{"id":1786,"date":"2016-05-17T08:49:43","date_gmt":"2016-05-17T00:49:43","guid":{"rendered":"http:\/\/systemsci.org\/jinshanw\/?p=1786"},"modified":"2017-11-03T14:31:54","modified_gmt":"2017-11-03T06:31:54","slug":"%e4%bb%8e%e5%85%b1%e7%8e%b0%e5%88%b0%e7%bb%93%e6%9e%84","status":"publish","type":"post","link":"https:\/\/www.systemsci.org\/jinshanw\/2016\/05\/17\/%e4%bb%8e%e5%85%b1%e7%8e%b0%e5%88%b0%e7%bb%93%e6%9e%84\/","title":{"rendered":"\u4ece\u5171\u73b0\u5230\u7ed3\u6784"},"content":{"rendered":"

\u8003\u8651\u4e00\u4e2a\u6982\u5ff5\u7f51\u7edc\uff0c\u5176\u4e2d\u7684\u9876\u70b9\u662f\u6982\u5ff5\uff0c\u8fde\u8fb9\u662f\u6982\u5ff5\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\u3002\u5047\u8bbe\u8fde\u8fb9\u7684\u5b58\u5728\u5c31\u4fdd\u8bc1\u4e86\u4e24\u4e2a\u8fde\u5728\u4e00\u8d77\u7684\u6982\u5ff5\u4ee5\u4e00\u5b9a\u7684\u6982\u7387\u5171\u73b0\u3002\u4e8e\u662f\uff0c\u6211\u4eec\u5f97\u5230\u7ed3\u6784\u77e9\u9635(\\Omega)\u3002<\/p>\n

\u5b9a\u4e49\u603b\u548c\u5173\u7cfb\u77e9\u9635(\\Sigma)\uff0c
\n\\begin{align}
\n\\Sigma = \\Omega + \\Omega^{2}+\\cdots = \\frac{1}{1-\\Omega} – 1.
\n\\end{align}
\n\u4e8e\u662f\uff0c
\n\\begin{align}
\n\\Omega = 1-\\frac{1}{1+\\Sigma}.
\n\\end{align}<\/p>\n

\u7136\u540e\uff0c\u6211\u4eec\u8003\u8651\u4ee5\u4e0b\u7684\u95ee\u9898\uff1a\u5982\u679c\u8fd9\u4e2a\u7f51\u7edc\u6ca1\u6709\u63d0\u4f9b\u7ed9\u6211\u4eec\uff0c\u4f46\u662f\uff0c\u6211\u4eec\u83b7\u5f97\u4e86\u4e00\u4e2a\u6765\u81ea\u4e8e\u5b9e\u8bc1\u6570\u636e\u7684\u5171\u73b0\u77e9\u9635\uff0c\u90a3\u4e48\u8fd9\u4e2a\u5171\u73b0\u77e9\u9635\u5c31\u662f(\\Omega)\u8fd8\u662f(\\Sigma)\uff1f<\/p>\n

\u6362\u4e00\u79cd\u5177\u4f53\u8fc7\u7a0b\u7684\u8bed\u8a00\uff1a\u5047\u8bbe\u6709\u4e00\u4e2a\u4f20\u67d3\u75c5\u76f4\u63a5\u63a5\u89e6\u4f20\u64ad\u7f51\u7edc(\\Omega)\uff0c\u7136\u540e\uff0c\u6211\u4eec\u540c\u6837\u5b9a\u4e49\u603b\u548c\u63a5\u89e6\u4f20\u64ad\u7f51\u7edc(\\Sigma)\uff0c\u95ee\u4ece\u5b9e\u9645\u4f20\u67d3\u8fc7\u7a0b\u53ef\u4ee5\u6d4b\u5f97\u4e00\u4e2a\u540c\u65f6\u53d1\u75c5\u77e9\u9635\uff0c\u8fd9\u4e2a\u77e9\u9635\u662f\u662f(\\Omega)\u8fd8\u662f(\\Sigma)\uff1f<\/p>\n

\u7c7b\u4f3c\u7684\u95ee\u9898\u8fd8\u53ef\u4ee5\u662f\uff1a\u6982\u5ff5\uff08\u6c49\u5b57\uff09\u4e4b\u95f4\u7684\u5185\u5728\u8054\u7cfb\u5bfc\u81f4\u7684\u540c\u65f6\u88ab\u7406\u89e3\u548c\u5b66\u4e60\u2014\u2014\u7ed3\u6784\u77e9\u9635\uff0c\u548c\uff0c\u6982\u5ff5\uff08\u6c49\u5b57\uff09\u4e4b\u95f4\u8868\u73b0\u51fa\u6765\u7684\u53ef\u4ee5\u76f4\u63a5\u68c0\u6d4b\u51fa\u6765\u7684\u540c\u65f6\u88ab\u8ba4\u8bc6\u7406\u89e3\u2014\u2014\u540c\u8bc6\u77e9\u9635\uff0c\u4e4b\u95f4\u7684\u5173\u7cfb\uff1bpacs\u4ee3\u7801\u4e4b\u95f4\u7684\u8868\u73b0\u51fa\u6765\u7684\u53ef\u89c2\u5bdf\u7684\u5171\u73b0\u2014\u2014\u5171\u73b0\u77e9\u9635\uff0c\u548c\uff0cpacs\u4ee3\u7801\u6240\u4ee3\u8868\u7684\u9886\u57df\u548c\u4e3b\u9898\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\u2014\u2014\u7ed3\u6784\u77e9\u9635\uff1b\u82f1\u6587\uff08\u6216\u8005\u4e2d\u6587\uff09\u8bcd\u4e4b\u95f4\u8868\u89c2\u5171\u73b0\u548c\u5185\u5728\u903b\u8f91\u5173\u7cfb\u3002<\/p>\n

\u5047\u5982\uff0c\u8fd9\u4e2a\u77e9\u9635\u662f(\\Sigma)\uff0c\u90a3\u4e48\uff0c\u6211\u4eec\u5c31\u6709\u4e86\u4e00\u4e2a\u4ece\u89c2\u6d4b\u5171\u73b0\u77e9\u9635\u6765\u8ba1\u7b97\u76f4\u63a5\u7ed3\u6784\u77e9\u9635(\\Omega)\u7684\u65b9\u6cd5\u3002<\/p>\n

\u53ef\u80fd\u7684\u5e94\u7528\u60c5\u666f\uff1a<\/p>\n

    \n
  1. \u627e\u4e00\u4e2a\u6c49\u5b57\u5728\u540c\u4e00\u53e5\u8bdd\u91cc\u9762\u5171\u73b0\u7684\u77e9\u9635\uff0c\u5c1d\u8bd5\u4e00\u4e0b\uff0c\u770b\u770b\u7b97\u51fa\u6765\u7684\u76f4\u63a5\u5171\u73b0\uff0c\u662f\u4e0d\u662f\u4ee3\u8868\u4e86\u610f\u4e49\u4e0a\u7684\u8054\u7cfb\u3002<\/li>\n
  2. \u627e\u4e00\u4e2a\u6c49\u5b57\u540c\u88ab\u8ba4\u7684\u77e9\u9635\uff0c\u5c1d\u8bd5\u4e00\u4e0b\uff0c\u770b\u770b\u7b97\u51fa\u6765\u7684\u76f4\u63a5\u88ab\u8ba4\uff0c\u662f\u4e0d\u662f\u4ee3\u8868\u4e86\u6c49\u5b57\u7ed3\u6784\u548c\u610f\u4e49\u4e0a\u7684\u8054\u7cfb\u3002<\/li>\n
  3. \u627e\u4e00\u4e2a\u7269\u7406\u6982\u5ff5\u540c\u88ab\u8ba4\u7684\u77e9\u9635\u2014\u2014\u4f8b\u5982\u901a\u8fc7\u8c03\u67e5\u95ee\u5377\u6765\u8bbf\u95ee\u88ab\u8bd5\u662f\u5426\u542c\u8bf4\u8fc7\u67d0\u4e2a\u6982\u5ff5\u6216\u8005\u540c\u65f6\u5728\u4e00\u904d\u6587\u732e\u4e2d\u51fa\u73b0\uff0c\u5c1d\u8bd5\u4e00\u4e0b\uff0c\u770b\u770b\u7b97\u51fa\u6765\u7684\u76f4\u63a5\u88ab\u8ba4\uff0c\u662f\u4e0d\u662f\u4ee3\u8868\u4e86\u7269\u7406\u6982\u5ff5\u610f\u4e49\u4e0a\u7684\u8054\u7cfb\u3002\u5982\u679c\u8fd9\u4e2a\u80fd\u591f\u505a\u6210\u529f\u2014\u2014\u9700\u8981\u5bf9\u6bd4\u540c\u88ab\u8ba4\u6216\u8005\u5171\u73b0\u77e9\u9635\u7ed9\u51fa\u7684\u4fe1\u606f\u548c\u5904\u7406\u4ee5\u540e\u7684\u76f4\u63a5\u5173\u7cfb\u77e9\u9635\u7ed9\u51fa\u7684\u4fe1\u606f\uff0c\u4f8b\u5982\u96c6\u56e2\u7ed3\u6784\uff0c\u6210\u529f\u6307\u540e\u8005\u8ddf\u6982\u5ff5\u903b\u8f91\u5173\u7cfb\u6709\u5f88\u597d\u7684\u8054\u7cfb\uff0c\u90a3\u4e48\u76f8\u5f53\u4e8e\u6211\u4eec\u80fd\u591f\u4ece\u6587\u732e\u4e2d\u6982\u5ff5\u7684\u5171\u73b0\u6216\u8005\u666e\u901a\u4eba\u5bf9\u6982\u5ff5\u7684\u540c\u8ba4\u4e4b\u4e2d\uff0c\u63d0\u53d6\u51fa\u6765\u6982\u5ff5\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb<\/strong>\u3002<\/li>\n
  4. \u6a21\u62df\u4e00\u4e2a\u4f20\u67d3\u75c5\u4f20\u64ad\u8fc7\u7a0b\uff0c\u8ba1\u7b97\u51fa\u6765\u4efb\u610f\u4e24\u70b9\u4e4b\u95f4\u7684\u540c\u67d3\u75c5\u51e0\u7387\uff0c\u7136\u540e\u8ba1\u7b97\u8fd9\u4e2a\u76f4\u63a5\u8054\u7cfb\u77e9\u9635\uff0c\u770b\u770b\u662f\u4e0d\u662f\u53cd\u6620\u7f51\u7edc\u8fde\u63a5\u3002<\/li>\n
  5. \u627e\u80a1\u7968\u5173\u8054\u6027\u7684\u77e9\u9635\uff0c\u5c1d\u8bd5\u4e00\u4e0b\uff0c\u770b\u770b\u7b97\u51fa\u6765\u7684\u76f4\u63a5\u5173\u7cfb\uff0c\u662f\u4e0d\u662f\u4ee3\u8868\u4e86\u80a1\u7968\u4e4b\u95f4\u7684\u67d0\u79cd\u6709\u610f\u4e49\u7684\u8054\u7cfb\u3002<\/li>\n<\/ol>\n

    \u4e00\u4e2a\u95ee\u9898\uff1a
    \n\u6709\u7684\u65f6\u5019\uff0c\u9700\u8981\u8ba1\u7b97\u51fa\u6765(\\Omega^2)\u4ee5\u540e\u5220\u9664\u5bf9\u89d2\u5143\u7d20\uff0c\u7136\u540e\u518d\u8ba1\u7b97(\\Omega \\left(\\Omega^2-D_{\\Omega^2}\\right))\uff0c\u4e5f\u5c31\u662f\u91cd\u590d\u5254\u9664\u81ea\u5df1\u5230\u81ea\u5df1\u7684\u4f20\u9012\u6548\u76ca\u3002
    \n[\\Sigma=\\left(\\Omega-D_{1}\\right) + \\left(\\left(\\Omega-D_{1}\\right)^2-D_{2}\\right) + \\left(\\left(\\Omega-D_{1}\\right)\\left(\\left(\\Omega-D_{1}\\right)^2-D_{2}\\right)-D_{3}\\right) + \\cdots,]
    \n\u5176\u4e2d\uff0c(D_{j})\u662f\u5bf9\u7b2c(j)\u9879\u7684\u7b80\u5199\u8bb0\u53f7\u3002\u8fd9\u4e2a\u8ba1\u7b97\u6709\u6ca1\u6709\u7b80\u5355\u7684\u5b9e\u73b0\u65b9\u5f0f\uff1f\u4f8b\u5982\uff0c\u662f\u5426\u8fd8\u80fd\u591f\u8868\u8ff0\u6210\u4e3a\u67d0\u79cd\u53d6\u548c\u5f62\u5f0f\u3002\u53cd\u8fc7\u6765\uff0c\u4ece(\\Sigma)\u8ba1\u7b97(\\Omega)\u7684\u65f6\u5019\u90a3\u4e9b\u5bf9\u89d2\u5143\u7d20\u7684\u5982\u4f55\u5254\u9664\uff1f\u662f\u4e0d\u662f\u4e00\u5b9a\u6761\u4ef6\u4e0b\uff0c\u5f53(\\Sigma)\u6ca1\u6709\u5bf9\u89d2\u5143\u7684\u65f6\u5019\uff0c(\\Omega)\u81ea\u7136\u5c31\u4e0d\u4f1a\u6709\u5bf9\u89d2\u5143\uff1f\u539f\u5219\u4e0a\uff0c\u5982\u679c\u6c42\u51fa\u6765\u7684(\\Omega)\u975e\u8d1f\u5c31\u786e\u5b9e\u662f\u8fd9\u6837\u7684\u3002\u4ec0\u4e48\u6761\u4ef6\u4e0b(\\Omega)\u975e\u8d1f\u5462\uff1f<\/p>\n

    \u53c2\u8003\u6587\u732e\uff1a\u5c0f\u601d\u627e\u51fa\u6765\u4e00\u7bc7\u7528\u540c\u6837\u7684\u601d\u8def\u548c\u65b9\u6cd5\u6765\u8ba8\u8bba\u540c\u6837\u7684\u95ee\u9898\u7684\u6587\u7ae0\u2014\u2014Network deconvolution as a general method to distinguish direct dependencies in networks<\/a>\u3002\u8fd9\u4e2a\u5de5\u4f5c\u8ba8\u8bba\u4e86\u5982\u4f55\u4ece\u89c2\u5bdf\u5230\u7684\u7f51\u7edc\u8fde\u63a5\u77e9\u9635(\\Sigma)\u5f97\u5230\u76f4\u63a5\u5173\u7cfb\u77e9\u9635(\\Omega)\uff0c\u95ee\u9898\u548c\u516c\u5f0f\u90fd\u662f\u4e00\u6837\u7684\u3002\u4e0d\u8fc7\uff0c\u6587\u7ae0\u4ec5\u4ec5\u8003\u8651\u4e86\u80fd\u591f\u5bf9\u89d2\u5316\u7684\u77e9\u9635\u3002\u5177\u4f53\u8ba1\u7b97\u7684\u4f8b\u5b50\u7528\u4e86\u51e0\u4e2a\u5b9e\u9645\u7f51\u7edc\u548c\u51e0\u4e2a\u7f16\u51fa\u6765\u7684\u7f51\u7edc\u3002\u5728\u5177\u4f53\u7cfb\u7edf\u7684\u5e94\u7528\u4ef7\u503c\u4e0a\uff0c\u5728\u66f4\u4e00\u822c\u7684\u77e9\u9635\u7684\u8ba1\u7b97\u4e0a\uff0c\u5728\u5bf9\u89d2\u5143\u7684\u5904\u7406\u4e0a\uff0c\u8fd8\u662f\u6709\u503c\u5f97\u8fdb\u4e00\u6b65\u7814\u7a76\u7684\u5730\u65b9\u3002\u5982\u679c\u8981\u505a\uff0c\u505a\u4e00\u4e0b\u8fd9\u4e2a\u6587\u7ae0\u7684\u8ddf\u8e2a\uff0c\u7136\u540e\uff0c\u9009\u62e9\u4e0a\u9762\u7684\u4e00\u4e2a\u5177\u4f53\u5e94\u7528\u95ee\u9898\uff0c\u518d\u89e3\u51b3\u4e00\u4e0b\u5bf9\u89d2\u5143\u53bb\u6389\u7684\u95ee\u9898\uff0c\u8fd8\u662f\u5f88\u6709\u610f\u601d\u7684\u3002<\/p>\n

    \u4e00\u4e2a\u8fdb\u4e00\u6b65\u7684\u95ee\u9898\u7684\u89e3\u91ca\uff1a\u4e3a\u4ec0\u4e48\uff08\u5728\u4ec0\u4e48\u60c5\u5f62\u4e0b\uff09\u9700\u8981\u5254\u9664\u5bf9\u89d2\u5143\uff1f<\/p>\n

    \u8003\u8651\u4e00\u4e2a\u4f20\u67d3\u75c5\u4f20\u64ad\u7684\u95ee\u9898\uff0c\u6211\u4eec\u53ef\u4ee5\u5206\u6b65\u6765\u8003\u8651\u3002
    \n\u4e00\u6b65\u5c31\u80fd\u4f20\u67d3\u4e0a\u7684
    \n[p\\left(1_{j}, t+1|1_{i},t\\right) = p\\left(1_{j}|1_{i}\\right) =\\Omega^{i}{j}]
    \n\u4e24\u6b65\u5c31\u80fd\u4f20\u67d3\u4e0a\u7684
    \n\\begin{align}
    \np\\left(1<\/em>{j}, t+2|1_{i},t\\right) & = &\\sum_{k} p\\left(1_{j}, t+2|1_{k}, t+1\\right) p\\left(1_{k}, t+1|1_{i}, t\\right) \\notag \
    \n & = & \\sum_{k\\neq i, j} p\\left(1_{j}, t+2|1_{k}, t+1\\right) p\\left(1_{k}, t+1|1_{i}, t\\right) \\notag \
    \n& + & p\\left(1_{j}, t+2|1_{j}, t+1\\right) p\\left(1_{j}, t+1|1_{i}, t\\right) \\notag \
    \n& + & p\\left(1_{j}, t+2|1_{i}, t+1\\right) p\\left(1_{i}, t+1|1_{i}, t\\right) \\notag \
    \n& = & \\sum_{k\\neq i, j} \\Omega^{k}{j}\\Omega^{i}<\/em>{k} + \\Omega^{j}{j}\\Omega^{i}<\/em>{j} + \\Omega^{i}{j}\\Omega^{i}<\/em>{i}
    \n\\end{align}
    \n\u4ee5\u53ca\u5176\u4ed6\u66f4\u591a\u6b65\u7684\u8ba1\u7b97\u3002<\/p>\n

    \u5982\u679c\u8fd9\u4e2a\u8ba1\u7b97\u76f4\u63a5\u6c42\u548c\uff0c\u6211\u4eec\u5c31\u5f97\u5230\u4e0a\u9762\u7684(\\Sigma)\u8ba1\u7b97(\\Omega)\u7684\u516c\u5f0f\u3002<\/p>\n

    \u4f46\u662f\uff0c\u6211\u4eec\u770b\u5230\uff0c\u5982\u679c\u4e2d\u95f4\u67d0\u4e00\u6b65\u51fa\u73b0\u4e86\u5bf9\u89d2\u5143(p\\left(1_{j}|1_{j}\\right)\\neq 0)\uff0c\u90a3\u4e48\uff0c\u6211\u4eec\u5f97\u5230\u7684\u7b2c\u4e8c\u6b65\u4e4b\u4e2d\u5c31\u5305\u542b\u4e86\u7b2c\u4e00\u6b65\u7684\u8d21\u732e\uff0c\u800c\u4e14\u8fd9\u4e2a\u8d21\u732e\u4e0d\u662f\u7b80\u5355\u5730\u628a\u7b2c\u4e00\u6b65\u7684\u6982\u7387\u5305\u542b\u8fdb\u6765\uff0c\u4e5f\u5c31\u662f\u91cd\u590d\u8ba1\u7b97\u2014\u2014\u9664\u975e\u51fa\u73b0\u4e86(j)\u9876\u70b9\u88ab\u6cbb\u6108\u4e4b\u540e\u518d\u6b21\u901a\u8fc7\u5468\u56f4\u9876\u70b9\u7684\u4f20\u67d3\u800c\u5f97\u75c5\uff0c\u7136\u540e\u518d\u4e00\u6b21\u611f\u67d3\u5468\u56f4\u5176\u4ed6\u9876\u70b9\u7684\u60c5\u51b5\uff08\u4e5f\u5c31\u662f\u8bf4\uff0c\u662f\u5426\u8981\u53bb\u6389\u5bf9\u89d2\u5143\uff0c\u8fd8\u9700\u8981\u5177\u4f53\u95ee\u9898\u5177\u4f53\u5206\u6790\uff09\u3002\u4e8e\u662f\uff0c\u5bf9\u89d2\u5143\u90e8\u5206\u5728\u67d0\u4e9b\u60c5\u51b5\u4e0b\u8981\u6bcf\u6b21\u77e9\u9635\u76f8\u4e58\u4e4b\u540e\u90fd\u53bb\u6389\u3002<\/p>\n

    \u6709\u4e24\u79cd\u5b9a\u4e49\u77e9\u9635(\\Omega)\u5bf9\u89d2\u5143\u7684\u529e\u6cd5\uff0c\u53d6\u505a(1)\uff0c\u6216\u8005\u53d6\u505a(0)\u3002\u6211\u4eec\u5148\u6765\u770b\u524d\u8005\u3002
    \n\\begin{align}
    \np\\left(1_{j}, t+2|1_{i},t\\right) = \\sum_{k\\neq i, j} \\Omega^{k}{j}\\Omega^{i}<\/em>{k} + \\Omega^{j}{j}\\Omega^{i}<\/em>{j} + \\Omega^{i}{j}\\Omega^{i}<\/em>{i} = \\sum_{k\\neq i, j} \\Omega^{k}{j}\\Omega^{i}<\/em>{k} + \\Omega^{i}{j} + \\Omega^{i}<\/em>{j}.
    \n\\end{align}
    \n\u51fa\u73b0\u4e86\u4e24\u6b21(\\Omega^{i}{j})\uff0c\u4e0d\u80fd\u7b80\u5355\u770b\u505a\u201c\u5bf9\u89d2\u5143\u662f(1)\u7684(\\Omega)\u77e9\u9635\u7684\u5e73\u65b9\u7b49\u4e8e\u5bf9\u89d2\u5143\u662f(0)\u7684(\\Omega)\u77e9\u9635\u7684\u5e73\u65b9\u52a0\u4e0a(\\Omega)\u77e9\u9635\u201d\u3002\u518d\u6765\u770b\u5bf9\u89d2\u5143\u7b49\u4e8e(0)\u7684\u5f62\u5f0f\uff0c
    \n\\begin{align}
    \np\\left(1<\/em>{j}, t+2|1_{i},t\\right) = \\sum_{k\\neq i, j} \\Omega^{k}{j}\\Omega^{i}<\/em>{k} + \\Omega^{j}{j}\\Omega^{i}<\/em>{j} + \\Omega^{i}{j}\\Omega^{i}<\/em>{i} = \\sum_{k\\neq i, j} \\Omega^{k}{j}\\Omega^{i}<\/em>{k}.
    \n\\end{align}
    \n\u56e0\u6b64\uff0c\u8ba1\u7b97\u603b\u548c\u6982\u7387\u7684\u65f6\u5019\uff0c\u8fd8\u9700\u8981\u628a( \\Omega^{i}_{j})\u518d\u52a0\u56de\u53bb\u3002<\/p>\n

    \u540c\u6837\u7684\u60c5\u51b5\u4f1a\u51fa\u73b0\u5728\u66f4\u9ad8\u9636\u7684\u6982\u7387\u2014\u2014\u5b83\u4eec\u4e5f\u8981\u901a\u8fc7\u77e9\u9635\u76f8\u4e58\u6765\u8ba1\u7b97\u2014\u2014\u4e0a\u3002\u4e8e\u662f\uff0c\u4e0d\u7ba1\u54ea\u4e00\u79cd\u5bf9\u89d2\u5143\u53d6\u503c\u65b9\u5f0f\uff0c\u5982\u4f55\u4e0d\u91cd\u590d\u8ba1\u7b97\u5bf9\u89d2\u5143\u7684\u8d21\u732e\uff0c\u53c8\u80fd\u591f\u628a\u5404\u9636\u6982\u7387\u76f8\u53e0\u52a0\uff0c\u662f\u4e00\u4e2a\u975e\u5e73\u5eb8\u7684\u6280\u672f\u95ee\u9898\u3002<\/p>\n

    \u5f53\u7136\uff0c\u5982\u679c\u6211\u4eec\u6709\u8fd9\u6837\u7684\u8ba1\u7b97\u4e0a\u7684\u7ed3\u679c\uff0c\u90a3\u4e48\u8fd9\u4e2a\u95ee\u9898\u4e5f\u5c31\u6210\u4e86\u4e00\u4e2a\u7b80\u5355\u7684\u95ee\u9898\uff1a\u4efb\u4f55\u4e00\u4e2a\u80fd\u591f\u8868\u8fbe\u6210(\\Sigma=\\Omega + \\Omega^2 + \\cdots )\uff08\u5176\u4e2d(\\Omega)\u7684\u5143\u7d20\u975e\u8d1f\uff09\u5e76\u4e14\u4e0d\u542b\u6709\u5bf9\u89d2\u5143\u7684(\\Sigma)\uff0c\u901a\u8fc7\u8ba1\u7b97(\\Omega = 1-\\frac{1}{1+\\Sigma})\u5f97\u5230\u7684(\\Omega)\u5fc5\u7136\u4e5f\u4e0d\u542b\u6709\u5bf9\u89d2\u5143\u3002\u9053\u7406\u4e0a\u6765\u8bf4\u662f\u5bf9\u7684\uff0c\u56e0\u4e3a(\\Omega)\u7684\u5143\u7d20\u975e\u8d1f\uff0c\u56e0\u6b64\u53ea\u6709\u67d0\u4e00\u9879\u51fa\u73b0\u4e86\u5bf9\u89d2\u5143\uff0c\u8fd9\u4e2a\u5bf9\u89d2\u5143\u80af\u5b9a\u4f1a\u88ab\u5f85\u5230\u6700\u540e\u7684(\\Sigma)\u4e2d\u3002\u7528\u5177\u4f53\u4f8b\u5b50\u7b97\u51fa\u6765\u770b\u770b\u3002\u4e0d\u662f\u968f\u4fbf\u627e\u4e00\u4e2a(\\Simga)\u90fd\u6ee1\u8db3\u8fd9\u6837\u7684\u8981\u6c42\u7684\u3002<\/p>\n

    \u5728\u4f20\u67d3\u75c5\u4e0a\u7684\u5e94\u7528<\/strong><\/p>\n

    \u73b0\u5728\u6211\u4eec\u628a\u4e0a\u9762\u7684\u4ece\u5171\u73b0\u5230\u7ed3\u6784\u7684\u4e00\u822c\u6846\u67b6\u7528\u6765\u8ba8\u8bba\u4f20\u67d3\u75c5\u95ee\u9898\uff0c\u4f01\u56fe\u4ece\u89c2\u6d4b\u5230\u7684\u540c\u75c5\u6570\u636e\u6765\u5f97\u5230\u4e2a\u4f53\u4e4b\u95f4\u7684\u611f\u67d3\u6982\u7387\uff0c\u5e76\u4e14\u8fdb\u800c\u5f97\u5230\u5e95\u5c42\u7f51\u7edc\u3002\u8003\u8651\u5230\u5bf9\u89d2\u5143\u7684\u95ee\u9898\uff0c\u6211\u4eec\u5148\u8ba8\u8bba\u6709\u5411\u65e0\u73af\u7f51\u7edc\u3002<\/p>\n

    \u5148\u6765\u770b\u4ece(\\Omega)\u5230(\\Sigma)\u7684\u601d\u8def\u3002\u4e3a\u7b80\u5355\u8ba1\uff0c\u6240\u6709\u4e2a\u4f53\u4e4b\u95f4\u7684\u4f20\u67d3\u6982\u7387\uff0c\u53ea\u8981\u76f8\u4e92\u63a5\u89e6\uff0c\u5c31\u662f(p)\u3002\u8003\u8651\u4e00\u4e2a\u6709\u5411\u65e0\u73af\u56fe1->2->3\u3002\u4e8e\u662f\uff0c
    \n\\begin{align}
    \n\\Omega = \\left[\\begin{array}0 & p & 0 \ 0 & 0 & p \0 & 0 & 0\\end{array}\\right]
    \n\\end{align}
    \n\u4ee3\u8868\u4e00\u6b65\u5c31\u80fd\u4f20\u64ad\u5230\u5176\u4ed6\u9876\u70b9\u7684\u6982\u7387\u3002\u63a5\u7740\uff0c\u4e24\u6b65\u7684\u4f20\u67d3\u6982\u7387\u5c31\u662f
    \n\\begin{align}
    \n\\Omega^{2} = \\left[\\begin{array}0 & 0 & p^2 \ 0 & 0 & 0 \0 & 0 & 0\\end{array}\\right].
    \n\\end{align}
    \n\u4e09\u6b65\u4ee5\u53ca\u4ee5\u4e0a\u90fd\u662f(0)\u3002\u56e0\u6b64\uff0c
    \n\\begin{align}
    \n\\Sigma = \\left[\\begin{array}0 & p & p^2 \ 0 & 0 & p \0 & 0 & 0\\end{array}\\right],
    \n\\end{align}
    \n\u975e\u5e38\u7b80\u5355\u3002<\/p>\n

    \u73b0\u5728\u6211\u4eec\u770b\u770b\u4ece\u4ec0\u4e48\u6837\u7684\u5b9e\u9645\u6570\u636e\u4e2d\uff0c\u53ef\u4ee5\u5f97\u5230\u8fd9\u6837\u7684(\\Sigma)\u3002\u4e00\u65e6\u627e\u5230\u4e86\u8fd9\u6837\u7684\u5b9e\u9645\u7cfb\u7edf\uff0c\u4e5f\u5c31\u662f\u5f97\u5230\u4e86(\\Sigma)\u7684\u5b9e\u8bc1\u6570\u636e\u503c\uff0c\u90a3\u4e48\uff0c(\\Omega)\u4e5f\u5c31\u5f97\u5230\u4e86\u3002\u8fd9\u4e2a\u5c31\u662f\u53cd\u8fc7\u6765\u4ece(\\Sigma)\u5f97\u5230(\\Omega)\u7684\u601d\u8def\u3002<\/p>\n

    (\\Omega)\u7684\u5143\u7d20\u662f
    \n\\begin{align}
    \n\\Omega^{i}{j} = p\\left(I<\/em>{j}|I_{i}\\right) = \\frac{p\\left(I_{i},I_{j}\\right)}{p\\left(I_{i}\\right)},
    \n\\end{align}
    \n\u4e8e\u662f\uff0c\u6211\u4eec\u731c\u6d4b\uff0c\u53ea\u8981\u4ece\u5b9e\u9645\u4f20\u64ad\u8fc7\u8fc7\u7a0b\u4e2d\u83b7\u5f97\u5927\u91cf\u6837\u672c\uff0c\u7136\u540e\u8ba1\u7b97\u8fd9\u4e2a\u6837\u672c\u91cc\u9762\u7684(\\frac{p\\left(I_{i},I_{j}\\right)}{p\\left(I_{i}\\right)})\uff0c\u81ea\u7136\u5c31\u5305\u542b\u4e86\u4e0a\u9762\u7684\u76f4\u63a5\u6548\u679c(\\Omega^{i}_{j})\u548c\u95f4\u63a5\u6548\u679c\u3002<\/p>\n

    \u4e0b\u9762\uff0c\u6211\u4eec\u6765\u9a8c\u8bc1\u4e00\u4e0b\u8fd9\u4e2a\u731c\u60f3\u3002\u6211\u4eec\u628a\u8fd9\u4e2a\u4e09\u9876\u70b9\u6709\u5411\u65e0\u73af\u7f51\u7edc\u4e0a\u7684\u4f20\u67d3\u75c5\u4f20\u64ad\u5206\u89e3\u6210\u51e0\u79cd\u60c5\u5f62\uff1a\u521d\u59cb\u6ca1\u6709\u67d3\u75c5\u9876\u70b9\u7684\u60c5\u51b5\uff081\u79cd\uff09\uff0c\u521d\u59cb\u67d3\u75c5\u9876\u70b9\u4ec5\u4ec5\u53ea\u6709\u4e00\u4e2a\u7684\u60c5\u51b5\uff083\u79cd\uff09\uff0c\u521d\u59cb\u4e24\u4e2a\u7684\u60c5\u51b5\uff083\u79cd\uff09\uff0c\u4ee5\u53ca\u521d\u59cb\u4e09\u4e2a\u7684\u60c5\u51b5\uff081\u79cd\uff09\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

    \u8003\u8651\u4e00\u4e2a\u6982\u5ff5\u7f51\u7edc\uff0c\u5176\u4e2d\u7684\u9876\u70b9\u662f\u6982\u5ff5\uff0c\u8fde\u8fb9\u662f\u6982\u5ff5\u4e4b\u95f4\u7684\u903b\u8f91\u5173\u7cfb\u3002\u5047\u8bbe\u8fde\u8fb9\u7684\u5b58\u5728\u5c31\u4fdd\u8bc1\u4e86\u4e24\u4e2a\u8fde\u5728\u4e00\u8d77\u7684\u6982\u5ff5\u4ee5\u4e00\u5b9a\u7684 … \u7ee7\u7eed\u9605\u8bfb\u201c\u4ece\u5171\u73b0\u5230\u7ed3\u6784\u201d<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[11,247],"tags":[140],"_links":{"self":[{"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/posts\/1786"}],"collection":[{"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/comments?post=1786"}],"version-history":[{"count":1,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/posts\/1786\/revisions"}],"predecessor-version":[{"id":4158,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/posts\/1786\/revisions\/4158"}],"wp:attachment":[{"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/media?parent=1786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/categories?post=1786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.systemsci.org\/jinshanw\/wp-json\/wp\/v2\/tags?post=1786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}