{"id":9219,"date":"2024-03-20T11:17:42","date_gmt":"2024-03-20T03:17:42","guid":{"rendered":"\/?p=9219"},"modified":"2024-03-23T00:35:53","modified_gmt":"2024-03-22T16:35:53","slug":"%e3%80%90%e5%9b%be%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9c%e5%ae%9e%e6%88%98%e3%80%91%e6%b7%b1%e5%85%a5%e6%b5%85%e5%87%ba%e5%9c%b0%e5%ad%a6%e4%b9%a0%e5%9b%be%e7%a5%9e%e7%bb%8f%e7%bd%91%e7%bb%9cgnn-2","status":"publish","type":"post","link":"\/?p=9219","title":{"rendered":"\u3010\u56fe\u795e\u7ecf\u7f51\u7edc\u5b9e\u6218\u3011\u6df1\u5165\u6d45\u51fa\u5730\u5b66\u4e60\u56fe\u795e\u7ecf\u7f51\u7edcGNN\uff08\u4e0a\uff09"},"content":{"rendered":"<h2>\u4e00\u3001\u56fe\u795e\u7ecf\u7f51\u7edc\u5e94\u7528\u9886\u57df<\/h2>\n<p><a href=\"https:\/\/distill.pub\/2021\/gnn-intro\/\">https:\/\/distill.pub\/2021\/gnn-intro\/<\/a><\/p>\n<h3>1.1 \u82af\u7247\u8bbe\u8ba1<\/h3>\n<p>\u82af\u7247\u7684\u8bbe\u8ba1\u6bd4\u8f83\u8017\u8d39\u4eba\u529b\u548c\u7269\u529b\uff0c\u5982\u679c\u53ef\u4ee5\u901a\u8fc7AI\u7b97\u6cd5\u81ea\u52a8\u8bbe\u8ba1\u82af\u7247\uff0c\u5219\u53ef\u4ee5\u5927\u5927\u63d0\u9ad8\u82af\u7247\u5236\u9020\u7684\u6548\u7387\uff0c\u964d\u4f4e\u82af\u7247\u5236\u9020\u7684\u6210\u672c<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/cb8230081dc54dfeb59967bb5bd850c2.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.2 \u573a\u666f\u5206\u6790\u4e0e\u95ee\u9898\u63a8\u7406<\/h3>\n<p>\u4f8b\u5982\u5267\u672c\u6740\u4e2d\u7684\u63a8\u7406\uff0c\u8b66\u532a\u7247\u4e2d\u5acc\u7591\u4eba\u7684\u56fe\u63a8\u7406\u7b49<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/47ccc9bf6c2b44a4a6d70e44ce005632.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.3 \u63a8\u8350\u7cfb\u7edf<\/h3>\n<p>\u4f8b\u5982\uff0c\u5237\u6296\u97f3\uff0c\u7ecf\u5e38\u770b\u82f1\u96c4\u8054\u76df\u7684\u6e38\u620f\u89c6\u9891\uff0c\u90a3\u4e48\u8bf4\u660e\u4f60\u5bf9\u6e38\u620f\u6bd4\u8f83\u611f\u5174\u8da3\uff0c\u7cfb\u7edf\u4f1a\u6839\u636e\u7f51\u7edc\u56fe\u7ed3\u6784\u63a8\u8350\u66f4\u591a\u548c\u82f1\u96c4\u8054\u76df\u76f8\u5173\u7684\u5185\u5bb9\u7ed9\u4f60<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/c4c428a54769424ab2327dc725fbbcf1.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.4 \u6b3a\u8bc8\u68c0\u6d4b\u4e0e\u98ce\u63a7\u76f8\u5173<\/h3>\n<p>\u8d37\u6b3e\u8f6f\u4ef6\uff0c\u8bfb\u53d6\u7528\u6237\u7684\u901a\u8baf\u5f55\u4fe1\u606f\u548capp\u4f7f\u7528\u60c5\u51b5\uff0c\u4ece\u800c\u6d4b\u8bc4\u7528\u6237\u7684\u8fd8\u6b3e\u80fd\u529b\uff0c\u7136\u540e\u51b3\u5b9a\u7528\u6237\u7684\u501f\u6b3e\u989d\u5ea6<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/c07cb5a9f9bb4818abe8e82e3b23cc5b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.5 \u77e5\u8bc6\u56fe\u8c31<\/h3>\n<p>\u667a\u80fd\u5ba2\u670d<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/b63c922822b24581ba94ae4ef39b6d72.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.6 \u9053\u8def\u4ea4\u901a\u7684\u6d41\u91cf\u9884\u6d4b<\/h3>\n<p>\u9884\u6d4b\u9053\u8def\u4e0a\u6bcf\u6761\u8fb9\u7684\u6d41\u91cf<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/44d5feb526704ff4a0861f6ec08c6168.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.7 \u81ea\u52a8\u9a7e\u9a76\uff08\u65e0\u4eba\u673a\u7b49\u573a\u666f\uff09<\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/4d930fede64e47719ddad0ddce7266ee.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.8 \u5316\u5b66\uff0c\u533b\u7597\u7b49\u573a\u666f<\/h3>\n<p>\u5229\u7528AI\u5bf9\u5316\u5b66\u7ed3\u6784\u8fdb\u884c\u5206\u6790\uff0c\u9884\u6d4b<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/17c65b86cc1f40adb2138e56ce3156c4.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>1.9 \u7269\u7406\u6a21\u578b\u76f8\u5173<\/h3>\n<p>\u6839\u636e\u5206\u5b50\u7ed3\u6784\u8fdb\u884c\u76f8\u5173\u5206\u6790<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/d17948bb07154441ad02c43ef70b2763.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<hr \/>\n<h2>\u4e8c\u3001\u56fe\u795e\u7ecf\u7f51\u7edc\u57fa\u672c\u77e5\u8bc6<\/h2>\n<h3>2.1 \u56fe\u57fa\u672c\u6a21\u5757\u5b9a\u4e49<\/h3>\n<p><strong>V<\/strong>\uff1a\u70b9\uff0c\u6bcf\u4e2a\u70b9\u90fd\u6709\u81ea\u5df1\u7684\u7279\u5f81\u5411\u91cf\uff08\u7279\u5f81\u4e3e\u4f8b\uff1a\u90bb\u5c45\u70b9\u6570\u91cf\u3001\u4e00\u9636\u4e8c\u9636\u76f8\u4f3c\u5ea6\uff09<br \/>\n<strong>E<\/strong>\uff1a\u8fb9\uff0c\u6bcf\u4e2a\u8fb9\u90fd\u6709\u81ea\u5df1\u7684\u7279\u5f81\u5411\u91cf\uff08\u7279\u5f81\u4e3e\u4f8b\uff1a\u8fb9\u7684\u6743\u91cd\u503c\u3001\u8fb9\u7684\u5b9a\u4e49\uff09<br \/>\n<strong>U<\/strong>\uff1a\u6574\u4e2a\u56fe\uff0c\u6bcf\u4e2a\u56fe\u90fd\u6709\u81ea\u5df1\u7684\u7279\u5f81\u5411\u91cf\uff08\u7279\u5f81\u4e3e\u4f8b\uff1a\u8282\u70b9\u6570\u91cf\u3001\u56fe\u76f4\u5f84\uff09<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/8cdec5e34e784550a04c169b95e5498b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>2.2 \u56fe\u795e\u7ecf\u7f51\u7edc\u8981\u505a\u7684\u4e8b\u60c5<\/h3>\n<ul>\n<li>\u4e3a\u6bcf\u4e2a\u8282\u70b9\u6574\u5408\u7279\u5f81\u5411\u91cf\uff0c\u6839\u636e\u5176\u5bf9\u8282\u70b9\u505a\u5206\u7c7b\u6216\u8005\u56de\u5f52<\/li>\n<li>\u4e3a\u6bcf\u6761\u8fb9\u6574\u5408\u7279\u5f81\u5411\u91cf\uff0c\u6839\u636e\u5176\u5bf9\u8fb9\u505a\u5206\u7c7b\u6216\u8005\u56de\u5f52<\/li>\n<li>\u4e3a\u6bcf\u5f20\u56fe\u6574\u5408\u7279\u5f81\u5411\u91cf\uff0c\u6839\u636e\u5176\u5bf9\u56fe\u505a\u5206\u7c7b\u6216\u8005\u56de\u5f52<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/3bcf82f8ef9d4fed83050a68b46d7704.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/li>\n<\/ul>\n<h3>2.3 \u90bb\u63a5\u77e9\u9635\u7684\u5b9a\u4e49<\/h3>\n<h4>2.3.1 \u56fe\u6570\u636e\u7684\u90bb\u63a5\u77e9\u9635<\/h4>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/e5a2c72fdedd467681839317e30ee3b9.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>2.3.2 \u6587\u672c\u6570\u636e\u7684\u90bb\u63a5\u77e9\u9635<\/h4>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/a4ddcd49ed614d5a9453eaf7970bec6f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>2.4 GNN\u4e2d\u7684\u5e38\u89c1\u4efb\u52a1<\/h3>\n<p>\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc\uff08CNN\u3001RNN\u3001DNN\uff09\u8981\u6c42\u8f93\u5165\u683c\u5f0f\u662f\u56fa\u5b9a\u7684\uff08\u598224\u00d724\u3001128\u00d7128\u7b49\uff09\u3002<\/p>\n<p>\u4f46\u5728\u5b9e\u9645\u573a\u666f\u4e2d\uff08\u4f8b\u5982\u9053\u8def\u4ea4\u901a\uff09\uff0c\u4e0d\u540c\u57ce\u5e02\u7684\u9053\u8def\u6570\u91cf\u548c\u8282\u70b9\u6570\u91cf\u90fd\u4e0d\u540c\uff0c\u5373<strong>\u8f93\u5165\u6570\u636e\u683c\u5f0f\u4e0d\u56fa\u5b9a<\/strong>\u3002\u5bf9\u6b64\uff0c\u4f20\u7edf\u795e\u7ecf\u7f51\u7edc\u4e0d\u80fd\u5f88\u597d\u5730\u89e3\u51b3\uff0c\u4f46\u662f<strong>GNN\u53ef\u4ee5\u7528\u6765\u89e3\u51b3\u6b64\u7c7b\u95ee\u9898<\/strong>\u3002<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/dd3d69cab0e84efa972272552e07fb72.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n\u5bf9\u4e8e\u8f93\u5165\u6570\u636e\u683c\u5f0f\u4e0d\u56fa\u5b9a\u7684\u60c5\u51b5\uff0cGNN\u7684\u5e38\u89c1\u4efb\u52a1\u6709\u4ee5\u4e0b\u51e0\u79cd\uff1a<\/p>\n<h4>2.4.1 Graph\u7ea7\u522b\u4efb\u52a1<\/h4>\n<p>\u57fa\u4e8e\u6574\u4e2a\u56fe\uff0c\u505a\u5206\u7c7b\u548c\u56de\u5f52\u3002<br \/>\n\u4f8b\u5982\uff0c\u7ed9\u5b9a\u4e00\u4e2a\u5206\u5b50\u7ed3\u6784\u56fe\uff0c\u5224\u65ad\u5b83\u91cc\u9762\u5b58\u5728\u51e0\u4e2a\u73af \u6216\u8005 \u5224\u65ad\u8be5\u5206\u5b50\u7ed3\u6784\u5c5e\u4e8e\u54ea\u4e00\u7c7b<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/8bdf266948394d7c97c7ec629e0fc45b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>2.4.2 Node\u4e0eEdge\u7ea7\u522b\u4efb\u52a1<\/h4>\n<p>\u9884\u6d4b\u8fd9\u4e2a\u70b9\u662f\u6559\u7ec3\u8fd8\u662f\u5b66\u5458\uff0c\u5373\u9884\u6d4b\u70b9<br \/>\n\u9884\u6d4b\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u5173\u7cfb\uff08\u662f\u6253\u67b6\u5173\u7cfb\u8fd8\u662f\u89c2\u770b\u5173\u7cfb\uff09\uff0c\u5373\u9884\u6d4b\u8fb9<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/70282608ab9a462cb7f4a9d3919c750b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>2.5 \u6d88\u606f\u4f20\u9012\u8ba1\u7b97\u65b9\u6cd5<\/h3>\n<h4>2.5.1 \u4f18\u5316\u90bb\u63a5\u77e9\u9635<\/h4>\n<p>\u4e4b\u524d\u5b66\u8fc7\uff0c\u90bb\u63a5\u77e9\u9635\u7684\u5927\u5c0f\u4e3aN*N\uff0c\u5f53\u8282\u70b9\u5f88\u591a\u7684\u65f6\u5019\uff0c\u90bb\u63a5\u77e9\u9635\u7684\u5927\u5c0f\u4e5f\u4f1a\u7279\u522b\u5927<\/p>\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u4e00\u822c\u91c7\u53d6\u53ea\u4fdd\u5b58source\u6570\u7ec4\u548ctarget\u6570\u7ec4\u7684\u65b9\u5f0f<\/p>\n<p>source\u6570\u7ec4\u5373\u8d77\u70b9\uff08\u8d77\u6e90\u70b9\uff09\u6570\u7ec4\uff0ctarget\u6570\u7ec4\u5373\u7ec8\u70b9\uff08\u76ee\u6807\u70b9\uff09\u6570\u7ec4<\/p>\n<p>\u8fd9\u4e24\u4e2a\u6570\u7ec4\u7684\u7ef4\u5ea6\u662f\u4e00\u6837\u7684<\/p>\n<p>\u5bf9\u5e94\u4f4d\u7f6e\u7684source\u548ctarget\u503c\u5c31\u53ef\u4ee5\u4ee3\u8868\u4e00\u6761\u53ef\u8fde\u63a5\u7684\u6709\u5411\u8fb9\uff0c\u5bf9\u4e8e\u6ca1\u6709\u8fde\u63a5\u5173\u7cfb\u7684\u8fb9\u5219\u4e0d\u9700\u8981\u4fdd\u5b58\u5176\u4fe1\u606f\uff0c\u8fd9\u6837\u5c31\u53ef\u4ee5\u5927\u5927\u51cf\u5c11\u6570\u636e\u89c4\u6a21<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/06e6b2507fe54d72980b599e94a7ba23.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>2.5.2 \u70b9\u7684\u7279\u5f81\u91cd\u6784<\/h4>\n<p><strong>\u6c47\u603b = \u81ea\u8eab\u7684\u4fe1\u606f + \u6240\u6709\u90bb\u5c45\u70b9\u7684\u4fe1\u606f<\/strong><\/p>\n<p><strong>\u6240\u6709\u90bb\u5c45\u70b9\u4fe1\u606f\u7684\u8868\u8fbe\u6709\u51e0\u79cd\uff1a<\/strong><\/p>\n<ul>\n<li><strong>\u6c42\u89e3Sum<\/strong><\/li>\n<li><strong>\u6c42\u5e73\u5747Mean<\/strong><\/li>\n<li><strong>\u6c42\u6700\u5927Max<\/strong><\/li>\n<li><strong>\u6c42\u6700\u5c0fMin<\/strong><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/7f093915fddb4e50837ab9d96e8993ed.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/li>\n<\/ul>\n<h3>2.6 \u591a\u5c42GNN\u7684\u4f5c\u7528<\/h3>\n<p>\u5c42\u6570\u8d8a\u591a\uff0cGNN\u7684\u201c\u611f\u53d7\u91ce\u201d\u8d8a\u5927\uff0c\u6bcf\u4e2a\u70b9\u8003\u8651\u5176\u4ed6\u70b9\u7684\u4fe1\u606f\u8d8a\u591a\uff0c\u8003\u8651\u8d8a\u5168\u9762<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/a62683fb5d584e218aacc8bd5afe0018.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>GNN\u8f93\u51fa\u7279\u5f81\u7684\u7528\u5904<\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/29d1b3e3aba94ce18cc8f74632557e67.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<hr \/>\n<h2>\u4e09\u3001GCN\u8be6\u89e3<\/h2>\n<h3>3.1 GCN\u57fa\u672c\u6a21\u578b\u6982\u8ff0<\/h3>\n<h4>3.1.1 \u5377\u79ef vs \u56fe\u5377\u79ef<\/h4>\n<p><strong>\u5377\u79ef<\/strong>\uff1a\u5377\u79ef\u6838\u5e73\u79fb\u8ba1\u7b97<\/p>\n<p><strong>\u56fe\u5377\u79ef<\/strong>\uff1a\u81ea\u8eab\u4fe1\u606f+\u6240\u6709\u90bb\u5c45\u4fe1\u606f<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/e0f2d20bb90647c583898c5bac18358c.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>3.1.2 \u56fe\u4e2d\u5e38\u89c1\u4efb\u52a1<\/h4>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/9ed5073240cd4dabbecca7683e3ef2c5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>3.1.3 \u5982\u679c\u83b7\u53d6\u7279\u5f81<\/h4>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/9e7bc354a77e4330b6e66a0faac1b9c8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>3.1.4 \u534a\u76d1\u7763\u5b66\u4e60<\/h4>\n<p>GCN\u5c5e\u4e8e\u534a\u76d1\u7763\u5b66\u4e60\uff08\u4e0d\u9700\u8981\u6bcf\u4e2a\u8282\u70b9\u90fd\u6709\u6807\u7b7e\u90fd\u53ef\u4ee5\u8fdb\u884c\u8bad\u7ec3\uff09<\/p>\n<p>\u8ba1\u7b97Loss\u65f6\uff0c\u53ea\u9700\u8981\u8003\u8651\u6709\u6807\u7b7e\u7684\u8282\u70b9\u5373\u53ef\u3002<\/p>\n<p>\u4e3a\u4e86\u51cf\u5c11\u6709\u6807\u7b7e\u8282\u70b9\u7684Loss\uff0c\u5176\u5468\u56f4\u7684\u70b9\u4e5f\u4f1a\u505a\u76f8\u5e94\u7684\u8c03\u6574\uff0c\u8fd9\u4e5f\u662f\u56fe\u7ed3\u6784\u7684\u7279\u70b9\uff0c\u56e0\u6b64GNN\u548cGCN\u4e2d\uff0c\u4e0d\u9700\u8981\u6240\u6709\u8282\u70b9\u90fd\u6709\u6807\u7b7e\u4e5f\u53ef\u4ee5\u8fdb\u884c\u8bad\u7ec3\uff08\u5f53\u7136\u81f3\u5c11\u9700\u8981\u4e00\u4e2a\u8282\u70b9\u6709\u6807\u7b7e\uff09<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/c1a4dd0b59724d1db84ac662598ff369.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>3.2 \u56fe\u5377\u79ef\u7684\u57fa\u672c\u8ba1\u7b97\u65b9\u6cd5<\/h3>\n<h4>3.2.1 GCN\u57fa\u672c\u601d\u60f3<\/h4>\n<ul>\n<li>\u5bf9\u6bcf\u4e2a\u8282\u70b9\u8ba1\u7b97\u7279\u5f81<\/li>\n<li>\u7136\u540e\u5408\u6210\u6bcf\u4e2a\u8282\u70b9\u7684\u7279\u5f81<\/li>\n<li>\u5c06\u5408\u6210\u7684\u7279\u5f81\u4f20\u5165\u5168\u8fde\u63a5\u7f51\u7edc\u8fdb\u884c\u5206\u7c7b<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/5100cc3ea18649fc85b797f40c0b29bd.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/li>\n<\/ul>\n<h4>3.2.2 GCN\u5c42\u6570<\/h4>\n<p>\u56fe\u5377\u79ef\u4e5f\u53ef\u4ee5\u505a\u591a\u5c42\uff0c\u4f46\u662f\u4e00\u822c\u4e0d\u505a\u592a\u6df1\u5c42\uff0c\u4e00\u822c\u53ea\u505a2-3\u5c42<br \/>\n\uff08\u7c7b\u4f3c\u4e8e\u4e00\u79cd\u8bf4\u6cd5\uff0c\u4f60\u53ea\u9700\u8981\u8ba4\u8bc66\u4e2a\u4eba\u5c31\u53ef\u4ee5\u8ba4\u8bc6\u5168\u4e16\u754c\uff09<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/f0c95a8731e3428aa1739eca28aba4b7.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/261cc824d93f4f29910c9d6c73e062b3.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n<strong>\u5b9e\u9a8c\u8868\u660e<\/strong>\uff1aGCN\u4e2d\uff0c\u6df1\u5c42\u7684\u7f51\u7edc\u7ed3\u6784\u5f80\u5f80\u4e0d\u4f1a\u5e26\u6765\u66f4\u597d\u7684\u6548\u679c\u3002<br \/>\n<strong>\u76f4\u89c2\u89e3\u91ca<\/strong>\uff1a\u6211\u8868\u54e5\u8ba4\u8bc6\u7684\u670b\u53cb\u7684\u670b\u53cb\u7684\u670b\u53cb\u7684\u670b\u53cb\u8ba4\u8bc6\u5e02\u957f\uff0c\u4e0d\u4ee3\u8868\u6211\u548c\u5e02\u957f\u5173\u7cfb\u5c31\u5f88\u597d\u3002<\/p>\n<p><strong>\u5c42\u6570\u8d8a\u591a\uff0c\u7279\u5f81\u8868\u8fbe\u5c31\u8d8a\u53d1\u6563<\/strong><\/p>\n<p><strong>\u4e00\u822c2-5\u5c42\u5373\u53ef<\/strong><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/996286c5699e4b33aac2c978e1238126.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>3.2.3 \u56fe\u4e2d\u57fa\u672c\u7ec4\u6210<\/h4>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/980813dec9d5433da0b002c1fc2a652f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>3.2.4 \u7279\u5f81\u8ba1\u7b97\u65b9\u6cd5<\/h4>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/e01890728302472c8f2aa21c3b692278.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>3.3 \u90bb\u63a5\u77e9\u9635\u7684\u53d8\u6362<\/h3>\n<p><strong>\u5355\u4f4d\u77e9\u9635\u76f8\u5f53\u4e8e\u7ed9\u6bcf\u4e2a\u8282\u70b9\u52a0\u4e86\u4e00\u6761\u81ea\u8fde\u63a5\u7684\u8fb9<\/strong><\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/482af8cf289941dd8c3d21f6ad8a3666.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n\u4f46\u662f\u73b0\u5728\u5b58\u5728\u4e00\u4e2a\u95ee\u9898\uff1a\u4e00\u4e2a\u8282\u70b9\u7684\u5ea6\u8d8a\u5927\uff0c\u5176\u505a\u77e9\u9635\u4e58\u6cd5\u540e\u7684\u503c\u5c31\u8d8a\u5927\uff08\u7d2f\u52a0\u6b21\u6570\u53d8\u591a\u4e86\uff09\uff0c\u8fd9\u79cd\u60c5\u51b5\u662f\u4e0d\u597d\u7684\uff08\u76f8\u5f53\u4e8e\u4e00\u4e2a\u4eba\u8ba4\u8bc6\u7684\u4eba\u8d8a\u591a\uff0c\u5176\u7684\u7279\u5f81\u503c\u5c31\u8d8a\u5927\uff0c\u8fd9\u6837\u4e0d\u597d)<\/p>\n<p>\u4e3a\u4e86\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u6211\u4eec\u9700\u8981\u5bf9\u5ea6\u77e9\u9635\u6c42\u5012\u6570\uff0c\u76f8\u5f53\u4e8e\u5e73\u5747\u7684\u611f\u89c9\uff0c\u5bf9\u5ea6\u6570\u5927\u7684\u8282\u70b9\u52a0\u4ee5\u9650\u5236<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/3176a275cf854ce1b255cfbf13b916b5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/6cbbe593ceed4df88a89bf79fab97d10.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n\u4e0a\u9762\u7684\u5de6\u4e58\u76f8\u5f53\u4e8e\u5bf9\u884c\u505a\u4e86\u5f52\u4e00\u5316\u64cd\u4f5c\uff0c\u90a3\u4e48\u5217\u4e5f\u9700\u8981\u505a\u5f52\u4e00\u5316\u64cd\u4f5c<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/81fe9d246b63467cb30b202e1dcc3f64.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n\u4f46\u662f\u53c8\u6709\u95ee\u9898\u4e86\uff0c\u884c\u548c\u5217\u90fd\u505a\u4e86\u5f52\u4e00\u5316\uff0c\u90a3\u4e0d\u662f\u4f1a\u5b58\u57282\u6b21\u5f52\u4e00\u5316\u7684\u60c5\u51b5\u5417\uff08\u884c\u5217\u91cd\u53e0\u5904)<\/p>\n<p>\u6240\u4ee5\u6211\u4eec\u9700\u8981\u5728\u5ea6\u77e9\u9635\u5012\u6570\u90a3\u52a0\u4e00\u4e2a0.5\u6b21\u65b9\u6765\u62b5\u6d88\u8fd9\u4e2a2\u6b21\u5f52\u4e00\u5316\u7684\u5f71\u54cd<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/cb61b359437f4b2b8c3e354b763a773e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>3.4 GCN\u53d8\u6362\u539f\u7406\u89e3\u8bfb<\/h3>\n<p>\u5982\u4e0b\u56fe\u6240\u793a\uff0c\u5047\u8bbe\u7eff\u8272\u6846\u4e2d\u7684\u4eba\u662f\u4e2a\u5bcc\u4eba\uff0c\u7ea2\u8272\u6846\u4e2d\u7684\u4eba\u662f\u4e2a\u7a77\u4eba\uff0c\u4ed6\u4eec\u53ea\u662f\u5c0f\u65f6\u5019\u8ba4\u8bc6\uff0c\u7a77\u4eba\u53ea\u8ba4\u8bc6\u5bcc\u4eba\uff0c\u800c\u5bcc\u4eba\u8ba4\u8bc6\u5f88\u591a\u4eba\u3002<\/p>\n<p>\u5982\u679c\u53ea\u5bf9\u884c\u505a\u5f52\u4e00\u5316\uff0c\u7531\u4e8e\u7a77\u4eba\u53ea\u8ba4\u8bc6\u5bcc\u4eba\uff0c\u6240\u4ee5\u5176\u5ea6\u4e3a1\uff0c\u5219\u5176\u5728\u8fdb\u884c\u7279\u5f81\u91cd\u6784\u7684\u65f6\u5019\u5f88\u5927\u4e00\u90e8\u5206\u4fe1\u606f\u4f1a\u6765\u81ea\u4e8e\u5bcc\u4eba\uff0c\u8fd9\u6837\u7684\u6a21\u578b\u5927\u6982\u7387\u4f1a\u8ba4\u4e3a\u7a77\u4eba\u548c\u5bcc\u4eba\u662f\u540c\u4e00\u79cd\u4eba\u3002\u663e\u7136\uff0c\u8fd9\u662f\u4e0d\u5408\u7406\u7684<\/p>\n<p>\u6240\u4ee5\uff0c\u6211\u4eec\u9700\u8981\u540c\u65f6\u5bf9\u884c\u548c\u5217\u90fd\u8fdb\u884c\u5f52\u4e00\u5316\uff0c\u8fd9\u6837\u4e0d\u4ec5\u53ea\u8003\u8651\u5bcc\u4eba\u5bf9\u7a77\u4eba\u7684\u5173\u7cfb\uff0c\u8fd8\u8003\u8651\u4e86\u7a77\u4eba\u5bf9\u5bcc\u4eba\u7684\u5173\u7cfb\u3002<\/p>\n<p>\u7b80\u5355\u6765\u8bf4\uff0c\u5bf9\u884c\u505a\u5f52\u4e00\u5316\u8003\u8651\u5230\u4e86\uff0c\u5bcc\u4eba\u5bf9\u7a77\u4eba\u6765\u8bf4\u5f88\u91cd\u8981\uff1b\u5bf9\u5217\u4f5c\u5f52\u4e00\u5316\uff0c\u8003\u8651\u5230\u4e86\u7a77\u4eba\u5bf9\u5bcc\u4eba\u53ef\u80fd\u6ca1\u90a3\u4e48\u91cd\u8981\uff08\u56e0\u4e3a\u5bcc\u4eba\u7684\u5ea6\u5f88\u5927\uff0c\u7a77\u4eba\u7684\u5ea6\u5f88\u5c0f\uff0c\u5bcc\u4eba\u5f88\u53ef\u80fd\u4e0d\u8bb0\u5f97\u7a77\u4eba\u4e86\uff09\uff0c\u8fd9\u6837\u76f8\u5bf9\u66f4\u52a0\u5408\u7406\u3002<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/89c495b2dc2048888ca5c178ff45048e.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>3.5 GCN\u4f20\u64ad\u516c\u5f0f<\/h3>\n<p>softmax\u662f\u4f5c\u591a\u5206\u7c7b\u5e38\u7528\u7684\u6fc0\u6d3b\u51fd\u6570<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/24c6a9203cf046ce90f319c76c7a87f5.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<hr \/>\n<h2>\u56db\u3001PyTorch Geometric \u5e93\u7684\u57fa\u672c\u4f7f\u7528<\/h2>\n<h3>4.1 PyTorch Geometric \u7684\u5b89\u88c5<\/h3>\n<pre><code>\u6ce8\u610f\uff1a \u5343\u4e07\u4e0d\u8981\u76f4\u63a5pip install \u53bb\u5b89\u88c5\u8fd9\u4e2a\u5e93\uff01\uff01\uff01<\/code><\/pre>\n<p>\u8fdb\u5165\u8fd9\u4e2aGitHub\u7f51\u5740\uff1a <a href=\"https:\/\/github.com\/pyg-team\/pytorch_geometric\">https:\/\/github.com\/pyg-team\/pytorch_geometric<\/a><\/p>\n<p>\u8fdb\u5165\u9875\u9762\u540e\u5f80\u4e0b\u6ed1\uff0c\u627e\u5230\u5982\u4e0b\u56fe\u6240\u793a\u7684\u5b57\u6837\uff0c\u70b9\u51fb<strong>here<\/strong><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/053b420ba22746b7a331e0608ce4b80f.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p><strong>\u9009\u62e9\u4f60\u7535\u8111\u4e2d\u5df2\u7ecf\u5b89\u88c5\u7684torch\u7248\u672c\uff08\u4e00\u5b9a\u8981\u548c\u4f60\u5df2\u7ecf\u5b89\u88c5\u7684torch\u7248\u672c\u4e00\u81f4\uff09<\/strong><\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/0b227791b5b742e2a00d8468ab185d12.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<p>\u600e\u4e48\u67e5\u770btorch\u7248\u672c\uff1f<\/p>\n<p>\u5728Pycharm\u4e2d\uff0c\u70b9\u51fb\u5e95\u90e8\u680f\u7684Terminal\uff0c\u8f93\u5165<code>pip show torch<\/code>\uff0c\u5373\u53ef\u67e5\u770btorch\u7248\u672c<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/893de836daff4ae8bc3ef61646c6b3d8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n\u9009\u62e9\u5b8c\u6b63\u786e\u7684torch\u7248\u672c\u540e\uff0c\u4f1a\u8fdb\u5165\u4e0b\u9762\u7684\u754c\u9762\uff0c\u4e00\u5171\u67094\u4e2a\u4e0d\u540c\u7684.whl\u6587\u4ef6\uff0c\u6bcf\u4e00\u79cd\u9009\u4e00\u4e2a\u7b26\u5408\u4f60\u7684\u7248\u672c\u4e0b\u8f7d\u5373\u53ef<\/p>\n<p><strong>\u4f8b\u5982<\/strong>\uff1atorch_cluster-1.5.9-cp36-cp36m-win_amd64.whl \u6307\u7684\u662fpython\u4e3a3.6\u7684windows\u7248\u672c<\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/3fdbf09edd994262afbb1f13d0974b81.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n\u6211\u7684\u7535\u8111\u662fwindows\u7684\uff0cpython\u7248\u672c\u4e3a3.8.12\uff0c\u6240\u4ee5\u6211\u4e0b\u8f7d\u7684\u56db\u4e2a\u5305\u5982\u4e0b\u56fe\u6240\u793a\uff1a<br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/95a6e74236b94ff09e90354bc83c2ae1.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n\u4e0b\u8f7d\u597d\u4e4b\u540e\uff0c\u76f4\u63a5<code>pip install \u4f60\u7684.whl\u6587\u4ef6\u5730\u5740<\/code><\/p>\n<p>\u4e0b\u9762\u662f\u6211\u5b89\u88c5\u65f6\u5019\u7684\u547d\u4ee4\uff08\u4ec5\u4f9b\u53c2\u8003\uff09:<\/p>\n<pre><code class=\"language-python\">pip install C:\\Users\\WSKH\\Desktop\\torch_cluster-1.5.9-cp38-cp38-win_amd64.whl\n\npip install \u202aC:\\Users\\WSKH\\Desktop\\torch_scatter-2.0.6-cp38-cp38-win_amd64.whl\n\npip install C:\\Users\\WSKH\\Desktop\\torch_sparse-0.6.9-cp38-cp38-win_amd64.whl\n\npip install \u202aC:\\Users\\WSKH\\Desktop\\torch_spline_conv-1.2.1-cp38-cp38-win_amd64.whl<\/code><\/pre>\n<p><strong>\u6700\u540e\uff0c\u4e00\u5b9a\u8981\u7b49\u4e0a\u9762\u56db\u6b65\u5b8c\u6210\u4e4b\u540e\uff0c\u518d\u6267\u884c\u4e0b\u9762\u7684\u64cd\u4f5c<\/strong><\/p>\n<pre><code class=\"language-python\">pip install torch-geometric<\/code><\/pre>\n<h3>4.2 \u6570\u636e\u96c6\u4e0e\u90bb\u63a5\u77e9\u9635\u683c\u5f0f<\/h3>\n<h4>4.2.1 \u6570\u636e\u96c6\u4ecb\u7ecd<\/h4>\n<p><strong>Hello World \u7ea7\u522b\u7684\u6570\u636e\u96c6\uff0c34\u4e2a\u8282\u70b9<\/strong><\/p>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/9bd7b497824845fa9e404d6599d079e8.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>4.2.2 \u6570\u636e\u63a2\u7d22<\/h4>\n<pre><code class=\"language-python\">from torch_geometric.datasets import KarateClub\n\ndataset = KarateClub()\nprint(f&#039;Dataset:{dataset}:&#039;)\nprint(&#039;=&#039; * 30)\nprint(f&#039;Number of graphs:{len(dataset)}&#039;)\nprint(f&#039;Number of features:{dataset.num_features}&#039;)\nprint(f&#039;Number of classes:{dataset.num_classes}&#039;)\n\nprint(&#039;=&#039; * 30)\ndata = dataset[0]\n# train_mask = [True,False,...] \uff1a\u4ee3\u8868\u7b2c1\u4e2a\u70b9\u662f\u6709\u6807\u7b7e\u7684\uff0c\u7b2c2\u4e2a\u70b9\u662f\u6ca1\u6807\u7b7e\u7684\uff0c\u65b9\u4fbf\u540e\u9762LOSS\u7684\u8ba1\u7b97\nprint(data)  # Data(x=[\u8282\u70b9\u6570, \u7279\u5f81\u6570], edge_index=[2, \u8fb9\u7684\u6761\u6570], y=[\u8282\u70b9\u6570], train_mask=[\u8282\u70b9\u6570])<\/code><\/pre>\n<p><strong>\u8f93\u51fa\uff1a<\/strong><\/p>\n<pre><code class=\"language-python\">Dataset:KarateClub():\n==============================\nNumber of graphs:1\nNumber of features:34\nNumber of classes:4\n==============================\nData(x=[34, 34], edge_index=[2, 156], y=[34], train_mask=[34])<\/code><\/pre>\n<h4>4.2.3 \u4f7f\u7528networkx\u8fdb\u884c\u53ef\u89c6\u5316\u5c55\u793a<\/h4>\n<pre><code class=\"language-python\">import os\nfrom torch_geometric.datasets import KarateClub\nfrom torch_geometric.utils import to_networkx\nimport networkx as nx\nimport matplotlib.pyplot as plt\n\n# \u753b\u56fe\u51fd\u6570\ndef visualize_graph(G, color):\n    plt.figure(figsize=(7, 7))\n    plt.xticks([])\n    plt.yticks([])\n    nx.draw_networkx(G, pos=nx.spring_layout(G, seed=42), with_labels=False,\n                     node_color=color, cmap=&quot;Set2&quot;)\n    plt.show()\n\n# \u753b\u70b9\u51fd\u6570\ndef visualize_embedding(h, color, epoch=None, loss=None):\n    plt.figure(figsize=(7, 7))\n    plt.xticks([])\n    plt.yticks([])\n    h = h.detach().cpu().numpy()\n    plt.scatter(h[:, 0], h[:, 1], s=140, c=color, cmap=&quot;Set2&quot;)\n    if epoch is not None and loss is not None:\n        plt.xlabel(f&#039;Epoch:{epoch},Loss:{loss.item():.4f}&#039;, fontsize=16)\n    plt.show()\n\nif __name__ == &#039;__main__&#039;:\n    # \u4e0d\u52a0\u8fd9\u4e2a\u53ef\u80fd\u4f1a\u62a5\u9519\n    os.environ[&#039;KMP_DUPLICATE_LIB_OK&#039;] = &#039;True&#039;\n\n    dataset = KarateClub()\n    print(f&#039;Dataset:{dataset}:&#039;)\n    print(&#039;=&#039; * 30)\n    print(f&#039;Number of graphs:{len(dataset)}&#039;)\n    print(f&#039;Number of features:{dataset.num_features}&#039;)\n    print(f&#039;Number of classes:{dataset.num_classes}&#039;)\n\n    print(&#039;=&#039; * 30)\n    data = dataset[0]\n    # train_mask = [True,False,...] \uff1a\u4ee3\u8868\u7b2c1\u4e2a\u70b9\u662f\u6709\u6807\u7b7e\u7684\uff0c\u7b2c2\u4e2a\u70b9\u662f\u6ca1\u6807\u7b7e\u7684\uff0c\u65b9\u4fbf\u540e\u9762LOSS\u7684\u8ba1\u7b97\n    print(data)  # Data(x=[\u8282\u70b9\u6570, \u7279\u5f81\u6570], edge_index=[2, \u8fb9\u7684\u6761\u6570], y=[\u8282\u70b9\u6570], train_mask=[\u8282\u70b9\u6570])\n\n    G = to_networkx(data, to_undirected=True)\n    visualize_graph(G, color=data.y)<\/code><\/pre>\n<p><strong>\u53ef\u89c6\u5316\u7ed3\u679c\uff1a<\/strong><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/f1f357f2d9ad4252bb6627f86288f780.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h4>4.2.4 GCN\u6a21\u578b\u642d\u5efa<\/h4>\n<pre><code class=\"language-python\">import torch\nfrom torch.nn import Linear\nfrom torch_geometric.nn import GCNConv\n\nclass GCN(torch.nn.Module):\n    def __init__(self, num_features, num_classes):\n        super(GCN, self).__init__()\n        torch.manual_seed(520)\n        self.num_features = num_features\n        self.num_classes = num_classes\n        self.conv1 = GCNConv(self.num_features, 4)  # \u53ea\u5b9a\u4e49\u5b50\u8f93\u5165\u7279\u8bc1\u548c\u8f93\u51fa\u7279\u8bc1\u5373\u53ef\n        self.conv2 = GCNConv(4, 4)\n        self.conv3 = GCNConv(4, 2)\n        self.classifier = Linear(2, self.num_classes)\n\n    def forward(self, x, edge_index):\n        # 3\u5c42GCN\n        h = self.convl(x, edge_index)  # \u7ed9\u5165\u7279\u5f81\u4e0e\u90bb\u63a5\u77e9\u9635\uff08\u6ce8\u610f\u683c\u5f0f\uff0c\u4e0a\u9762\u90a3\u79cd\uff09\n        h = h.tanh()\n        h = self.conv2(h.edge_index)\n        h = h.tanh()\n        h = self.conv3(h, edge_index)\n        h = h.tanh()\n        # \u5206\u7c7b\u5c42\n        out = self.classifier(h)\n        return out, h<\/code><\/pre>\n<h4>4.2.5 \u4f7f\u7528\u642d\u5efa\u597d\u7684GCN\u6a21\u578b<\/h4>\n<pre><code class=\"language-python\">import os\nimport time\n\nfrom torch_geometric.datasets import KarateClub\nimport networkx as nx\nimport matplotlib.pyplot as plt\nimport torch\nfrom torch.nn import Linear\nfrom torch_geometric.nn import GCNConv\n\n# \u753b\u56fe\u51fd\u6570\ndef visualize_graph(G, color):\n    plt.figure(figsize=(7, 7))\n    plt.xticks([])\n    plt.yticks([])\n    nx.draw_networkx(G, pos=nx.spring_layout(G, seed=42), with_labels=False,\n                     node_color=color, cmap=&quot;Set2&quot;)\n    plt.show()\n\n# \u753b\u70b9\u51fd\u6570\ndef visualize_embedding(h, color, epoch=None, loss=None):\n    plt.figure(figsize=(7, 7))\n    plt.xticks([])\n    plt.yticks([])\n    h = h.detach().cpu().numpy()\n    plt.scatter(h[:, 0], h[:, 1], s=140, c=color, cmap=&quot;Set2&quot;)\n    if epoch is not None and loss is not None:\n        plt.xlabel(f&#039;Epoch:{epoch},Loss:{loss.item():.4f}&#039;, fontsize=16)\n    plt.show()\n\nclass GCN(torch.nn.Module):\n    def __init__(self, num_features, num_classes):\n        super(GCN, self).__init__()\n        torch.manual_seed(520)\n        self.num_features = num_features\n        self.num_classes = num_classes\n        self.conv1 = GCNConv(self.num_features, 4)  # \u53ea\u5b9a\u4e49\u5b50\u8f93\u5165\u7279\u8bc1\u548c\u8f93\u51fa\u7279\u8bc1\u5373\u53ef\n        self.conv2 = GCNConv(4, 4)\n        self.conv3 = GCNConv(4, 2)\n        self.classifier = Linear(2, self.num_classes)\n\n    def forward(self, x, edge_index):\n        # 3\u5c42GCN\n        h = self.conv1(x, edge_index)  # \u7ed9\u5165\u7279\u5f81\u4e0e\u90bb\u63a5\u77e9\u9635\uff08\u6ce8\u610f\u683c\u5f0f\uff0c\u4e0a\u9762\u90a3\u79cd\uff09\n        h = h.tanh()\n        h = self.conv2(h, edge_index)\n        h = h.tanh()\n        h = self.conv3(h, edge_index)\n        h = h.tanh()\n        # \u5206\u7c7b\u5c42\n        out = self.classifier(h)\n        return out, h\n\n# \u8bad\u7ec3\u51fd\u6570\ndef train(data):\n    optimizer.zero_grad()\n    out, h = model(data.x, data.edge_index)\n    loss = criterion(out[data.train_mask], data.y[data.train_mask])\n    loss.backward()\n    optimizer.step()\n    return loss, h\n\nif __name__ == &#039;__main__&#039;:\n    # \u4e0d\u52a0\u8fd9\u4e2a\u53ef\u80fd\u4f1a\u62a5\u9519\n    os.environ[&#039;KMP_DUPLICATE_LIB_OK&#039;] = &#039;True&#039;\n\n    # \u6570\u636e\u96c6\u51c6\u5907\n    dataset = KarateClub()\n    data = dataset[0]\n\n    # \u58f0\u660eGCN\u6a21\u578b\n    model = GCN(dataset.num_features, dataset.num_classes)\n\n    # \u635f\u5931\u51fd\u6570 \u4ea4\u53c9\u71b5\u635f\u5931\n    criterion = torch.nn.CrossEntropyLoss()\n    # \u4f18\u5316\u5668 Adam\n    optimizer = torch.optim.Adam(model.parameters(), lr=0.01)\n\n    # \u8bad\u7ec3\n    for epoch in range(401):\n        loss, h = train(data)\n        if epoch % 100 == 0:\n            visualize_embedding(h, color=data.y, epoch=epoch, loss=loss)\n            time.sleep(0.3)<\/code><\/pre>\n<p><strong>\u8f93\u51fa\u56fe\u7247\uff1a<\/strong><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/f3f04301907f4245bfeaab28c1a05df7.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/0d0cc3a9d1604f78922f41b51536e500.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/dcb6bab51c384e9db7c5af9fc4e1809b.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/3bb816c0ffdc45d99610671b36a2d919.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><br \/>\n<img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/917f85509cec40c59dd1939fec75ee89.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<hr \/>\n<h2>\u4e94\u3001\u6587\u732e\u5f15\u7528\u6570\u636e\u96c6\u5206\u7c7b\u6848\u4f8b\u5b9e\u6218\uff08\u57fa\u4e8e\u70b9\u7684\u4efb\u52a1\uff09<\/h2>\n<h3>5.1 \u6570\u636e\u96c6\u4ecb\u7ecd<\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/34f6e2f0850a428db5a641f1088b914a.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n<h3>5.2 \u6570\u636e\u63a2\u7d22<\/h3>\n<pre><code class=\"language-python\">from torch_geometric.datasets import Planetoid\nfrom torch_geometric.transforms import NormalizeFeatures\n\nif __name__ == &quot;__main__&quot;:\n    # \u6570\u636e\u51c6\u5907\n    dataset = Planetoid(root=&#039;..\/data\/Planetoid&#039;, name=&#039;Cora&#039;, transform=NormalizeFeatures())  # transform\u9884\u5904\u7406\n    data = dataset[0]\n    print(f&#039;Dataset:{dataset}:&#039;)\n    print(f&#039;Number of graphs:{len(dataset)}&#039;)\n    print(f&#039;Number of features:{dataset.num_features}&#039;)\n    print(f&#039;Number of classes:{dataset.num_classes}&#039;)\n    print(f&#039;Number of nodes:{data.num_nodes}&#039;)\n    print(f&#039;Number of edges:{data.num_edges}&#039;)\n    print(f&#039;Average node degree:{data.num_edges \/ data.num_nodes}&#039;)\n    print(f&#039;Number of training nodes:{data.train_mask.sum()}&#039;)\n    print(f&#039;Training node label rate:{int(data.train_mask.sum()) \/ data.num_nodes}&#039;)\n    print(f&#039;Has isolated nodes:{data.has_isolated_nodes()}&#039;)\n    print(f&#039;Has self-loops:{data.has_self_loops()}&#039;)<\/code><\/pre>\n<p><strong>\u8f93\u51fa\uff1a<\/strong><\/p>\n<pre><code class=\"language-python\">Dataset:Cora():\nNumber of graphs:1\nNumber of features:1433\nNumber of classes:7\nNumber of nodes:2708\nNumber of edges:10556\nAverage node degree:3.8980797636632203\nNumber of training nodes:140\nTraining node label rate:0.051698670605613\nHas isolated nodes:False\nHas self-loops:False<\/code><\/pre>\n<h3>5.3 \u8bd5\u8bd5\u4f20\u7edfMLP\u7684\u6548\u679c<\/h3>\n<pre><code class=\"language-python\">import torch\nfrom torch.nn import Linear\nimport torch.nn.functional as F\nfrom torch_geometric.datasets import Planetoid\nfrom torch_geometric.transforms import NormalizeFeatures\n\nclass MLP(torch.nn.Module):\n    def __init__(self, hidden_channels):\n        super(MLP, self).__init__()\n        torch.manual_seed(520)\n        self.lin1 = Linear(dataset.num_features, hidden_channels)\n        self.lin2 = Linear(hidden_channels, dataset.num_classes)\n\n    def forward(self, x):\n        x = self.lin1(x)\n        x = x.relu()\n        x = F.dropout(x, p=0.5, training=self.training)\n        x = self.lin2(x)\n        return x\n\ndef train():\n    model.train()\n    optimizer.zero_grad()\n    out = model(data.x)\n    loss = criterion(out[data.train_mask], data.y[data.train_mask])\n    loss.backward()\n    optimizer.step()\n    return loss\n\ndef ttt():\n    model.eval()\n    out = model(data.x)\n    pred = out.argmax(dim=1)\n    test_correct = pred[data.test_mask] == data.y[data.test_mask]\n    test_acc = int(test_correct.sum()) \/ int(data.test_mask.sum())\n    return test_acc\n\nif __name__ == &#039;__main__&#039;:\n    # \u6570\u636e\u51c6\u5907\n    dataset = Planetoid(root=&#039;..\/data\/Planetoid&#039;, name=&#039;Cora&#039;, transform=NormalizeFeatures())  # transform\u9884\u5904\u7406\n    data = dataset[0]\n    # \u6a21\u578b\u5efa\u7acb\n    model = MLP(hidden_channels=16)\n    print(model)\n    print(&quot;=&quot; * 50)\n    criterion = torch.nn.CrossEntropyLoss()\n    optimizer = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4)  # Define optimizer.\n\n    # \u8fed\u4ee3\u8bad\u7ec3\n    for epoch in range(1, 201):\n        loss = train()\n        if epoch % 20 == 0:\n            print(f&#039;Epoch:{epoch} , loss:{loss.item()}&#039;)\n\n    # \u6d4b\u8bd5\n    print(&quot;\u6b63\u786e\u7387\uff1a&quot;, ttt())<\/code><\/pre>\n<p><strong>\u8f93\u51fa\uff1a<\/strong><\/p>\n<pre><code class=\"language-python\">MLP(\n  (lin1): Linear(in_features=1433, out_features=16, bias=True)\n  (lin2): Linear(in_features=16, out_features=7, bias=True)\n)\n==================================================\nEpoch:20 , loss:1.7634577751159668\nEpoch:40 , loss:1.3432351350784302\nEpoch:60 , loss:0.8805856108665466\nEpoch:80 , loss:0.6011439561843872\nEpoch:100 , loss:0.612098753452301\nEpoch:120 , loss:0.6141201853752136\nEpoch:140 , loss:0.4915192723274231\nEpoch:160 , loss:0.45700499415397644\nEpoch:180 , loss:0.4424014687538147\nEpoch:200 , loss:0.32399505376815796\n\u6b63\u786e\u7387\uff1a 0.53<\/code><\/pre>\n<h3>5.4 \u518d\u770b\u770bGCN\u7684\u6548\u679c<\/h3>\n<pre><code class=\"language-python\">import torch\nfrom torch_geometric.nn import GCNConv\nimport torch.nn.functional as F\nfrom torch_geometric.datasets import Planetoid\nfrom torch_geometric.transforms import NormalizeFeatures\n\nclass GCN(torch.nn.Module):\n    def __init__(self, hidden_channels):\n        super(GCN, self).__init__()\n        torch.manual_seed(520)\n        self.conv1 = GCNConv(dataset.num_features, hidden_channels)\n        self.conv2 = GCNConv(hidden_channels, dataset.num_classes)\n\n    def forward(self, x, edge_index):\n        x = self.conv1(x, edge_index)\n        x = x.relu()\n        x = F.dropout(x, p=0.5, training=self.training)\n        x = self.conv2(x, edge_index)\n        return x\n\ndef train():\n    model.train()\n    optimizer.zero_grad()\n    out = model(data.x, data.edge_index)\n    loss = criterion(out[data.train_mask], data.y[data.train_mask])\n    loss.backward()\n    optimizer.step()\n    return loss\n\ndef ttt():\n    model.eval()\n    out = model(data.x, data.edge_index)\n    pred = out.argmax(dim=1)\n    test_correct = pred[data.test_mask] == data.y[data.test_mask]\n    test_acc = int(test_correct.sum()) \/ int(data.test_mask.sum())\n    return test_acc\n\nif __name__ == &#039;__main__&#039;:\n    # \u6570\u636e\u51c6\u5907\n    dataset = Planetoid(root=&#039;..\/data\/Planetoid&#039;, name=&#039;Cora&#039;, transform=NormalizeFeatures())  # transform\u9884\u5904\u7406\n    data = dataset[0]\n    # \u6a21\u578b\u5efa\u7acb\n    model = GCN(hidden_channels=16)\n    print(model)\n    print(&quot;=&quot; * 50)\n    criterion = torch.nn.CrossEntropyLoss()\n    optimizer = torch.optim.Adam(model.parameters(), lr=0.01, weight_decay=5e-4)  # Define optimizer.\n\n    # \u8fed\u4ee3\u8bad\u7ec3\n    for epoch in range(1, 201):\n        loss = train()\n        if epoch % 20 == 0:\n            print(f&#039;Epoch:{epoch} , loss:{loss.item()}&#039;)\n\n    # \u6d4b\u8bd5\n    print(&quot;\u6b63\u786e\u7387\uff1a&quot;, ttt())<\/code><\/pre>\n<p><strong>\u8f93\u51fa\uff1a<\/strong><\/p>\n<pre><code class=\"language-python\">GCN(\n  (conv1): GCNConv(1433, 16)\n  (conv2): GCNConv(16, 7)\n)\n==================================================\nEpoch:20 , loss:1.7255724668502808\nEpoch:40 , loss:1.3229681253433228\nEpoch:60 , loss:0.9705381989479065\nEpoch:80 , loss:0.7201246619224548\nEpoch:100 , loss:0.5934590697288513\nEpoch:120 , loss:0.4580436646938324\nEpoch:140 , loss:0.4311455488204956\nEpoch:160 , loss:0.4086465537548065\nEpoch:180 , loss:0.3476596772670746\nEpoch:200 , loss:0.32204487919807434\n\u6b63\u786e\u7387\uff1a 0.813\n\u53ef\u4ee5\u770b\u51fa\uff0c\u4f7f\u7528GCN\u7684\u51c6\u786e\u7387\u4e3a81%\uff0c\u4f7f\u7528MLP\u7684\u51c6\u786e\u7387\u4e3a59%\uff0c\u63d0\u9ad8\u4e8622%<\/code><\/pre>\n<hr \/>\n<h2>\u516d\u3001\u6784\u5efa\u81ea\u5df1\u7684\u56fe\u6570\u636e\u96c6<\/h2>\n<pre><code class=\"language-python\">import torch\nfrom torch_geometric.data import Data\n\nif __name__ == &#039;__main__&#039;:\n    # \u5b9a\u4e49\u8282\u70b9\u7279\u5f81\u5411\u91cfx\u548c\u6807\u7b7ey\n    x = torch.tensor([[2, 1], [5, 6], [3, 7], [12, 0]], dtype=torch.float)\n    y = torch.tensor([0, 1, 0, 1], dtype=torch.float)\n\n    # \u5b9a\u4e49\u8fb9\n    edge_index = torch.tensor([[0, 1, 2, 0, 3],  # \u8d77\u59cb\u70b9\n                               [1, 0, 1, 3, 2]], dtype=torch.long)  # \u7ec8\u6b62\u70b9\n\n    # \u5b9a\u4e49train_mask\n    train_mask = [(True if d is not None else False) for d in y]\n\n    # \u6784\u5efadata\n    data = Data(x=x, y=y, edge_index=edge_index, train_mask=train_mask)\n    print(&quot;data:&quot;, data)\n    print(&quot;train_mask:&quot;, data.train_mask)\n12345678910111213141516171819<\/code><\/pre>\n<p><strong>\u8f93\u51fa\uff1a<\/strong><\/p>\n<pre><code class=\"language-python\">data: Data(x=[4, 2], edge_index=[2, 5], y=[4], train_mask=[4])\ntrain_mask: [True, True, True, True]<\/code><\/pre>\n<p><strong>\u4e0a\u9762\u7684\u4f8b\u5b50\u4e2d\uff0c\u53ea\u6784\u5efa\u4e86\u4e00\u5f20\u56fe\uff0c\u5982\u679c\u9700\u8981\u6784\u5efa\u5f88\u591a\u56fe\uff0c\u5219\u91cd\u590d\u64cd\u4f5c\u5373\u53ef\u3002<br \/>\n\u6700\u540e\u5c06\u6240\u6709\u56fe\u653e\u5230\u4e00\u4e2alist\u5217\u8868\u91cc\u5c31\u53ef\u4ee5\u4e86<\/strong><\/p>\n<hr \/>\n<h2>\u4e03\u3001\u57fa\u4e8e\u56fe\u795e\u7ecf\u7f51\u7edc\u7684\u7535\u5546\u8d2d\u4e70\u9884\u6d4b\u5b9e\u4f8b<\/h2>\n<h3>7.1 \u6570\u636e\u96c6\u4ecb\u7ecd<\/h3>\n<p><img src=\"https:\/\/lemon-guess.oss-cn-hangzhou.aliyuncs.com\/img\/536cb46d9a3247f1a7a9ced9093e8ea7.png\" alt=\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\" \/><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u4e00\u3001\u56fe\u795e\u7ecf\u7f51\u7edc\u5e94\u7528\u9886\u57df https:\/\/distill.pub\/2021\/gnn-intro\/ 1.1 \u82af\u7247\u8bbe\u8ba1 \u82af\u7247\u7684\u8bbe\u8ba1\u6bd4\u8f83\u8017\u8d39\u4eba\u529b   \u2026 &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0},"categories":[233],"tags":[252,253,249],"_links":{"self":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9219"}],"collection":[{"href":"\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=9219"}],"version-history":[{"count":2,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9219\/revisions"}],"predecessor-version":[{"id":9232,"href":"\/index.php?rest_route=\/wp\/v2\/posts\/9219\/revisions\/9232"}],"wp:attachment":[{"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=9219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=9219"},{"taxonomy":"post_tag","embeddable":true,"href":"\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=9219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}