\u57fa\u5c3c\u6307\u6570\uff08gini coefficient\uff09\u4ee3\u8868\u4e86\u6a21\u578b\u7684\u4e0d\u7eaf\u5ea6\uff0c\u57fa\u5c3c\u6307\u6570\u8d8a\u5c0f\uff0c\u5219\u4e0d\u7eaf\u5ea6\u8d8a\u4f4e\uff1b\u57fa\u5c3c\u6307\u6570\u8d8a\u5927\uff0c\u5219\u4e0d\u7eaf\u5ea6\u8d8a\u9ad8\uff0c\u8fd9\u548c\u4fe1\u606f\u589e\u76ca\u6bd4\u662f\u76f8\u53cd\u7684\u3002<\/p>\n
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\n$$
\nG(p) = \\sum<\/em>{k=1}^K p_k (1-pk) = 1 – \\sum<\/em>{k=1}^K p_k^2
\n$$
\n \u5982\u679c\u662f\u4e8c\u5206\u7c7b\u95ee\u9898\uff0c\u5176\u4e2d\u4e00\u4e2a\u5206\u7c7b\u7684\u6982\u7387\u4e3a$p$\uff0c\u5219\u5b83\u7684\u57fa\u5c3c\u6307\u6570\u4e3a
\n$$
\nG(p) = 2 p(1-p)
\n$$
\n \u5bf9\u4e8e\u67d0\u4e00\u4e2a\u8bad\u7ec3\u96c6$D$\uff0c\u5047\u8bbe\u8bad\u7ec3\u96c6\u6709$K$\u4e2a\u7c7b\u522b\uff0c\u5e76\u4e14\u7b2c$k$\u4e2a\u7c7b\u522b\u6709$Ck$\u4e2a\u6837\u672c\uff0c\u5219$D$\u7684\u57fa\u5c3c\u6307\u6570\u4e3a
\n$$
\nG(D) = 1 – \\sum<\/em>{k=1}^K ({\\frac {|C_k|} {|D|}})^2
\n$$
\n \u5bf9\u4e8e\u67d0\u4e00\u8bad\u7ec3\u96c6$D$\uff0c\u5982\u679c\u6839\u636e\u7279\u5f81$T$\u7684\u67d0\u4e2a\u7279\u5f81\u503c\u662f\u5426\u7b49\u4e8e$t$\u628a$D$\u5206\u6210\u4e24\u4e2a\u5b50\u96c6$D_1$\u548c$D_2$
\n$$
\nD_1 = {(x,y)\\in{D}|A(x)=t},\\quad D_2 = D-D_1
\n$$
\n\u5219$D$\u7684\u57fa\u5c3c\u6307\u6570\u4e3a
\n$$
\nG(D,A) = ({\\frac {|D_1|} {|D|}})G(D_1) + ({\\frac {|D_2|} {|D|}})G(D_2)
\n$$
\n \u57fa\u5c3c\u6307\u6570$G(D)$\u8868\u793a$D$\u7684\u4e0d\u786e\u5b9a\u6027\uff0c\u57fa\u5c3c\u6307\u6570$G(D,A)$\u8868\u793a\u7ecf\u8fc7$T=t$\u5206\u5272\u540e$D$\u7684\u4e0d\u786e\u5b9a\u6027\u3002\u57fa\u5c3c\u6307\u6570\u8d8a\u5927\uff0c\u6837\u672c\u96c6\u5408\u7684\u4e0d\u786e\u5b9a\u6027\u4e5f\u5c31\u8d8a\u5927\uff0c\u4e0d\u7eaf\u5ea6\u8d8a\u9ad8\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"