{"id":1569,"date":"2012-05-06T18:35:41","date_gmt":"2012-05-06T10:35:41","guid":{"rendered":"http:\/\/www.yewen.us\/blog\/?p=1569"},"modified":"2012-05-06T18:35:41","modified_gmt":"2012-05-06T10:35:41","slug":"machine-learning-1-pearson-r","status":"publish","type":"post","link":"https:\/\/www.yewen.us\/blog\/2012\/05\/machine-learning-1-pearson-r\/","title":{"rendered":"\u673a\u5668\u5b66\u4e60\u624b\u8bb0\u7cfb\u5217 1: Pearson \u76f8\u5173\u7cfb\u6570"},"content":{"rendered":"<p><strong>\u7cfb\u5217\u8bf4\u660e<\/strong><\/p>\n<p>\u6309\u5408\u603b\u6307\u793a, \u7ed9\u4eba\u4eba\u7684<a title=\"\u4eba\u4eba\u5c0f\u7ec4: \u673a\u5668\u5b66\u4e60\u7684\u7b97\u6cd5\u7814\u7a76\" href=\"http:\/\/xiaozu.renren.com\/xiaozu\/121443\">\u673a\u5668\u5b66\u4e60\u5c0f\u7ec4<\/a>\u5199\u70b9\u79d1\u666e\u6027\u8d28\u7684\u4e1c\u897f. \u5176\u5b9e\u81ea\u5df1\u597d\u50cf\u4e00\u76f4\u90fd\u6ca1\u53bb\u7cfb\u7edf\u7684\u5b66\u8fc7\u8fd9\u4e9b\u4e1c\u897f, \u90fd\u662f\u91ce\u8def\u5b50\u4e71\u641e, \u8fd9\u91cc\u628a\u8fc7\u53bb\u5b66\u7684\u4e00\u70b9\u4e1c\u897f\u5199\u51fa\u6765, \u8bb0\u5f55\u4e00\u4e0b, \u73ed\u95e8\u5f04\u65a7, \u6b22\u8fce\u62cd\u7816.<\/p>\n<p>\u81ea\u5df1\u63a5\u89e6\u5230\u7684\u673a\u5668\u5b66\u4e60, \u51e0\u4e4e\u90fd\u662f\u5728\u7528\u5386\u53f2\u9884\u4f30\u672a\u6765\u67d0\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387 (\u5e7f\u544a\u70b9\u51fb\u7387, \u63a8\u8350\u63a5\u53d7\u5ea6, \u7b49\u7b49).<\/p>\n<p>\u5c06\u8fd9\u4e2a\u8fc7\u7a0b\u7ec6\u5316\u4e00\u4e0b, \u9996\u5148\u90fd\u662f\u5bf9\u5386\u53f2\u6837\u672c\u63d0\u53d6\u7279\u5f81, \u5c06\u6837\u672c\u8f6c\u6362\u6210\u7528\u7279\u5f81\u5e8f\u5217\u6765\u63cf\u8ff0, \u5c06\u540c\u7c7b\u4e8b\u4ef6\u5408\u5e76, \u7136\u540e\u901a\u8fc7\u67d0\u79cd\u62df\u5408\u65b9\u5f0f\u53bb\u8ba9\u7279\u5f81\u5e26\u4e0a\u5408\u9002\u7684\u6743\u91cd, \u7528\u4e8e\u63cf\u8ff0\u4e8b\u4ef6\u53d1\u751f\u7684\u6982\u7387, \u6700\u540e\u5bf9\u8fd8\u672a\u53d1\u751f\u7684\u540c\u7c7b\u4e8b\u4ef6, \u540c\u6837\u5c06\u5176\u8f6c\u6362\u6210\u7279\u5f81\u5e8f\u5217, \u7528\u5b66\u51fa\u6765\u7684\u6743\u91cd\u8f6c\u6362\u6210\u9884\u4f30\u6982\u7387.<\/p>\n<p>\u8fd9\u91cc\u6709\u4e24\u4e2a\u5173\u952e\u95ee\u9898, \u4e00\u662f\u7279\u5f81\u9009\u53d6, \u4e8c\u662f\u62df\u5408\u8fd8\u539f\u65b9\u6cd5. \u7279\u5f81\u9009\u53d6\u662f\u4e3a\u4e86\u5c06\u6837\u672c\u505a\u5408\u7406\u62c6\u5206\u5408\u5e76, \u540c\u8d28\u7684\u624d\u5212\u5206\u5230\u4e00\u8d77, \u4e0d\u7136\u5c31\u6700\u540e\u7684\u9884\u4f30\u8fd8\u662f\u968f\u673a\u731c. \u62df\u5408\u8fd8\u539f\u65b9\u6cd5\u662f\u4fdd\u8bc1\u5728\u5bf9\u6570\u636e\u505a\u4e86\u5408\u7406\u62c6\u5206\u540e, \u80fd\u5c06\u7279\u5f81\u7684\u6743\u91cd\u62df\u5408\u5230\u539f\u6570\u636e\u4e0a\u4e14\u80fd\u5728\u9884\u4f30\u65f6\u8fd8\u539f\u6210\u6982\u7387.<\/p>\n<p><strong>\u95ee\u9898<\/strong><\/p>\n<p>\u5bf9\u600e\u4e48\u9009\u7279\u5f81, \u4f3c\u4e4e\u4ece\u6765\u90fd\u6ca1\u6709\u597d\u7684\u666e\u9002\u6027\u65b9\u6cd5, \u4f46\u662f\u600e\u4e48\u9a8c\u8bc1\u9009\u7684\u7279\u5f81\u9760\u4e0d\u9760\u8c31, \u65b9\u6cd5\u5012\u662f\u633a\u591a. \u5148\u629b\u5f00\u9009\u7279\u5f81\u7684\u6307\u5bfc\u65b9\u5411\u4e0d\u8bf4 (\u8bf4\u4e5f\u8bf4\u4e0d\u6e05), \u5982\u679c\u6211\u4eec\u9009\u51fa\u4e86\u4e00\u7c7b\u63cf\u8ff0\u7279\u5f81, \u600e\u4e48\u9a8c\u8bc1\u5176\u6548\u679c?<\/p>\n<p><strong>\u7279\u5f81\u6548\u679c\u9a8c\u8bc1<\/strong><\/p>\n<p>\u6700\u76f4\u63a5\u7c97\u66b4\u4e5f\u662f\u7ec8\u6781\u65b9\u6848\u5c31\u662f\u76f4\u63a5\u62ff\u5230\u7ebf\u4e0a\u53bb\u5e94\u7528, \u597d\u5c31\u662f\u597d, \u4e0d\u597d\u5c31\u662f\u4e0d\u597d. \u8fd9\u662f\u4e00\u53e5\u5f7b\u5e95\u7684\u5e9f\u8bdd, \u4e5f\u662f\u771f\u7406&#8230; \u4e0d\u8fc7\u5b9e\u9645\u64cd\u4f5c\u4e2d\u5f88\u96be\u771f\u7684\u53bb\u8fd9\u4e48\u505a, \u4e00\u662f\u5982\u679c\u8981\u5b8c\u6210\u6574\u4e2a\u6d41\u7a0b\u4f1a\u6bd4\u8f83\u8017\u65f6\u548c\u9ebb\u70e6, \u4e8c\u662f\u6ca1\u6709\u90a3\u4e48\u591a\u7ebf\u4e0a\u8d44\u6e90\u62ff\u6765\u5b9e\u9a8c, \u4e09\u662f\u5982\u679c\u5b9e\u9a8c\u4e0d\u597d\u5e26\u6765\u7684\u8d1f\u9762\u5f71\u54cd\u4f1a\u975e\u5e38\u5927, \u5e7f\u544a\u4f1a\u635f\u5931\u6536\u5165, \u63a8\u8350\u4f1a\u4e25\u91cd\u5f71\u54cd\u7528\u6237\u4f53\u9a8c. \u6240\u4ee5\u5982\u679c\u7ebf\u4e0b\u6ca1\u9a8c\u8bc1\u7684\u5fc3\u91cc\u6709\u8c31, \u6ca1\u4eba\u6562\u76f4\u63a5\u62cd\u4e0a\u53bb\u5b9e\u9a8c\u7684, \u8001\u677f\u4e5f\u4e0d\u4f1a\u8ba9\u4e71\u6765, \u90fd\u662f\u94b1\u548c\u80fd\u8f6c\u6362\u6210\u94b1\u7684\u7528\u6237\u554a.<\/p>\n<p>\u9000\u56de\u5230\u79bb\u7ebf\u9a8c\u8bc1\u4e0a, \u7ec8\u6781\u79bb\u7ebf\u9a8c\u8bc1\u4e5f\u8fd8\u662f\u62ff\u673a\u5668\u5b66\u4e60\u7684\u4ea7\u51fa (\u5206\u7c7b\u6811, LR \u6a21\u578b, \u6216\u522b\u7684\u4ec0\u4e48) \u53bb\u8bc4\u4f30\u4e00\u90e8\u5206\u5b9e\u9a8c\u6570\u636e, \u7136\u540e\u770b\u5bf9\u5b9e\u9a8c\u6570\u636e\u7684\u9884\u4f30\u7ed3\u679c\u662f\u5426\u548c\u5b9e\u9a8c\u6570\u636e\u7684\u5b9e\u9645\u8868\u73b0\u4e00\u81f4. \u8fd9\u4e2a\u8fd8\u662f\u5b58\u5728\u8017\u65f6\u8017\u8d44\u6e90\u7684\u95ee\u9898, \u540e\u9762\u518d\u8bf4, \u5148\u8bf4\u7b80\u5355\u7684.<\/p>\n<p>\u4e0d\u7ba1\u662f\u5206\u7c7b\u6811, \u8fd8\u662f LR \u6216\u522b\u7684 boosting \u4ec0\u4e48\u7684, \u90fd\u662f\u5e0c\u671b\u80fd\u627e\u5230\u6709\u533a\u5206\u5ea6\u7684\u7279\u5f81, \u80fd\u5c06\u672a\u6765\u4e0d\u540c\u7684\u6570\u636e\u5c3d\u53ef\u80fd\u5212\u5f00. \u5982\u679c\u7279\u5f81\u662f\u4e00\u4e2a 0\/1 \u7279\u5f81, \u90a3\u6570\u636e\u5c31\u5e94\u8be5\u80fd\u660e\u663e\u88ab\u5206\u6210\u4e0d\u4e00\u6837\u7684\u4e24\u4efd. \u6bd4\u5982\u5728\u8c46\u74e3, &#8220;\u5386\u53f2\u4e0a\u5173\u6ce8\u8fc7\u8ba1\u7b97\u673a\u7c7b\u522b\u4e66\u76ee\u7684\u4eba&#8221; \u662f\u4e00\u4e2a 0\/1 \u7279\u5f81, \u5982\u679c\u62ff\u8fd9\u4e2a\u7279\u5f81\u6765\u5206\u62c6\u4eba\u7fa4, \u5e76\u8bc4\u4f30 &#8220;\u672a\u6765\u662f\u5426\u5173\u6ce8\u8ba1\u7b97\u673a\u7c7b\u522b\u4e66\u76ee&#8221;, \u8bc4\u4f30\u6307\u6807\u7684 1 \u7edd\u5927\u90e8\u5206\u90fd\u843d\u5728\u533a\u5206\u7279\u5f81\u7684 1 \u4e2d, \u90a3\u8bf4\u660e\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u6b63\u76f8\u5173\u7684\u533a\u5206 (\u66fe\u7ecf\u5e72\u8fc7\u67d0\u4e8b\u7684\u4eba\u4f1a\u7ee7\u7eed\u5e72\u53e6\u4e00\u4ef6\u4e8b), \u6548\u679c\u5f88\u597d, \u53cd\u4e4b\u62ff\u53bb\u8bc4\u4f30 &#8220;\u672a\u6765\u662f\u5426\u5173\u6ce8\u5973\u6027\u8a00\u60c5\u5c0f\u8bf4\u7c7b\u522b\u4e66\u76ee&#8221;, \u5f88\u53ef\u80fd\u8bc4\u4f30\u6307\u6807\u7684 1 \u7edd\u5927\u90e8\u5206\u90fd\u843d\u5728\u533a\u5206\u7279\u5f81\u7684 0 \u91cc, \u90a3\u662f\u975e\u5e38\u8d1f\u76f8\u5173\u7684\u533a\u5206 (\u66fe\u7ecf\u5e72\u8fc7\u67d0\u4e8b\u7684\u4eba\u4e0d\u4f1a\u518d\u5e72\u53e6\u4e00\u4ef6\u7279\u5b9a\u7684\u4e8b), \u6548\u679c\u4e5f\u633a\u597d, \u4f46\u662f\u5982\u679c\u662f\u8bc4\u4f30 &#8220;\u672a\u6765\u662f\u5426\u4f1a\u5173\u6ce8\u6b66\u4fa0&#8221;, \u8bc4\u4f30\u6307\u6807\u7684 1 \u662f\u6bd4\u8f83\u5747\u5300\u7684\u6563\u5e03\u5728\u533a\u5206\u7279\u5f81\u7684 0\/1 \u91cc, \u90a3\u5c31\u8bf4\u660e\u8fd9\u4e2a\u7279\u5f81\u5bf9\u8be5\u8bc4\u4f30\u6307\u6807\u6ca1\u6709\u533a\u5206\u5ea6, \u8fd8\u4e0d\u5982\u6ca1\u6709. (\u8fd9\u4e9b\u4f8b\u5b50\u662f\u968f\u4fbf\u62cd\u8111\u888b\u5199\u7684, \u4e0d\u4fdd\u8bc1\u5176\u6b63\u786e\u6027)<\/p>\n<p>\u5982\u679c\u662f\u4e00\u7ef4\u8fde\u7eed\u7279\u5f81, \u5219\u6700\u540e\u603b\u7279\u5f81\u603b\u53ef\u4ee5\u8f6c\u6362\u6210\u4e00\u4e2a\u4e00\u7ef4\u5411\u91cf (\u8fde\u7eed\u503c\u53ef\u4ee5\u79bb\u6563\u5316\u6210\u6574\u6570\u533a\u95f4), \u8ddf 0\/1 \u7279\u5f81\u4e00\u6837, \u6bd4\u8f83\u8fd9\u4e2a\u7279\u5f81\u7684\u81ea\u53d8\u91cf\u53d6\u503c\u5411\u91cf\u548c\u5bf9\u5e94\u5230\u8bc4\u4f30\u6570\u636e\u4e0a\u7684\u53d6\u503c\u5411\u91cf\u7684\u76f8\u5173\u5ea6\u5c31\u80fd\u5224\u65ad\u6548\u679c\u597d\u574f (\u6b63\u76f8\u5173\u6216\u8d1f\u76f8\u5173\u90fd\u662f\u597d\u7684). \u4e00\u822c\u6700\u7b80\u5355\u7684\u662f\u4f7f\u7528 Pearson (\u76ae\u5c14\u751f) \u4e58\u79ef\u77e9\u76f8\u5173\u7cfb\u6570 r \u6765\u505a\u662f\u5426\u7ebf\u6027\u76f8\u5173\u7684\u5224\u65ad, \u82f1\u6587 wiki \u4e0a\u7684\u6761\u76ee <a href=\"http:\/\/en.wikipedia.org\/wiki\/Pearson_product-moment_correlation_coefficient\" title=\"Pearson (\u76ae\u5c14\u751f) \u76f8\u5173\u7cfb\u6570\">Pearson product-moment correlation coefficient<\/a> \u5bf9\u8be5\u7cfb\u6570\u7684\u542b\u4e49\u548c\u8ba1\u7b97\u65b9\u6cd5\u6709\u6bd4\u8f83\u8be6\u7ec6\u7684\u8bf4\u660e, \u4e2d\u6587\u7ffb\u8bd1\u6bd4\u8f83\u6742, \u767e\u5ea6\u767e\u79d1\u4e0a\u7684\u662f<a href=\"http:\/\/baike.baidu.com\/view\/3028699.htm\" title=\"\u76ae\u5c14\u68ee\u76f8\u5173\u7cfb\u6570\">\u76ae\u5c14\u68ee\u76f8\u5173\u7cfb\u6570<\/a>, \u5fae\u8f6f\u7684\u7ffb\u8bd1\u662f\u76ae\u5c14\u751f\u76f8\u4f3c\u5ea6. \u7b80\u8981\u7684\u8bf4, pearson \u76f8\u5173\u7cfb\u6570\u662f\u4e00\u4e2a [-1, 1] \u4e4b\u95f4\u7684\u5b9e\u6570, \u53d6\u503c\u8d8a\u63a5\u8fd1 -1 \u8868\u793a\u7279\u5f81\u503c\u548c\u8bc4\u4f30\u503c\u8d8a\u8d1f\u7ebf\u6027\u76f8\u5173, \u8d8a\u63a5\u8fd1 1 \u8868\u793a\u8d8a\u6b63\u76f8\u5173, \u8d8a\u63a5\u8fd1 0 \u8868\u793a\u8d8a\u4e0d\u76f8\u5173 (\u53ea\u662f\u7ebf\u6027, \u53ef\u80fd\u4f1a\u6709\u5176\u4ed6\u76f8\u5173\u7684\u5173\u7cfb).<\/p>\n<p>\u8fd8\u662f\u62ff\u8c46\u74e3\u7684\u4f8b\u5b50\u8bf4, \u6bd4\u5982 &#8220;\u5386\u53f2\u4e0a\u5173\u6ce8\u8fc7\u8ba1\u7b97\u673a\u7c7b\u522b\u4e66\u7684\u6570\u91cf&#8221; \u4f5c\u4e3a\u4e00\u4e2a\u4eba\u7fa4\u5212\u5206\u7279\u5f81, \u90a3\u8fd9\u7ef4\u7279\u5f81\u7684\u81ea\u53d8\u91cf\u5411\u91cf\u4f1a\u662f <0, 1, 2, ...>, \u4e3a\u4e86\u53d6\u503c\u65b9\u4fbf, \u5c06\u5176\u622a\u65ad\u5230\u8d85\u8fc7\u5341\u672c\u7684\u4e5f\u7b49\u4e8e 10, \u5219\u5411\u91cf\u53d8\u4e3a <0, 1, ..., 10>, \u5982\u679c\u53bb\u8bc4\u4f30 &#8220;\u7ee7\u7eed\u5173\u6ce8\u8ba1\u7b97\u673a\u7c7b\u522b\u4e66\u7684\u6982\u7387&#8221;, \u8fd9\u4e2a\u6982\u7387\u53d6\u503c\u53ef\u80fd\u662f <0.0, 0.1, ..., 1.0>, \u5219\u5176 Pearson \u76f8\u4f3c\u5ea6\u4f1a\u662f 1. (\u5f53\u7136, \u8fd9\u4e2a\u4f8b\u5b50\u4e3e\u7684\u592a\u5047\u4e86\u70b9, \u5148\u8fd9\u4e48\u7740\u5427)<\/p>\n<p>\u5c06\u95ee\u9898\u5316\u7b80\u4e3a\u7b97\u7279\u5f81\u53d6\u503c\u548c\u8bc4\u4f30\u6307\u6807\u7684 Pearson \u76f8\u4f3c\u5ea6\u540e\u9700\u8981\u505a\u7684\u5de5\u4f5c\u5c31\u4f1a\u5c11\u5f88\u591a, \u76f4\u63a5\u8dd1\u4e2a Map\/Reduce \u4ece LOG \u91cc\u63d0\u53d6\u4e0b\u6570\u636e, \u7136\u540e\u770b\u770b\u503c\u7684\u76f8\u5173\u6027\u5c31\u77e5\u9053\u7279\u5f81\u662f\u5426\u6709\u533a\u5206\u5ea6\u4e86, \u6ca1\u533a\u5206\u5ea6\u7684\u53ef\u4ee5\u5148\u4e0d\u8003\u8651 (\u6216\u8005\u5c06\u66f2\u7ebf\u76f8\u5173\u7684\u53ef\u80fd\u8f6c\u53d8\u6210\u7ebf\u6027\u5173\u7cfb, \u518d\u5224\u65ad), \u6709\u533a\u5206\u5ea6\u7684\u624d\u7ee7\u7eed\u8d70\u66f4\u5b8c\u6574\u7684\u79bb\u7ebf\u9a8c\u8bc1, \u52a0\u5165\u5206\u7c7b\u6811\u6216\u6982\u7387\u6a21\u578b\u548c\u5176\u4ed6\u7279\u5f81\u4e00\u8d77\u4f5c\u7528\u770b\u6548\u679c, \u5982\u679c\u8fd8\u4e0d\u9519\u5c31\u4e0a\u7ebf\u5b9e\u9a8c.<\/p>\n<p>\u5fae\u8f6f\u7684 Excel \u91cc\u5c31\u5e26\u4e86 Pearson \u76f8\u4f3c\u5ea6\u7684\u8ba1\u7b97\u516c\u5f0f, \u53ef\u4ee5\u5f88\u65b9\u4fbf\u7684\u62ff\u6765\u8bc4\u4f30, \u8bf4\u660e\u548c\u7528\u6cd5\u8bf7\u89c1\u5fae\u8f6f\u5e2e\u52a9\u9875\u9762 <a href=\"http:\/\/office.microsoft.com\/zh-cn\/excel-help\/HP010342758.aspx\" title=\"Excel \u91cc\u7684 PEARSON \u51fd\u6570\">PEARSON \u51fd\u6570<\/a>. \u5982\u679c\u8981\u81ea\u5df1\u8ba1\u7b97, \u53ef\u4ee5\u53c2\u8003 wiki \u7684\u8fd9\u4e2a\u516c\u5f0f:<\/p>\n<p><img decoding=\"async\" src=\"http:\/\/upload.wikimedia.org\/wikipedia\/en\/math\/b\/e\/1\/be19a3bb58acb318983384212f152bc3.png\" alt=\"Pearson \u76f8\u4f3c\u5ea6\u8ba1\u7b97\u516c\u5f0f\" \/><\/p>\n<p>C \u7684\u5b9e\u73b0\u6e90\u7801\u5982\u4e0b (\u6ce8\u610f\u67d0\u4e9b\u60c5\u51b5\u4e0b\u53ef\u80fd\u4f1a\u6709\u8ba1\u7b97\u7cbe\u5ea6\u4e22\u5931, \u5e26\u6765\u7ed3\u679c\u7684\u4e0d\u786e\u5b9a\u6027)<\/p>\n<pre class=\"brush: cpp; title: ; notranslate\" title=\"\">double pearson_r(double x&#x5B;], int x_n, double y&#x5B;], int y_n) {\n  if (x_n != y_n || x_n == 0) {\n    return 0;\n  }\n\n  double n = (double)(x_n);\n  double sum_x = 0;\n  double sum_y = 0;\n  double sum_x_sq = 0;\n  double sum_y_sq = 0;\n  double sum_x_by_y = 0;\n  \n  for (int i = 0; i &lt; x_n; ++i) {\n    sum_x += x&#x5B;i];\n    sum_y += y&#x5B;i];\n    sum_x_sq += x&#x5B;i]*x&#x5B;i];\n    sum_y_sq += y&#x5B;i]*y&#x5B;i];\n    sum_x_by_y += x&#x5B;i]*y&#x5B;i];\n  }\n  double res = n*sum_x_by_y - sum_x*sum_y;\n  res \/= sqrt(n*sum_x_sq - sum_x*sum_x);\n  res \/= sqrt(n*sum_y_sq - sum_y*sum_y);\n  return res;\n}<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>\u7cfb\u5217\u8bf4\u660e \u6309\u5408\u603b\u6307\u793a, \u7ed9\u4eba\u4eba\u7684\u673a\u5668\u5b66\u4e60\u5c0f\u7ec4\u5199\u70b9\u79d1\u666e\u6027\u8d28\u7684\u4e1c\u897f. \u5176\u5b9e\u81ea\u5df1\u597d\u50cf\u4e00\u76f4\u90fd\u6ca1\u53bb\u7cfb\u7edf\u7684\u5b66\u8fc7\u8fd9\u4e9b\u4e1c\u897f,  [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[5,7,9],"tags":[115,123,310,372,373],"class_list":["post-1569","post","type-post","status-publish","format-standard","hentry","category-work-life","category-tech-notes","category-machine-learning","tag-pearson","tag-predict","tag-310","tag-372","tag-373"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4aR5e-pj","_links":{"self":[{"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/posts\/1569","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/comments?post=1569"}],"version-history":[{"count":0,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/posts\/1569\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/media?parent=1569"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/categories?post=1569"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/tags?post=1569"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}