{"id":2875,"date":"2025-03-11T09:57:54","date_gmt":"2025-03-11T01:57:54","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2875"},"modified":"2025-03-11T11:02:39","modified_gmt":"2025-03-11T03:02:39","slug":"relational-graph-convolutional-neural-network","status":"publish","type":"post","link":"http:\/\/gnn.club\/?p=2875","title":{"rendered":"Relational Graph Convolutional Neural Network"},"content":{"rendered":"\n

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\u4e0eGCN\u4e0d\u540c\uff0cRGCN\uff08Relational Graph Convolutional Neural Network\uff09\u88ab\u8bbe\u8ba1\u7528\u6765\u5904\u7406\u5177\u6709\u591a\u79cd\u5173\u7cfb\u7684\u5f02\u6784\u56fe\u3002\u6b64\u65f6\uff0c\u8282\u70b9\u6216\u8fb9\u7684\u79cd\u7c7b\u6709\u5f88\u591a\u79cd\u60c5\u51b5\uff0c\u6bcf\u79cd\u7c7b\u578b\u53ef\u80fd\u6709\u5176\u7279\u5b9a\u7684\u5c5e\u6027\u548c\u8bed\u4e49\u3002\u4f8b\u5982\uff0c\u5728\u751f\u7269\u533b\u5b66\u7684\u5f02\u6784\u56fe\u4e2d\uff0c\u4e0d\u540c\u7c7b\u578b\u7684\u8282\u70b9\uff08\u5982\u836f\u7269\u5206\u5b50\u3001\u75be\u75c5\u540d\u79f0\u3001\u86cb\u767d\u8d28\u540d\u79f0\u3001\u751f\u7269\u901a\u8def\u7b49\uff09\u548c\u8fb9\uff08\u5982\u4fc3\u8fdb\u3001\u6291\u5236\u3001\u6cbb\u7597\u3001\u5305\u542b\u7b49\uff09\u5305\u542b\u4e30\u5bcc\u7684\u8bed\u4e49\u4fe1\u606f\u3002RGNN\u80fd\u591f\u5bf9\u8fd9\u4e9b\u4e0d\u540c\u7c7b\u578b\u7684\u5b9e\u4f53\u548c\u5173\u7cfb\u5206\u522b\u5b66\u4e60\u8868\u793a\uff0c\u8fd9\u6837\u80fd\u591f\u66f4\u597d\u5730\u7406\u89e3\u5b83\u4eec\u5404\u81ea\u4ee5\u53ca\u5b83\u4eec\u4e4b\u95f4\u7684\u590d\u6742\u5173\u7cfb\u3002\u7528\u516c\u5f0f\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n

\\(G=(V,E,R,T)\\)<\/p>\n\n\n

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\u3010\u4f8b1\u3011\u8fb9\u6709\u4e09\u79cd\u4e0d\u540c\u7684\u7c7b\u578b\\((r_1,r_2,r_3)\\)\uff0c\u5206\u522b\u7528\u4e09\u79cd\u4e0d\u540c\u7684\u7ebf\u6bb5\u683c\u5f0f\u8868\u793a\uff0c\u5982\u56fe1\u6240\u793a\u3002\u4f8b\u5982\uff0c\u8282\u70b9A\u901a\u8fc7\u7c7b\u578b\u4e3a\\(r_{1}\\) \u7684\u8fb9\u4e0e\u8282\u70b9B\u548cD\u76f8\u8fde\uff0c\u901a\u8fc7\u7c7b\u578b\u4e3a\\(r_{2}\\) \u7684\u8fb9\u4e0e\u8282\u70b9C\u76f8\u8fde\u7b49\u7b49\u3002\u56fe1\u4e2d\u4e5f\u5c55\u793a\u4e86\u5173\u7cfb\u56fe\u5377\u79ef\u7f51\u7edc\uff08RGCN\uff09\u7684\u4e00\u4e2a\u5173\u952e\u7279\u70b9\uff1a\u4e0d\u540c\u7c7b\u578b\u7684\u8fb9\u4f7f\u7528\u4e0d\u540c\u7684\u6743\u91cd\u77e9\u9635\\((W_{_{r1}},W_{_{r2}},W_{_{r3}})\\)\u6765\u5904\u7406\u4fe1\u606f\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5f53\u66f4\u65b0\u4e00\u4e2a\u8282\u70b9\u7684\u7279\u5f81\u65f6\uff0cRGCN \u4f1a\u6839\u636e\u8fb9\u7684\u7c7b\u578b\u4f7f\u7528\u4e0d\u540c\u7684\u6743\u91cd\u77e9\u9635\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\\(r_{1}\\) \u6709\u4e09\u79cd\u7c7b\u578b\uff0c\u4f46\u8fd9\u5e76\u4e0d\u610f\u5473\u7740\u8981\u7ef4\u62a4\u4e09\u4e2a\u72ec\u7acb\u7684\u795e\u7ecf\u7f51\u7edc\u3002\u5b9e\u9645\u4e0a\uff0c\\(W_{_{r1}},W_{_{r2}},W_{_{r3}}\\)\u53ef\u4ee5\u5171\u540c\u7ec4\u6210\u4e00\u5c42\u795e\u7ecf\u7f51\u7edc\u7684\u53c2\u6570\u3002\u5047\u8bbe\u7528\u4e8e\u66f4\u65b0\u8fb9\u4fe1\u606f\u7684\u795e\u7ecf\u7f51\u7edc\u8f93\u5165\u8f93\u51fa\u90fd\u662f\u753112\u4e2a\u795e\u7ecf\u5143\u7ec4\u6210\u7684\u7f51\u7edc\u5c42\uff0c\u90a3\u4e48\u7b2c1-3\u4e2a\u795e\u7ecf\u5143\u53ef\u4ee5\u7528\u4e8e\u66f4\u65b0\u7b2c\u4e00\u79cd\u8fb9\u7c7b\u578b\uff1b\u7b2c4-6\u4e2a\u795e\u7ecf\u5143\u7528\u4e8e\u66f4\u65b0\u7b2c\u4e8c\u79cd\u8fb9\u7c7b\u578b\uff1b\u7b2c7-9\u4e2a\u795e\u7ecf\u5143\u7528\u4e8e\u66f4\u65b0\u7b2c\u4e09\u79cd\u8fb9\u7c7b\u578b\u3002<\/p>\n\n\n

\n
\"\"
\u56fe1 \u8282\u70b9\u6620\u5c04<\/figcaption><\/figure><\/div>\n\n\n

RGCN\u4e3a\u6bcf\u79cd\u7c7b\u578b\u7684\u8fb9\u5f15\u5165\u4e86\u4e0d\u540c\u7684\u6743\u91cd\u77e9\u9635\uff0c\u4ee5\u6b64\u6765\u6355\u83b7\u4e0d\u540c\u5173\u7cfb\u7c7b\u578b\u4e4b\u95f4\u7684\u7ec6\u5fae\u5dee\u5f02\u3002\u6bcf\u4e00\u79cd\u5173\u7cfb\u7c7b\u578b\u7684\u6743\u91cd\u77e9\u9635\u8d1f\u8d23\u7f16\u7801\u7279\u5b9a\u7c7b\u578b\u7684\u8fb9\u5bf9\u8282\u70b9\u7279\u5f81\u66f4\u65b0\u7684\u8d21\u732e\u3002\u8fd9\u6837\uff0cRGCN\u80fd\u591f\u7efc\u5408\u8282\u70b9\u7684\u7279\u5f81\u4ee5\u53ca\u4e0e\u5176\u76f8\u8fde\u7684\u5404\u79cd\u7c7b\u578b\u8fb9\u7684\u4fe1\u606f\uff0c\u751f\u6210\u66f4\u4e30\u5bcc\u7684\u8282\u70b9\u8868\u5f81\u3002\u5b9e\u9645\u4e0a\uff0cRGNN\u66f4\u50cf\u662f\u4e00\u79cd\u601d\u60f3\uff0c\u800c\u4e0d\u662f\u56fa\u5b9a\u7684\u6a21\u578b\uff0c\u5b83\u53ef\u4ee5\u6269\u5c55\u5230\u5176\u5b83GNN\u6a21\u578b\u4e0a\uff0c\u5982GraphSAGE\u3001RGAT\u7b49\u3002\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u7279\u5f81\u66f4\u65b0\u89c4\u5219\u5728RGCN\u4e2d\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n\n\n

\\(\\boldsymbol{h}_i^{(l+1)}=\\sigma\\left(\\sum_{r\\in R}\\sum_{j\\in N_r(i)}\\frac{1}{c_{i,r}}\\boldsymbol{W}_r^{(l)}\\boldsymbol{h}_j^{(l)}\\right)\\)<\/p>\n\n\n

\u5176\u4e2d\uff1a<\/p>\n\n\n\n

    \n
  • \\(h_j^{(l)}\\)\u662f\u8282\u70b9\\(\\mathrm{j}\\)\u5728\u7b2c\\(\\mathrm{l}\\)\u5c42\u7684\u7279\u5f81\u5411\u91cf\u3002<\/li>\n\n\n\n
  • \\(W_r^{(l)}\\)\u662f\u5173\u7cfb\u7c7b\u578b\\(\\mathrm{r}\\)\u5bf9\u5e94\u7684\u6743\u91cd\u77e9\u9635\uff0c\u5728\u7b2c\\(\\mathrm{l}\\)\u5c42\u4e2d\u7528\u4e8e\u8f6c\u6362\u7279\u5f81\u3002<\/li>\n\n\n\n
  • \\(N_{r}(i)\\)\u8868\u793a\u4e0e\u8282\u70b9\\(\\mathrm{i}\\)\u76f8\u8fde\u7684\u7279\u5b9a\u5173\u7cfb\u7c7b\u578b\\(\\mathrm{r}\\)\u7684\u90bb\u5c45\u8282\u70b9\u96c6\u5408\u3002<\/li>\n\n\n\n
  • \\(c_{i,r}\\)\u662f\u4e00\u4e2a\u5f52\u4e00\u5316\u9879\uff0c\u901a\u5e38\u662f\u8282\u70b9\\(\\mathrm{i}\\)\u7684\u7c7b\u578b\\(\\mathrm{r}\\)\u5173\u7cfb\u7684\u90bb\u5c45\u6570\u91cf\uff0c\u7528\u4e8e\u5e73\u8861\u4e0d\u540c\u8282\u70b9\u4e4b\u95f4\u4e0d\u540c\u6570\u91cf\u90bb\u5c45\u7684\u5f71\u54cd\u3002<\/li>\n\n\n\n
  • \\(\\sigma\\)\u662f\u4e00\u4e2a\u975e\u7ebf\u6027\u6fc0\u6d3b\u51fd\u6570, \u5982ReLU\u3002<\/li>\n<\/ul>\n\n\n\n

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    <\/p>\n","protected":false},"excerpt":{"rendered":"

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