{"id":2883,"date":"2025-03-12T10:33:37","date_gmt":"2025-03-12T02:33:37","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2883"},"modified":"2025-03-12T11:02:44","modified_gmt":"2025-03-12T03:02:44","slug":"graphgan","status":"publish","type":"post","link":"http:\/\/gnn.club\/?p=2883","title":{"rendered":"GraphGAN"},"content":{"rendered":"\n<p>GraphGAN\u662f\u4e00\u79cd\u7ed3\u5408\u4e86\u56fe\u795e\u7ecf\u7f51\u7edc\u548c\u751f\u6210\u5bf9\u6297\u7f51\u7edc\uff08GAN\uff09\u6982\u5ff5\u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\u3002\u5b83\u65e8\u5728\u901a\u8fc7\u5bf9\u6297\u5b66\u4e60\u6846\u67b6\u89e3\u51b3\u56fe\u6570\u636e\u4e2d\u7684\u8282\u70b9\u5206\u7c7b\u548c\u94fe\u63a5\u9884\u6d4b\u95ee\u9898\uff0c\u7279\u522b\u662f\u5728\u7f3a\u5c11\u6807\u7b7e\u6570\u636e\u7684\u60c5\u51b5\u4e0b\u3002GraphGAN\u901a\u8fc7\u7ed3\u5408\u751f\u6210\u5668\u548c\u5224\u522b\u5668\u4e24\u4e2a\u4e3b\u8981\u7ec4\u4ef6\u6765\u5b66\u4e60\u56fe\u4e2d\u8282\u70b9\u7684\u6709\u6548\u8868\u793a\u3002<\/p>\n\n\n\n<p>GraphGAN\u7684\u6846\u67b6\u5982\u4e0b\uff1a\u8bbe\\(G=(V,\\mathcal{E})\\)\u4e3a\u4e00\u4e2a\u7ed9\u5b9a\u7684\u56fe\uff0c\u5176\u4e2d\\(V=\\begin{Bmatrix}v_1,\\ldots,v_V\\end{Bmatrix}\\)\u4ee3\u8868\u9876\u70b9\u7684\u96c6\u5408\uff0c\u800c$\\mathcal{E} = \\left\\{ e_{ij} \\right\\}_{i,j=1}^{V}$\u4ee3\u8868\u8fb9\u7684\u96c6\u5408\u3002\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u9876\u70b9\\(\\nu_{c}\\)\uff0c\u5b9a\u4e49\\(\\mathcal{N}\\left(\\nu_{c}\\right)\\)\u4e3a\u76f4\u63a5\u8fde\u63a5\u5230\\(\\nu_{c}\\)\u7684\u9876\u70b9\u96c6\uff0c\u4e5f\u5c31\u662f\u9876\u70b9\\(\\nu_{c}\\)\u76841-hop\u90bb\u5c45\u3002\u6211\u4eec\u5c06\u9876\u70b9\\(\\nu_{c}\\)\u7684\u771f\u5b9e\u8fde\u901a\u6027\u5206\u5e03\u8868\u793a\u4e3a\u6761\u4ef6\u6982\u7387\\(p_{\\mathrm{true}}\\left(\\nu|\\nu_{c}\\right)\\)\uff0c\u5b83\u53cd\u6620\u4e86\\(\\nu_{c}\\)\u7684\u8fde\u901a\u6027\u504f\u597d\u548c\u5b83\u6240\u8fde\u63a5\u9876\u70b9\u7684\u7c7b\u578b\u3002\u4ece\u8fd9\u4e2a\u89c6\u89d2\u6765\u770b\uff0c\\(\\mathcal{N}\\left(\\nu_{c}\\right)\\)\u53ef\u4ee5\u88ab\u770b\u4f5c\u662f\u4ece\\(p_{\\mathrm{true}}\\left(\\nu|\\nu_{c}\\right)\\)\u62bd\u53d6\u7684\u4e00\u7ec4\u89c2\u5bdf\u6837\u672c\u3002\u7ed9\u5b9a\u56fe\\(\\mathrm{G}\\)\uff0cGraphGAN\u65e8\u5728\u5b66\u4e60\u4ee5\u4e0b\u4e24\u4e2a\u6a21\u578b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u751f\u6210\u5668\\(G(\\nu|\\nu_c;\\theta_G)\\)\uff1a\u5c1d\u8bd5\u8fd1\u4f3c\u9876\u70b9\\(\\nu_{c}\\)\u7684\u771f\u5b9e\u8fde\u901a\u6027\u5206\u5e03\\(p_{\\mathrm{true}}\\left(\\nu|\\nu_{c}\\right)\\)\uff0c\u5e76\u751f\u6210\uff08\u6216\u9009\u62e9\uff09\u6700\u6709\u53ef\u80fd\u4e0e\\(\\nu_{c}\\)\u76f8\u8fde\u63a5\u7684\u9876\u70b9\u96c6\u3002<\/li>\n\n\n\n<li>\u5224\u522b\u5668\\(D\\left(\\nu,\\nu_{c};\\theta_{D}\\right)\\)\uff1a\u65e8\u5728\u9274\u522b\u9876\u70b9\u5bf9\\(\\begin{pmatrix}\\nu,\\nu_{c}\\end{pmatrix}\\)\u7684\u8fde\u901a\u6027\u3002\\(D\\left(\\nu,\\nu_{c};\\theta_{D}\\right)\\)\u8f93\u51fa\u4e00\u4e2a\u6807\u91cf\u503c\uff0c\u8868\u793a\u8fb9\\(\\begin{pmatrix}\\nu,\\nu_{c}\\end{pmatrix}\\)\u5b58\u5728\u7684\u6982\u7387\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u751f\u6210\u5668\\(\\mathrm{G}\\)\u548c\u5224\u522b\u5668\\(\\mathrm{D}\\)\u4f5c\u4e3a\u4e24\u4e2a\u5bf9\u624b: \u751f\u6210\u5668\\(\\mathrm{G}\\)\u5c06\u8bd5\u56fe\u5b8c\u7f8e\u5730\u5339\u914d\\(p_{\\mathrm{true}}\\left(\\nu|\\nu_{c}\\right)\\)\u5e76\u751f\u6210\u7c7b\u4f3c\u4e8e\\(\\nu_{c}\\)\u7684\u771f\u5b9e\u76f4\u63a5\u90bb\u5c45\u7684\u76f8\u5173\u9876\u70b9\u4ee5\u6b3a\u9a97\u5224\u522b\u5668\u3002\u800c\u5224\u522b\u5668\\(\\mathrm{D}\\)\u5219\u76f8\u53cd\uff0c\u4f1a\u5c1d\u8bd5\u68c0\u6d4b\u8fd9\u4e9b\u9876\u70b9\u662f\\(\\nu_{c}\\)\u7684\u771f\u5b9e\u90bb\u5c45\u8fd8\u662f\u7531\u5176\u5bf9\u624b\\(\\mathrm{G}\\)\u751f\u6210\u7684\u3002\u5f62\u5f0f\u4e0a\uff0c \\(\\mathrm{G}\\)\u548c\\(\\mathrm{D}\\)\u5728\u4e00\u4e2a\u6709\u4ee5\u4e0b\u4ef7\u503c\u51fd\u6570\\(V(G,D)\\)\u7684\u53cc\u4eba\u535a\u5f08\u4e2d\u8fdb\u884c\u5bf9\u6297\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\min_{\\theta_G}\\max_{\\theta_D}V(G,D)=\\sum_{c=1}^V\\left(\\mathbb{E}_{\\nu\\sim p_{\\mathbf{tne}}(\\nu|\\nu_c)}\\left[\\log D(\\nu,\\nu_c;\\theta_D)\\right]+\\mathbb{E}_{\\nu\\sim p_G(\\nu|\\nu_c;\\theta_G)}\\left[\\log\\left(1-D(\\nu,\\nu_c;\\theta_D)\\right)\\right]\\right)\\)\u00a0 \u00a0 \u00a0 \u00a0\uff081\uff09<\/p>\n\n\n<p>\u4e0a\u5f0f\u63cf\u8ff0\u7684\u6700\u5c0f\u6700\u5927\uff08Minimax\uff09\u535a\u5f08\u516c\u5f0f\u662f\u751f\u6210\u5bf9\u6297\u7f51\u7edc\u7684\u6838\u5fc3\u3002\u5728\u56fe\u751f\u6210\u5bf9\u6297\u7f51\u7edc\uff08GraphGAN\uff09\u7684\u4e0a\u4e0b\u6587\u4e2d\uff0c\u751f\u6210\u5668\\(\\mathrm{G}\\)\u7684\u76ee\u6807\u662f\u751f\u6210\u770b\u8d77\u6765\u50cf\u771f\u5b9e\u6570\u636e\u7684\u6837\u672c\u3002\u5728GraphGAN\u7684\u60c5\u5883\u4e0b\uff0c\u751f\u6210\u5668\u8bd5\u56fe\u751f\u6210\u770b\u4f3c\u662f\\(\\nu_{c}\\)\u76841-hop\u90bb\u5c45\u7684\u9876\u70b9\u3002\u800c\u9274\u522b\u5668\\(\\mathrm{D}\\)\u7684\u76ee\u6807\u662f\u533a\u5206\u8f93\u5165\u6837\u672c\u662f\u6765\u81ea\u4e8e\u771f\u5b9e\u6570\u636e\u8fd8\u662f\u751f\u6210\u5668\u751f\u6210\u7684\u5047\u6570\u636e\u3002\u5728GraphGAN\u4e2d\uff0c\u5b83\u8bd5\u56fe\u533a\u5206\u4e00\u4e2a\u9876\u70b9\u5bf9\\((\\nu,\\nu_{c})\\)\u662f\u5426\u662f\u771f\u5b9e\u76841-hop\u90bb\u70b9\u5bf9\u3002\u8fd9\u4e2a\u516c\u5f0f\u5305\u542b\u4e86\u4e24\u4e2a\u671f\u671b\uff08Expectations\uff09\uff1a<\/p>\n\n\n\n<p>\u7b2c\u4e00\u90e8\u5206\u4e3a\u771f\u5b9e\u6570\u636e\u7684\u671f\u671b\\(E_{v\\sim p_{\\mathrm{true}}\\left(v\\mid v_{c}\\right)}\\left[\\log D\\left(v,v_{c};\\theta_{D}\\right)\\right]\\)\u3002\u8fd9\u4e2a\u671f\u671b\u8868\u793a\u5bf9\u6240\u6709\u771f\u5b9e\u7684\u9876\u70b9\u5bf9\\(\\begin{pmatrix}\\nu,\\nu_{c}\\end{pmatrix}\\)\uff0c\u9274\u522b\u5668\\(\\mathrm{D}\\)\u8f93\u51fa\u5b83\u4eec\u662f\u771f\u5b9e\u90bb\u5c45\u7684\u6982\u7387\u7684\u5bf9\u6570\u3002\\({\\mathcal{V}}\\)\u662f\u4ece\u9876\u70b9\\(\\nu_{c}\\)\u7684\u771f\u5b9e\u90bb\u5c45\u5206\u5e03\\(p_{\\mathrm{true}}\\left(\\nu|\\nu_{c}\\right)\\)\u4e2d\u91c7\u6837\u7684\u3002\u7406\u60f3\u60c5\u51b5\u4e0b: \u5982\u679c\\(\\nu\\)\u786e\u5b9e\u662f\\(\\nu_{c}\\)\u7684\u771f\u5b9e\u90bb\u5c45\uff0c\u6211\u4eec\u5e0c\u671b\u9274\u522b\u5668\\(\\mathrm{D}\\)\u7684\u8f93\u51fa\\(D\\left(\\nu,\\nu_{c};\\theta_{D}\\right)\\)\u63a5\u8fd1\u4e8e1 (\u6700\u5927\u7684\u53ef\u80fd\u6027)\u3002\u6b64\u65f6\\(\\log D\\left(\\nu,\\nu_{c};\\theta_{D}\\right)\\)\u4f1a\u63a5\u8fd10\uff08\u56e0\u4e3a\\(\\log(1){=}0\\)\uff09\u3002<\/p>\n\n\n\n<p>\u7b2c\u4e8c\u90e8\u5206\u662f\u5173\u4e8e\u751f\u6210\u6570\u636e\u7684\u671f\u671b\\(E_{\\nu\\sim p_G\\left(\\nu|\\nu_c;\\theta_G\\right)}\\left[\\log\\left(1-D\\left(\\nu,\\nu_c;\\theta_D\\right)\\right)\\right]\\)\u3002\u8fd9\u4e2a\u671f\u671b\u8868\u793a\u5bf9\u6240\u6709\u751f\u6210\u5668\\(\\mathrm{G}\\)\u751f\u6210\u7684\u9876\u70b9\u5bf9\\(\\begin{pmatrix}\\nu,\\nu_{c}\\end{pmatrix}\\)\uff0c\u9274\u522b\u5668\\(\\mathrm{D}\\)\u8f93\u51fa\u5b83\u4eec\u4e0d\u662f\u771f\u5b9e\u90bb\u5c45\u7684\u6982\u7387\u7684\u5bf9\u6570\u3002\\(\\nu\\)\u662f\u4ece\u751f\u6210\u5668\\(\\mathrm{G}\\)\u7684\u5206\u5e03\\(p_{G}\\left(\\nu|\\nu_{c};\\theta_{G}\\right)\\)\u4e2d\u91c7\u6837\u7684\u3002\u7406\u60f3\u60c5\u51b5\u4e0b\uff1a\u5982\u679c\\(\\nu\\)\u662f\u751f\u6210\u5668\\(\\mathrm{G}\\)\u751f\u6210\u7684\uff0c\u5e76\u4e0d\u662f\\(\\nu_{c}\\)\u7684\u771f\u5b9e\u90bb\u5c45\uff0c\u6211\u4eec\u5e0c\u671b\u5224\u522b\u5668\\(\\mathrm{D}\\)\u7684\u8f93\u51fa\\(D\\left(\\nu,\\nu_{c};\\theta_{D}\\right)\\)\u63a5\u8fd1\u4e8e0\u3002\u6b64\u65f6, \\(\\log\\left(1-D\\left(\\nu,\\nu_c;\\theta_D\\right)\\right)\\)\u4e5f\u4f1a\u63a5\u8fd10\uff08\u56e0\u4e3a\\(\\log(1-0)=0\\)\uff09\u3002<\/p>\n\n\n\n<p>\u53ef\u4ee5\u770b\u51fa\u8fd9\u4e24\u90e8\u5206\u671f\u671b\u7684\u76ee\u6807\u90fd\u662f\u5e0c\u671b\u7ecf\u8fc7\u8bad\u7ec3\u540e\uff0c\u5176\u503c\u8d8a\u6765\u8d8a\u5c0f\uff0c\u7406\u60f3\u60c5\u51b5\u4e0b\u4e3a0\uff0c\u56e0\u6b64\u53ef\u4ee5\u770b\u4f5cGraphGAN\u7684\u635f\u5931\u51fd\u6570\uff0cGraphGAN\u7684\u8bad\u7ec3\u72b6\u6001\u5982\u56fe1\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"613\" height=\"325\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250312100036904.png\" alt=\"\" class=\"wp-image-2890\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250312100036904.png 613w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250312100036904-300x159.png 300w\" sizes=\"auto, (max-width: 613px) 100vw, 613px\" \/><figcaption class=\"wp-element-caption\">\u56fe1 GraphGAN\u8bad\u7ec3\u72b6\u6001<\/figcaption><\/figure><\/div>\n\n\n<p>\u9634\u5f71\u7684\u5706\u4ee3\u8868\u4ece\u771f\u5b9e\u56fe\u7ed3\u6784\u4e2d\u91c7\u6837\u7684\u771f\u5b9e\u4e0e\u9876\u70b9\\(\\nu_{c}\\)\u8fde\u63a5\u7684\u90bb\u5c45\uff0c\u6a2a\u6761\u7eb9\u7684\u5706\u4ee3\u8868\u751f\u6210\u5668\u8ba4\u4e3a\u7684\u5e94\u8be5\u4e0e\\(\\nu_{c}\\)\u8fde\u63a5\u7684\u90bb\u5c45\u3002\u5728\u8bad\u7ec3\u7684\u521d\u59cb\u9636\u6bb5\uff08\u5de6\u56fe\uff09\uff0c\u751f\u6210\u5668\\(\\mathrm{G}\\)\u7684\u8868\u73b0\u5e76\u4e0d\u4f73\uff0c\u5176\u751f\u6210\u7684\u9876\u70b9\u4e0e\u5b9e\u9645\u7684\u90bb\u5c45\u76f8\u6bd4\uff0c\u5dee\u5f02\u8f83\u5927\uff0c\u5f88\u5bb9\u6613\u88ab\u9274\u522b\u5668\\(\\mathrm{D}\\)\u533a\u5206\u3002\u968f\u7740\u5bf9\u6297\u8bad\u7ec3\u7684\u8fdb\u884c\uff08\u4e2d\u56fe\uff09\uff0c\u751f\u6210\u5668\\(\\mathrm{G}\\)\u9010\u6e10\u5b66\u4e60\u5230\u66f4\u597d\u7684\u751f\u6210\u7b56\u7565\uff0c\u4f7f\u5f97\u751f\u6210\u7684\u90bb\u5c45\u548c\u5b9e\u9645\u7684\u90bb\u5c45\u66f4\u96be\u4ee5\u533a\u5206\u3002\u5728\u7ecf\u8fc7\u5145\u5206\u7684\u8bad\u7ec3\u4e4b\u540e\uff0c\u751f\u6210\u5668\\(\\mathrm{G}\\)\u751f\u6210\u7684\u90bb\u5c45\u4e0e\u5b9e\u9645\u7684\u90bb\u5c45\u975e\u5e38\u63a5\u8fd1\uff0c\u5373\u53f3\u56fe\u4e2d\uff0c\u9634\u5f71\u7684\u5706\u548c\u6a2a\u6761\u7eb9\u7684\u5706\u5b58\u5728\u5927\u91cf\u91cd\u53e0\u3002\u9274\u522b\u5668\\(\\mathrm{D}\\)\u51e0\u4e4e\u65e0\u6cd5\u533a\u5206\u3002\u5728\u8fd9\u4e2a\u535a\u5f08\u4e2d\uff0c\u9274\u522b\u5668\u5c3d\u91cf\u63d0\u9ad8\u8bc6\u522b\u771f\u5b9e\u548c\u751f\u6210\u6570\u636e\u5bf9\u7684\u51c6\u786e\u6027\uff0c\u800c\u751f\u6210\u5668\u5c3d\u91cf\u751f\u6210\u770b\u8d77\u6765\u8d8a\u771f\u5b9e\u7684\u6570\u636e\u3002\u901a\u8fc7\u8fd9\u79cd\u5bf9\u7acb\u7684\u8bad\u7ec3\u8fc7\u7a0b\uff0c\u4e24\u4e2a\u6a21\u578b\u90fd\u5728\u4e0d\u65ad\u6539\u8fdb\uff0c\u76f4\u5230\u8fbe\u5230\u4e00\u4e2a\u5e73\u8861\u70b9\uff0c\u5373\u751f\u6210\u5668\u751f\u6210\u7684\u6570\u636e\u975e\u5e38\u903c\u771f\uff0c\u9274\u522b\u5668\u5f88\u96be\u533a\u5206\u771f\u5047\u6570\u636e\u5bf9\u3002<\/p>\n\n\n\n<p>\u4e0b\u9762\u5177\u4f53\u7684\u8bb2\u89e3GraphGAN\u7684\u4f18\u5316\u8fc7\u7a0b\uff0c\u5bf9\u4e8e\u5224\u522b\u5668\u800c\u8a00\uff0c\u5b9a\u4e49\u9274\u522b\u5668\\(\\mathrm{D}\\)\u7684\u8f93\u51fa\u4e3a\u4e24\u4e2a\u8f93\u5165\u9876\u70b9\\((\\nu,\\nu_{c})\\)\u5185\u79ef\u7684Sigmoid\u51fd\u6570\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(D\\left(\\nu,\\nu_c\\right)=\\sigma\\left(d_\\nu^\\top d_{\\nu_c}\\right)=\\frac{1}{1+\\exp\\left(-d_\\nu^\\top d_{\\nu_c}\\right)}\\) \u00a0 \u00a0 \u00a0\uff082\uff09<\/p>\n\n\n<p>\u5b9a\u4e49\\(\\theta_{D}\\)\u662f\u5224\u522b\u5668\u7684\u53ef\u5b66\u4e60\u53c2\u6570\u3002\u4efb\u4f55\u5177\u6709\u533a\u5206\u80fd\u529b\u7684\u6a21\u578b\u90fd\u53ef\u4ee5\u5728\u6b64\u4f5c\u4e3a\\(\\mathrm{D}\\)\uff0c\u4f8b\u5982\u4e00\u4e2a\u795e\u7ecf\u7f51\u7edc\u6a21\u578b\uff0c\u5bf9\u9876\u70b9\\(\\nu\\)\u548c\\(\\nu_{c}\\)\u7684\u7279\u5f81\u5411\u91cf\u8fdb\u884c\u5b66\u4e60\u6620\u5c04\u540e\u5f97\u5230\u7684\\(\\mathrm{k}\\)\u7ef4\u65b0\u7684\u5411\u91cf\u8868\u793a\u4e3a\\(d_{\\nu},d_{\\nu_{c}}\\)\uff0c\u7136\u540e\u8fdb\u884c\u5185\u79ef\u548cSigmoid\u5904\u7406\u3002\u8fd9\u4e2a\u5185\u79ef\u8868\u793a\u4e86\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u6216\u5173\u7cfb\u5f3a\u5ea6\u3002\u5185\u79ef\u7684\u7ed3\u679c\u901a\u8fc7Sigmoid\u51fd\u6570\u8fdb\u884c\u5904\u7406\uff0c\u5f97\u5230\u4e00\u4e2a\u57280\u52301\u4e4b\u95f4\u7684\u503c\uff0c\u53ef\u4ee5\u89e3\u91ca\u4e3a\u9876\u70b9\u5bf9\\(\\nu\\)\u548c\\(\\nu_{c}\\)\u662f\u56fe\u4e2d\u771f\u5b9e\u8fde\u63a5\u7684\u6982\u7387\u3002\u5176\u4e2d\\(\\nu\\)\u7684\u91c7\u6837\u6709\u4e24\u79cd\u60c5\u51b5\uff0c\u6362\u53e5\u8bdd\u8bf4\uff0c\u5224\u522b\u5668\u968f\u673a\u63a5\u6536\u4e24\u7c7b\u8f93\u5165\u6570\u636e\uff08\\(\\nu\\sim p_{\\mathrm{true}}\\)\u6216\\(\\nu\\sim G\\)\uff09\u3002\u6839\u636e\u635f\u5931\u51fd\u6570\u516c\u5f0f(1)\uff0c\u5224\u522b\u5668\u7684\u68af\u5ea6\\(\\nabla_{\\theta_{D}}V(G,D)\\)\u8ba1\u7b97\u5982\u4e0b\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\nabla_{\\theta_D}V(G,D)=\\begin{cases}\\nabla_{\\theta_D}\\log D\\left(\\nu,\\nu_c\\right),\\mathrm{~if~}\\nu\\sim p_\\mathrm{true}\\\\\\nabla_{\\theta_D}\\left(1-\\log D\\left(\\nu,\\nu_c\\right)\\right),\\mathrm{~if~}\\nu\\sim G.&amp;&amp;\\end{cases}\\)\u00a0 \u00a0 \u00a0 \u00a0 \uff083\uff09<\/p>\n\n\n<p>\u5728\u8bad\u7ec3\u8fc7\u7a0b\u4e2d\uff0cGraphGAN\u4ea4\u66ff\u5730\u66f4\u65b0\u751f\u6210\u5668\\(\\mathrm{G}\\)\u548c\u5224\u522b\u5668\\(\\mathrm{D}\\)\u7684\u53c2\u6570\uff0c\u4ee5\u4fbf\u6700\u5c0f\u5316\u751f\u6210\u5668\u7684\u635f\u5931\u51fd\u6570\u548c\u6700\u5927\u5316\u5224\u522b\u5668\u7684\u635f\u5931\u51fd\u6570\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u901a\u5e38\u88ab\u79f0\u4e3a\u5bf9\u6297\u8bad\u7ec3\u3002\u5f0f(3)\u4fbf\u662f\u56fa\u5b9a\u751f\u6210\u5668\\(\\mathrm{G}\\)\u66f4\u65b0\u5224\u522b\u5668\\(\\mathrm{D}\\)\u65f6\uff0c\u5224\u522b\u5668\u7684\u68af\u5ea6\u8ba1\u7b97\u65b9\u6cd5\u3002<\/p>\n\n\n\n<p>\u7c7b\u4f3c\u7684\uff0c\u751f\u6210\u5668\\(\\mathrm{G}\\)\u5177\u4f53\u7684\u6a21\u578b\u7c7b\u578b\u4e5f\u6ca1\u6709\u9650\u5236\uff0cGCN\u3001GAT\u751a\u81f3\u7b80\u5355\u7684\u795e\u7ecf\u7f51\u7edc\u7b49\u7b49\u90fd\u53ef\u4ee5\uff0c\u53ea\u8981\u80fd\u5177\u5907\u9884\u6d4b\u67d0\u9876\u70b9\u4e0e\u5176\u4ed6\u9876\u70b9\u95f4\u8fde\u63a5\u6982\u7387\u7684\u80fd\u529b\u5373\u53ef\u3002\u5f53\u56fa\u5b9a\u5224\u522b\u5668\\(\\mathrm{D}\\)\uff0c\u66f4\u65b0\u751f\u6210\u5668\\(\\mathrm{G}\\)\u7684\u53c2\u6570\u65f6\uff0c\u5f0f(1)\u4e2d\u7684\\(E_{\\nu\\sim p_{\\mathrm{true}}(\\cdot\\mid\\nu_{c})}\\left[\\log D\\left(\\nu,\\nu_{c};\\theta_{D}\\right)\\right]\\)\u90e8\u5206\u53ef\u4ee5\u770b\u4f5c\u5e38\u6570\uff0c\u53ea\u9700\u8981\u5173\u6ce8\u53e6\u4e00\u90e8\u5206\uff0c\u5373\\(\\left.E_{\\nu\\sim G\\left(\\cdot\\mid\\nu_c;\\theta_G\\right)}\\left[\\log\\left(1-D\\left(\\nu,\\nu_c;\\theta_D\\right)\\right)\\right]\\right)\\)\u3002\u6b64\u65f6\uff0c\u751f\u6210\u5668\u7684\u68af\u5ea6\\(\\nabla_{\\theta_{G}}V(G,D)\\)\u4e3a\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(\\begin{aligned}\\nabla_{\\theta_{G}}V(G,D)&amp;=\\nabla_{\\theta_G}\\sum_{c=1}^{V}E_{\\nu\\sim G\\left(\\cdot\\mid\\nu_c\\right)}\\left[\\log\\left(1-D\\left(\\nu,\\nu_c\\right)\\right)\\right]\\\\&amp;=\\sum_{c=1}^V\\sum_{i=1}^N\\nabla_{\\theta_G}G\\left(\\nu_i|\\nu_c\\right)\\mathrm{log}\\left(1-D\\left(\\nu_i,\\nu_c\\right)\\right)\\\\&amp;=\\sum_{c=1}^V\\sum_{i=1}^NG\\left(\\nu_i|\\nu_c\\right)\\nabla_{\\theta_G}\\log G\\left(\\nu_i|\\nu_c\\right)\\log\\left(1-D\\left(\\nu_i,\\nu_c\\right)\\right)\\\\&amp;=\\sum_{c=1}^V\\mathbb{E}_{\\nu\\sim G\\left(\\cdot|\\nu_c\\right)}\\left[\\nabla_{\\theta_G}\\log G\\left(\\nu|\\nu_c\\right)\\mathrm{log}\\left(1-D\\left(\\nu,\\nu_c\\right)\\right)\\right]\\end{aligned}\\)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \uff084\uff09<\/p>\n\n\n<p>\u5728\u5f0f(4)\u7684\u63a8\u5bfc\u4e2d\uff0c\\(\\sum_{c=1}^VE_{\\nu\\sim G(\\cdot\\nu_c)}\\left[\\log\\left(1-D\\left(\\nu,\\nu_c\\right)\\right)\\right]\\)\u662f\u5bf9\u6240\u6709\u9876\u70b9\\(\\nu_{c}\\)\u7684\u671f\u671b\u6c42\u548c\uff0c\u5176\u4e2d\u6bcf\u4e2a\u671f\u671b\u662f\u4ece\u751f\u6210\u5668\\(\\mathrm{G}\\)\u751f\u6210\u7684\u9876\u70b9\\(\\nu\\)\u5bf9\u5e94\u7684\\(\\log\\left(1-D\\left(\\nu,\\nu_c\\right)\\right)\\)\u7684\u5e73\u5747\u503c\u3002\u8fd9\u8868\u660e\u6211\u4eec\u5728\u8003\u8651\u6240\u6709\u751f\u6210\u5668\u4ea7\u751f\u7684\u5047\u9876\u70b9\u4e0e\u771f\u5b9e\u9876\u70b9\\(\\nu_{c}\\)\u4e4b\u95f4\u5173\u7cfb\u7684\u5e73\u5747\u5bf9\u6570\u6982\u7387\u3002\u671f\u671b\u7684\u5b9e\u73b0\u53ef\u4ee5\u8f6c\u5316\u6210\u5bf9\u6bcf\u4e2a\u751f\u6210\u6837\u672c\u7684\u6c42\u548c\uff0c\u5373\\(\\sum_{i=1}^N\\nabla_{\\theta_G}G\\left(\\nu_i|\\nu_c\\right)\\log\\left(1-D\\left(\\nu_i,\\nu_c\\right)\\right)\\)\uff0c\u8fd9\u91cc\u5bf9\u6bcf\u4e2a\u751f\u6210\u6837\u672c\\({\\mathcal{V}}_{i}\\)\u6c42\u548c\uff0c\u8ba1\u7b97\u751f\u6210\u6982\u7387\u76f8\u5bf9\u4e8e\\(\\theta_{G}\\)\u7684\u68af\u5ea6\u4e0e\\(\\log\\left(1-D\\left(\\nu_i,\\nu_c\\right)\\right)\\)\u7684\u4e58\u79ef\u3002\u53c8\u56e0\u4e3a\u6982\u7387\u7684\u68af\u5ea6\u53ef\u4ee5\u5199\u4f5c\u6982\u7387\u4e58\u4ee5\u4f3c\u7136\u6bd4\u4f8b\u7684\u68af\u5ea6\uff0c\u56e0\u6b64\u53ef\u4ee5\u4f7f\u7528\\(G\\left(\\nu_i|\\nu_c\\right)\\nabla_{\\theta_G}\\log G\\left(\\nu_i|\\nu_c\\right)\\mathrm{log}\\left(1-D\\left(\\nu_i,\\nu_c\\right)\\right)\\)\u4ee3\u66ff\\(\\nabla_{\\theta_G}G\\left(\\nu_i|\\nu_c\\right)\\mathrm{log}\\left(1-D\\left(\\nu_i,\\nu_c\\right)\\right)\\)\u3002\u6700\u540e\uff0c\u6211\u4eec\u7528\u671f\u671b\u503c\u6765\u4ee3\u66ff\u6c42\u548c\uff0c\u56e0\u4e3a\u671f\u671b\u503c\u662f\u968f\u673a\u53d8\u91cf\u7684\u5e73\u5747\u503c\uff0c\u8fd9\u91cc\u7684\u968f\u673a\u53d8\u91cf\u662f\\(\\nu\\)\u7684\u751f\u6210\u6982\u7387\uff0c\u5f97\u5230\u63a8\u5bfc\u540e\u751f\u6210\u5668\u7684\u68af\u5ea6\u8ba1\u7b97\u516c\u5f0f\uff1a\\(E_{\\nu\\sim G(\\cdot\\mid\\nu_c)}\\left[\\nabla_{\\theta_G}\\log G\\left(\\nu|\\nu_c\\right)\\mathrm{log}\\left(1-D\\left(\\nu,\\nu_c\\right)\\right)\\right]\\)\u3002\u6574\u4f53\u4e0a\uff0c\u8fd9\u4e2a\u68af\u5ea6\u8868\u8fbe\u5f0f\u8bf4\u660e\uff1a\u4e3a\u4e86\u66f4\u65b0\u751f\u6210\u5668\\(\\mathrm{G}\\)\u7684\u53c2\u6570\uff0c\u6211\u4eec\u9700\u8981\u8003\u8651\u7531\\(\\mathrm{G}\\)\u751f\u6210\u7684\u6bcf\u4e2a\u9876\u70b9\\(\\mathrm{v}\\)\u5bf9\u635f\u5931\u51fd\u6570\u7684\u8d21\u732e\uff0c\u5e76\u6839\u636e\u8be5\u8d21\u732e\u6765\u8c03\u6574\\(\\theta_{G}\\)\u3002\u68af\u5ea6\u7684\u65b9\u5411\u6307\u793a\u4e86\u5982\u4f55\u66f4\u65b0\u53c2\u6570\\(\\theta_{G}\\)\u4ee5\u51cf\u5c11\u751f\u6210\u7684\u9876\u70b9\\(\\mathrm{v}\\)\u88ab\u5224\u522b\u5668\\(\\mathrm{D}\\)\u8bc6\u522b\u51fa\u7684\u6982\u7387\uff0c\u4ece\u800c\u4f7f\u751f\u6210\u5668\u4ea7\u751f\u66f4\u771f\u5b9e\u7684\u6837\u672c\u3002<\/p>\n\n\n\n<p>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u5728\u7ed9\u5b9a\u9876\u70b9\\(\\nu_{c}\\)\u65f6\uff0c\u751f\u6210\u5668\\(\\mathrm{G}\\)\u8ba1\u7b97\u5176\u4ed6\u9876\u70b9\u4e0e\\(\\nu_{c}\\)\u7684\u8fde\u901a\u6027\u6982\u7387\\(G\\left(\\nu|\\nu_{c}\\right)\\)\u9700\u8981\u4f7f\u7528Softmax\u51fd\u6570\u8ba1\u7b97\u51fa\\(\\nu_{c}\\)\u5916\u7684\u6240\u4ee5\u8282\u70b9\u3002\u516c\u5f0f\u5982\u4e0b\u6240\u793a\uff1a<\/p>\n\n\n<p style=\"text-align: center;\">\\(G\\left(v|v_c\\right)=\\frac{\\exp\\left(g_v^\\top g_{v_c}\\right)}{\\sum_{v\\neq v_c}\\exp\\left(g_v^\\top g_{v_c}\\right)}\\)\u00a0 \u00a0 \u00a0 \u00a0 \uff085\uff09<\/p>\n\n\n<p>\u5f53\u56fe\u6570\u636e\u4f53\u91cf\u5e9e\u5927\u65f6\uff0c\u4e0a\u8ff0\u516c\u5f0f\u7684\u8ba1\u7b97\u590d\u6742\u5ea6\u662f\u975e\u5e38\u9ad8\u7684\u3002\u56e0\u6b64\uff0c\u5728GraphGAN\u6846\u67b6\u4e2d\uff0c\u63d0\u51fa\u4e86\u4e00\u79cd\u79f0\u4e3aGraph Softmax\u7684\u65b0\u65b9\u6cd5\uff0c\u5b83\u7684\u6838\u5fc3\u601d\u60f3\u6709\u4e09\u70b9\uff1a<\/p>\n\n\n\n<p>\uff081\uff09\u89c4\u8303\u5316\uff08Normalized\uff09\uff1a\u751f\u6210\u5668\u5e94\u8be5\u4ea7\u751f\u4e00\u4e2a\u6709\u6548\u7684\u6982\u7387\u5206\u5e03\uff0c\u8fd9\u610f\u5473\u7740\u5bf9\u4e8e\u4e00\u4e2a\u7ed9\u5b9a\u7684\u9876\u70b9\\(\\nu_{c}\\)\uff0c\u6240\u6709\u53ef\u80fd\u4e0e\u4e4b\u76f8\u8fde\u7684\u9876\u70b9\\(\\mathrm{v}\\)\u7684\u751f\u6210\u6982\u7387\u4e4b\u548c\u5e94\u8be5\u7b49\u4e8e1\uff0c\u8fd9\u4e5f\u662fSoftmax\u51fd\u6570\u7684\u57fa\u672c\u601d\u60f3\u3002<\/p>\n\n\n\n<p>\uff082\uff09\u56fe\u7ed3\u6784\u610f\u8bc6\uff08Graph-structure-aware\uff09\uff1a\u751f\u6210\u5668\u5728\u786e\u5b9a\u9876\u70b9\u4e4b\u95f4\u7684\u8fde\u901a\u6027\u6982\u7387\u65f6\uff0c\u5e94\u8be5\u5229\u7528\u56fe\u7684\u7ed3\u6784\u4fe1\u606f\u3002\u5177\u4f53\u6765\u8bf4\uff0c\u5982\u679c\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u7684\u6700\u77ed\u8def\u5f84\u8ddd\u79bb\u589e\u52a0\uff0c\u5b83\u4eec\u88ab\u8ba4\u4e3a\u662f\u76f8\u8fde\u7684\u6982\u7387\u5e94\u8be5\u4e0b\u964d\u3002<\/p>\n\n\n\n<p>\uff083\uff09\u8ba1\u7b97\u6548\u7387\uff08Computationally Efficient\uff09\uff1a\u4e0eSoftmax\u4e0d\u540c\uff0cGraph Softmax\u5728\u8ba1\u7b97\u65f6\u53ea\u8003\u8651\u56fe\u4e2d\u5c11\u6570\u7684\u7279\u5b9a\u9876\u70b9\uff0c\u4ece\u800c\u63d0\u9ad8\u8ba1\u7b97\u6548\u7387\u3002<\/p>\n\n\n\n<p>\u4e3a\u4e86\u5b9e\u73b0Graph Softmax\uff0c\u9996\u5148\u9700\u8981\u6267\u884c\u4e00\u4e2a\u4ece\u9876\u70b9\\(\\nu_{c}\\)\u51fa\u53d1\u7684\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\uff08Breadth-First Search\uff0cBFS\uff09\uff0c\u6765\u6784\u5efa\u4e00\u68f5\u4ee5\\(\\nu_{c}\\)\u4e3a\u6839\u7684BFS\u6811\\(T_{c}\\)\u3002\u4f7f\u7528\u8fd9\u68f5\u6811\uff0c\u6211\u4eec\u53ef\u4ee5\u8ba1\u7b97\u6bcf\u4e2a\u90bb\u5c45\u9876\u70b9\\(\\nu_{i}\\)\u76f8\u5bf9\u4e8e\\(\\nu_{c}\\)\u7684\u76f8\u5173\u6027\u6982\u7387\\(p_{c}\\left(\\nu_{i}\\right)\\)\uff0c\u8fd9\u662f\u4e00\u4e2a\u6807\u51c6\u7684Softmax\u51fd\u6570\uff0c\u5b83\u5728\\(\\nu_{c}\\)\u7684\u76f4\u63a5\u90bb\u5c45\u96c6\\(N_{c}(\\nu)\\)\u4e0a\u8fd0\u7b97\u3002 \u63a5\u7740\uff0c\u4e3a\u4e86\u8ba1\u7b97\u4efb\u610f\u9876\u70b9\\(\\nu\\)\u4e0e\\(\\nu_{c}\\)\u4e4b\u95f4\u7684\u8fde\u901a\u6027\u6982\u7387\\(G\\left(\\nu|\\nu_c;\\theta_G\\right)\\)\uff0c\u6211\u4eec\u4f7f\u7528\\(T_{c}\\)\u4e2d\u4ece\\(\\nu_{c}\\)\u5230\\(\\nu\\)\u7684\u552f\u4e00\u8def\u5f84\u3002\u8def\u5f84\u4e0a\u6bcf\u5bf9\u76f8\u90bb\u9876\u70b9\u7684\u76f8\u5173\u6027\u6982\u7387\u7684\u4e58\u79ef\u5b9a\u4e49\u4e86\\(\\nu\\)\u548c\\(\\nu_{c}\\)\u4e4b\u95f4\u7684\u8fde\u901a\u6027\u6982\u7387\u3002\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u56feSoftmax\u53ea\u5173\u6ce8\\(\\nu_{c}\\)\u901a\u8fc7BFS\u53ef\u8fbe\u7684\u90e8\u5206\u56fe\uff0c\u800c\u4e0d\u662f\u6574\u4e2a\u56fe\uff0c\u8fd9\u6781\u5927\u5730\u63d0\u9ad8\u4e86\u8ba1\u7b97\u6548\u7387\u3002\u540c\u65f6\uff0c\u5b83\u4e5f\u81ea\u7136\u5730\u8003\u8651\u5230\u4e86\u56fe\u7684\u7ed3\u6784\u4fe1\u606f\uff0c\u56e0\u4e3a\u5b83\u76f4\u63a5\u5728BFS\u6811\u4e0a\u8fdb\u884c\u64cd\u4f5c\uff0c\u8fd9\u68f5\u6811\u53cd\u6620\u4e86\u56fe\u4e2d\u9876\u70b9\u4e4b\u95f4\u7684\u771f\u5b9e\u8ddd\u79bb\u5173\u7cfb\u3002\u56e0\u6b64\u8fd9\u79cd\u65b9\u6cd5\u662f\u89c4\u8303\u5316\u7684\uff0c\u5177\u6709\u56fe\u7ed3\u6784\u610f\u8bc6\uff0c\u4e14\u8ba1\u7b97\u6548\u7387\u9ad8\uff0c\u5177\u4f53\u793a\u4f8b\u5982\u56fe2\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"864\" height=\"162\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250312105830885.png\" alt=\"\" class=\"wp-image-2895\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250312105830885.png 864w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250312105830885-300x56.png 300w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2025\/03\/20250312105830885-768x144.png 768w\" sizes=\"auto, (max-width: 864px) 100vw, 864px\" \/><figcaption class=\"wp-element-caption\">\u56fe2 BFS\u6811<\/figcaption><\/figure><\/div>\n\n\n<p>\u5982\u56fe2\u6240\u793a\uff0c\u4ece\u9876\u70b9\\(\\nu_{c}\\)\u5f00\u59cb\uff0c\u6211\u4eec\u6709\u539f\u59cb\u7684\u56fe\\(\\mathrm{G}\\)\u548c\u4e00\u4e2a\u4ee5\\(\\nu_{c}\\)\u4e3a\u6839\u8282\u70b9\u7684 BFS \u6811\u3002\u7b2c\u4e00\u6b65\u662f\u4ece\\(\\nu_{c}\\)\u7684\u76f4\u63a5\u90bb\u5c45\u4e2d\u9009\u62e9\u4e0b\u4e00\u4e2a\u9876\u70b9\u3002\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u9876\u70b9\\(\\nu_{r1}\\)\u88ab\u9009\u4e2d\uff0c\u4e0e\u5b83\u76f8\u5173\u8054\u7684\u6982\u7387\u662f0.7\u3002\u63a5\u4e0b\u6765\uff0c\u4ece\\(\\nu_{r1}\\)\u7684\u90bb\u5c45\u4e2d\u9009\u62e9\u4e0b\u4e00\u4e2a\u9876\u70b9\u3002\u9876\u70b9\\(\\nu_{r2}\\)\u88ab\u9009\u4e2d\uff0c\u4e0e\u5b83\u76f8\u5173\u8054\u7684\u6982\u7387\u662f 0.3\u3002\u7136\u540e\uff0c\u4ece\\(\\nu_{r2}\\)\u7684\u90bb\u5c45\u4e2d\u9009\u62e9\u4e0b\u4e00\u4e2a\u9876\u70b9\u3002\u53ef\u80fd\u7684\u9009\u62e9\u53ea\u6709\u4e24\u79cd\uff0c\u4e0e\u5b83\u4eec\u76f8\u5173\u8054\u7684\u6982\u7387\u662f 0.6\u548c0.4\uff0c\u5047\u8bbe\u6b64\u65f6\u4ee50.6\u7684\u6982\u7387\u9009\u62e9\u4e86\\(\\nu_{r1}\\)\uff0c\u90a3\u4e48\\(\\nu_{r2}\\)\u7684\u8def\u5f84\u91c7\u6837\u8fc7\u7a0b\u5b8c\u6210\uff0c\u5426\u5219\u8def\u5f84\u91c7\u6837\u7ee7\u7eed\u5ef6\u7eed\u3002\u6700\u540e\u4e00\u6b65\u662f\u66f4\u65b0\u91c7\u6837\u8def\u5f84\u4e0a\u6240\u6709\u9876\u70b9\u7684\u6982\u7387\u3002\u8ba1\u7b97\u8def\u5f84\\(\\nu_{c}\\to\\nu_{r1}\\to\\nu_{r2}\\)\u4e0a\u6240\u6709\u9876\u70b9\u7684\u76f8\u5173\u6027\u6982\u7387\u7684\u4e58\u79ef\u5f97\u52300.7\u00d70.3\u00d70.6=0.126 \uff0c\u8fd9\u4e2a\u6570\u5b57\u4ee3\u8868\u4ece\\(\\nu_{c}\\)\u5230\\(\\nu_{r2}\\)\u7684\u8fde\u901a\u6027\u6982\u7387\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>GraphGAN\u662f\u4e00\u79cd\u7ed3\u5408\u4e86\u56fe\u795e\u7ecf\u7f51\u7edc\u548c\u751f\u6210\u5bf9\u6297\u7f51\u7edc\uff08GAN\uff09\u6982\u5ff5\u7684\u673a\u5668\u5b66\u4e60\u6a21\u578b\u3002\u5b83\u65e8\u5728\u901a\u8fc7\u5bf9\u6297\u5b66\u4e60\u6846\u67b6\u89e3\u51b3\u56fe [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":2890,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23,26],"tags":[22],"class_list":["post-2883","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-23","category-26","tag-22"],"_links":{"self":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2883","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2883"}],"version-history":[{"count":7,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2883\/revisions"}],"predecessor-version":[{"id":2896,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/posts\/2883\/revisions\/2896"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=\/wp\/v2\/media\/2890"}],"wp:attachment":[{"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2883"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2883"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/gnn.club\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2883"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}