\u6b64\u65f6\u7684$X_1\\omega_1+X_2\\omega_2$\u5219\u6a21\u62df\u4e86$Y$\uff0c\u5373$\\omega=[\\omega_1,\\omega_2]$\u3002<\/p>\n
\u524d\u5411\u9009\u62e9\u6cd5\u4f18\u7f3a\u70b9<\/h2>\n
\u4f18\u70b9<\/h3>\n
    \n
  1. \u7b97\u6cd5\u5bf9\u6bcf\u4e2a$X_i$\u53ea\u505a\u4e00\u6b21\u64cd\u4f5c\uff0c\u901f\u5ea6\u5feb\u3002<\/li>\n<\/ol>\n
    \u7f3a\u70b9<\/h3>\n
      \n
    1. \u7531\u4e8e\u53d8\u91cf$X_i$\u4e4b\u95f4\u4e0d\u662f\u6b63\u4ea4\u7684\uff0c\u6240\u4ee5\u6bcf\u6b21\u90fd\u5fc5\u987b\u505a\u6295\u5f71\u7f29\u5c0f\u6b8b\u5dee\uff0c\u6240\u4ee5\u524d\u5411\u9009\u62e9\u6cd5\u6700\u540e\u53ea\u80fd\u7ed9\u51fa\u4e00\u4e2a\u5c40\u90e8\u8fd1\u4f3c\u89e3\u3002(\u53ef\u4ee5\u8003\u8651\u4e0b\u9762\u7684\u524d\u5411\u68af\u5ea6\u6cd5)<\/li>\n<\/ol>\n
      \u524d\u5411\u68af\u5ea6\u6cd5<\/h1>\n
        \u524d\u5411\u68af\u5ea6\u6cd5\u7c7b\u4f3c\u4e8e\u524d\u5411\u9009\u62e9\u6cd5\uff0c\u4e0d\u540c\u4e4b\u5904\u5728\u4e8e\u524d\u5411\u68af\u5ea6\u6cd5\u5e9f\u9664\u4e86\u524d\u5411\u9009\u62e9\u6cd5\u7684\u6295\u5f71\u903c\u8fd1$Y$\uff0c\u53d6\u800c\u4ee3\u4e4b\u7684\u662f\u5728\u6bcf\u6b21\u6700\u63a5\u8fd1$Y$\u7684\u5411\u91cf$X_i$\u7684\u65b9\u5411\u4e0a\u79fb\u52a8\u4e00\u5c0f\u6b65\uff0c\u5e76\u4e14\u5411\u91cf$X_i$\u79fb\u52a8\u4f1a\u4e0d\u4f1a\u88ab\u5254\u9664\uff0c\u800c\u662f\u7ee7\u7eed\u4ece$Xi \\quad(i=1,2,i-1,i,i+1,\\cdots,n)$\u4e2d\u9009\u62e9\u4e00\u4e2a\u6700\u63a5\u8fd1\u6b8b\u5dee$Y<\/em>{err}$(\u6ce8\uff1a\u6b8b\u5dee\u8ba1\u7b97\u65b9\u5f0f\u7c7b\u4f3c\u4e8e\u524d\u5411\u9009\u62e9\u6cd5)\u7684\u5411\u91cf$X_i$\uff0c\u7136\u540e\u518d\u8d70\u4e00\u5c0f\u6b65\uff0c\u76f4\u81f3\u6b8b\u5dee\u4e3a0\uff0c\u505c\u6b62\u7b97\u6cd5\uff0c\u5373\u53ef\u5f97\u5230$\\omega$\u3002<\/p>\n
      \u4e3e\u4f8b<\/h2>\n
      # \u4e3e\u4f8b\u56fe\u4f8b\nimport matplotlib.pyplot as plt\nfrom matplotlib.font_manager import FontProperties\n%matplotlib inline\nfont = FontProperties(fname='\/Library\/Fonts\/Heiti.ttc')\n\n# X1\nplt.annotate(xytext=(2, 5), xy=(3, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(2.4, 4.8, s='$\\epsilon{X_1}$', color='g')\n# eX1\nplt.annotate(xytext=(2, 5), xy=(4, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(3.2, 4.8, s='$\\epsilon{X_1}$', color='g')\n# eX1\nplt.annotate(xytext=(2, 5), xy=(5, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(4.2, 4.8, s='$\\epsilon{X_1}$', color='g')\n# eX1\nplt.annotate(xytext=(2, 5), xy=(2.8, 5), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(1.9, 4.8, s='$X_1$', color='g')\n# eX1\nplt.annotate(xytext=(6.1, 6.2), xy=(7, 6.2), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(6.2, 6, s='$\\epsilon{X_1}$', color='g')\n\n# ex2\nplt.annotate(xytext=(5, 5), xy=(6.2, 6.2), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='r'))\nplt.text(5.2, 5.8, s='$\\epsilon{X_2}$', color='g')\n# X2\nplt.annotate(xytext=(2, 5), xy=(3, 6), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(2, 5.5, s='$X_2$', color='g')\n# X2\nplt.annotate(xytext=(5, 5), xy=(6, 6), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(5.6, 5.5, s='$X_2$', color='g')\n\n# Y\nplt.annotate(xytext=(2, 5), xy=(8, 7), s='', color='r',\n             arrowprops=dict(arrowstyle="->", color='k'))\nplt.text(5, 6.2, s='$Y$', color='g')\n\nplt.annotate(xytext=(5, 5), xy=(8, 7), s='', color='r',\n             arrowprops=dict(arrowstyle="-", color='gray'))\n\nplt.xlim(1, 9)\nplt.ylim(4, 8)\nplt.title('\u524d\u5411\u68af\u5ea6\u6cd5\u4e3e\u4f8b', fontproperties=font, fontsize=20)\nplt.show()<\/code><\/pre>\n
      \"\"<\/div><\/p>\n
        \u4e0a\u56fe\u5047\u8bbe$X$\u4e3a$2$\u7ef4\uff0c\u9996\u5148\u53ef\u4ee5\u770b\u51fa\uff0c\u79bb$Y$\u6700\u63a5\u8fd1\u7684\u662f$X_1$\uff0c\u56e0\u6b64\u6cbf\u7740\u5411\u91cf$Xi$\u7684\u65b9\u5411\u8d70\u4e0a\u4e00\u6bb5\u8ddd\u79bb\uff0c\u6b64\u5904\u7684$\\epsilon$\u662f\u4e00\u4e2a\u624b\u52a8\u8c03\u6574\u7684\u8d85\u53c2\u6570\uff0c\u8d70\u4e86\u4e00\u6bb5\u8ddd\u79bb\u540e\u53d1\u73b0\uff0c\u79bb\u6b8b\u5dee$Y<\/em>{err}$\u6700\u8fd1\u63a5\u7684\u8fd8\u662f$X1$\uff0c\u56e0\u6b64\u7ee7\u7eed\u63a5\u7740\u8d70\u4e00\u6bb5\u8ddd\u79bb\uff0c\u76f4\u5230\u8d70\u5230\u79bb\u6b8b\u5dee$Y<\/em>{err}$\u6700\u8fd1\u7684\u4e3a$X_2$\u7684\u65f6\u5019\uff0c\u6cbf\u7740\u5411\u91cf$X2$\u7684\u65b9\u5411\u8d70\u4e0a\u4e00\u6bb5\u8ddd\u79bb\uff0c\u53d1\u73b0\u6b64\u65f6\u6b8b\u5dee$Y<\/em>{err}$\u79bb$X_1$\u66f4\u8fd1\uff0c\u5219\u6cbf\u7740$X_1$\u8d70\u4e00\u6bb5\u8ddd\u79bb\uff0c\u76f4\u5230\u8d70\u5230\u6700\u540e\u6b8b\u5dee\u4e3a0\uff0c\u505c\u6b62\u7b97\u6cd5\uff0c\u5373\u53ef\u5f97\u5230$\\omega$\u3002<\/p>\n
      \u524d\u5411\u68af\u5ea6\u6cd5\u4f18\u7f3a\u70b9<\/h2>\n
      \u4f18\u70b9<\/h3>\n
        \n
      1. \u53ef\u4ee5\u624b\u52a8\u63a7\u5236$\\epsilon$\u7684\u5927\u5c0f\uff0c\u5373\u53ef\u4ee5\u63a7\u5236\u7b97\u6cd5\u7684\u7cbe\u51c6\u5ea6\uff0c\u5982\u679c$\\epsilon$\u8f83\u5c0f\u7684\u65f6\u5019\u7b97\u6cd5\u7cbe\u51c6\u5ea6\u5f88\u9ad8<\/li>\n<\/ol>\n
        \u7f3a\u70b9<\/h3>\n
          \n
        1. $\\epsilon$\u5c0f\uff0c\u7b97\u6cd5\u7cbe\u51c6\u5ea6\u9ad8\uff0c\u540c\u65f6\u7b97\u6cd5\u8fed\u4ee3\u6b21\u6570\u589e\u52a0\uff1b$\\epsilon$\u5927\uff0c\u7b97\u6cd5\u7cbe\u51c6\u5ea6\u964d\u4f4e\u3002\u7c7b\u4f3c\u4e8e\u68af\u5ea6\u4e0b\u964d\uff0c\u8fd9\u662f\u524d\u5411\u68af\u5ea6\u6cd5\u8f83\u5927\u7684\u4e00\u4e2a\u95ee\u9898\u3002(\u53c2\u8003\u6700\u5c0f\u89d2\u56de\u5f52\u6cd5)<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"
          \u524d\u5411\u9009\u62e9\u6cd5\u548c\u524d\u5411\u68af\u5ea6\u6cd5   \u7531\u4e8e\u524d\u5411\u9009\u62e9\u6cd5\u548c\u524d\u5411\u68af\u5ea6\u6cd5\u7684\u5b9e\u73b0\u539f\u7406\u6d89\u53ca\u8fc7\u591a\u7684\u77e9\u9635\u8fd0\u7b97\uff0c\u672c\u6587\u53ea […]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[276,303,304],"tags":[],"_links":{"self":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3333"}],"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=3333"}],"version-history":[{"count":0,"href":"https:\/\/egonlin.com\/index.php?rest_route=\/wp\/v2\/posts\/3333\/revisions"}],"wp:attachment":[{"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3333"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3333"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/egonlin.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3333"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}