{"id":758,"date":"2023-02-08T10:01:08","date_gmt":"2023-02-08T02:01:08","guid":{"rendered":"http:\/\/www.algmain.com\/?page_id=758"},"modified":"2023-02-13T10:10:40","modified_gmt":"2023-02-13T02:10:40","slug":"one-dimension","status":"publish","type":"page","link":"http:\/\/www.algmain.com\/index.php\/algorithm-article\/projective-variance-split\/one-dimension\/","title":{"rendered":"\u4e00\u7ef4\u6295\u5f71\u65b9\u5dee\u5206\u5272"},"content":{"rendered":"\n<p>\u4e3a\u4e86\u7814\u7a76\u4e0a\u9762\u63d0\u51fa\u7684\u8fd9\u4e2a\u95ee\u9898\uff0c\u8fd8\u662f\u628a\u95ee\u9898\u5148\u62c9\u56de\u5230\u4e00\u7ef4\u76f4\u7ebf\u70b9\u96c6\u4e0a\u3002<\/p>\n\n\n\n<p>\u5728\u4e00\u6761\u76f4\u7ebf&nbsp;\\(l\\)\u4e0a\u5206\u5e03\u7684\u70b9\u96c6\\(A=\\{ a_i \u2208 l | i=1,2,&#8230;N\\}\\)&nbsp;\uff0c\u5982\u4f55\u9009\u62e9\u4e00\u4e2a\u5206\u5272\u70b9&nbsp;\\(x\\)\uff0c\u4f7f\u5f97\u8fd9\u4e9b\u70b9\u5230\u8fd9\u4e2a\u5206\u5272\u70b9\u7684\u8ddd\u79bb\\(d\\)\u65b9\u5dee\u6700\u5927\u3002\u4e0d\u59a8\u5c06\u76f4\u7ebf&nbsp;\\(l\\)\u4e0e\\(x\\)\u8f74\u91cd\u5408\uff0c\u70b9\u96c6\u81ea\u7136\u53d8\u6362\u6210&nbsp;\\(A=\\{ x_i \u2208 l | i=1,2,&#8230;N\\}\\)&nbsp;\u3002<\/p>\n\n\n\n<p>\u8ddd\u79bb\u65b9\u5dee\u53ef\u63cf\u8ff0\u4e3a\uff1a<\/p>\n\n\n\n<p>\\[ H = \\sum\\limits_{i = 1}^N {{{({x_i} &#8211; x)}^2}} \\]<\/p>\n\n\n\n<p>\u5bf9\u6b64\u5f0f\u8fdb\u884c\u6574\u7406\uff0c\u5e76\u6c42\u5176\u6781\u503c\u3002<\/p>\n\n\n\n<p>\\[ H = \\sum\\limits_{i = 1}^N {{{({x_i} &#8211; x)}^2}} = N \\cdot {x^2} &#8211; 2 \\cdot x \\cdot \\sum\\limits_{i = 1}^N {{x_i} + \\sum\\limits_{i = 1}^N {x_i^2} } \\]<\/p>\n\n\n\n<p>\u663e\u7136\u5f53<\/p>\n\n\n<p>\\[ x =  &#8211; \\frac{b}{{2a}} =  &#8211; \\frac{{2\\sum\\limits_{i = 1}^N {{x_i}} }}{{2N}} = \\frac{1}{N}\\sum\\limits_{i = 1}^N {{x_i}} \\]<\/p>\n\n\n\n<p>\u65f6\\(H\\)\u5b58\u5728\u6781\u503c\u3002\u4e5f\u5373\uff1a\u8fd9\u4e2a\u5206\u5272\u70b9\\(x\\)\u8981\u9009\u62e9\u4e3a\u70b9\u96c6\\(A\\)\u7684\u8d28\u5fc3\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e3a\u4e86\u7814\u7a76\u4e0a\u9762\u63d0\u51fa\u7684\u8fd9\u4e2a\u95ee\u9898\uff0c\u8fd8\u662f\u628a\u95ee\u9898\u5148\u62c9\u56de\u5230\u4e00\u7ef4\u76f4\u7ebf\u70b9\u96c6\u4e0a\u3002 \u5728\u4e00\u6761\u76f4\u7ebf&nbsp;\u4e0a\u5206\u5e03\u7684\u70b9\u96c6&nbsp; [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":591,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-758","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/758"}],"collection":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/comments?post=758"}],"version-history":[{"count":7,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/758\/revisions"}],"predecessor-version":[{"id":1513,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/758\/revisions\/1513"}],"up":[{"embeddable":true,"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/pages\/591"}],"wp:attachment":[{"href":"http:\/\/www.algmain.com\/index.php\/wp-json\/wp\/v2\/media?parent=758"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}