{"id":37394,"date":"2025-01-27T20:00:12","date_gmt":"2025-01-27T12:00:12","guid":{"rendered":"https:\/\/17aitech.com\/?p=37394"},"modified":"2025-01-27T20:00:12","modified_gmt":"2025-01-27T12:00:12","slug":"%e5%9b%be%e5%ad%a6%e4%b9%a0%e6%96%b0%e7%aa%81%e7%a0%b4%ef%bc%9a%e4%b8%80%e4%b8%aa%e7%bb%9f%e4%b8%80%e6%a1%86%e6%9e%b6%e8%bf%9e%e6%8e%a5%e7%a9%ba%e5%9f%9f%e5%92%8c%e9%a2%91%e5%9f%9f","status":"publish","type":"post","link":"https:\/\/17aitech.com\/?p=37394","title":{"rendered":"\u56fe\u5b66\u4e60\u65b0\u7a81\u7834\uff1a\u4e00\u4e2a\u7edf\u4e00\u6846\u67b6\u8fde\u63a5\u7a7a\u57df\u548c\u9891\u57df"},"content":{"rendered":"<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a href=\"https:\/\/www.jiqizhixin.com\/articles\/2024-12-23-2\" target=\"_blank\">\u56fe\u5b66\u4e60\u65b0\u7a81\u7834\uff1a\u4e00\u4e2a\u7edf\u4e00\u6846\u67b6\u8fde\u63a5\u7a7a\u57df\u548c\u9891\u57df<\/a><\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-6f3c798db2fce3006afc26d753818dbb.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-6f3c798db2fce3006afc26d753818dbb.png\"><\/a><\/p>\n<blockquote data-author-name=\"\" data-content-utf8-length=\"166\" data-source-title=\"\" data-type=\"2\" data-url=\"\">\n<section>\n<p>AIxiv\u4e13\u680f\u662f\u673a\u5668\u4e4b\u5fc3\u53d1\u5e03\u5b66\u672f\u3001\u6280\u672f\u5185\u5bb9\u7684\u680f\u76ee\u3002\u8fc7\u53bb\u6570\u5e74\uff0c\u673a\u5668\u4e4b\u5fc3AIxiv\u4e13\u680f\u63a5\u6536\u62a5\u9053\u4e862000\u591a\u7bc7\u5185\u5bb9\uff0c\u8986\u76d6\u5168\u7403\u5404\u5927\u9ad8\u6821\u4e0e\u4f01\u4e1a\u7684\u9876\u7ea7\u5b9e\u9a8c\u5ba4\uff0c\u6709\u6548\u4fc3\u8fdb\u4e86\u5b66\u672f\u4ea4\u6d41\u4e0e\u4f20\u64ad\u3002\u5982\u679c\u60a8\u6709\u4f18\u79c0\u7684\u5de5\u4f5c\u60f3\u8981\u5206\u4eab\uff0c\u6b22\u8fce\u6295\u7a3f\u6216\u8005\u8054\u7cfb\u62a5\u9053\u3002\u6295\u7a3f\u90ae\u7bb1\uff1aliyazhou@jiqizhixin.com\uff1bzhaoyunfeng@jiqizhixin.com<\/p>\n<\/section>\n<\/blockquote>\n<p><strong>\u9648\u67b3\u6266\u535a\u58eb\uff1a\u73b0\u4efb\u5bc6\u897f\u897f\u6bd4\u5dde\u7acb\u5927\u5b66\u8ba1\u7b97\u673a\u7cfb\u52a9\u7406\u6559\u6388\uff0c\u4e13\u6ce8\u4e8e\u56fe\u673a\u5668\u5b66\u4e60\u53ca\u5e94\u7528\u9886\u57df\uff0c\u5728\u8c31\u57df\u89c6\u89d2\u4e0e\u4e0d\u786e\u5b9a\u6027\u7814\u7a76\u65b9\u9762\u7740\u529b\u9887\u6df1\u3002\u5176\u7814\u7a76\u6210\u679c\u89c1\u8bf8\u4e8e AAAI\u3001IJCAI\u3001ACM\u3001ICDM\u3001EMNLP\u3001Computing Surveys\u3001Nature Communication \u7b49\u3002\u4ed6\u7684\u79d1\u7814\u5de5\u4f5c\u627f\u8499\u7f8e\u56fd\u56fd\u5bb6\u79d1\u5b66\u57fa\u91d1\u4f1a\uff08NSF\uff09\u53ca\u7f8e\u56fd\u519c\u4e1a\u90e8\uff08USDA\uff09\u591a\u4e2a\u9879\u76ee\u7684\u8d44\u52a9\uff0c\u4e14\u8363\u83b7\u4e30\u7530\u7814\u7a76\u9662\u6770\u51fa\u8d21\u732e\u5956\u4e0e ACM SIGPSATIAL 2020 \u6700\u4f73\u8bba\u6587\u5956\u3002<\/strong><\/p>\n<p><strong>\u5f20\u78ca\u535a\u58eb\uff1a\u4e8e 2024 \u5e74\u6bd5\u4e1a\u4e8e\u5f17\u5409\u5c3c\u4e9a\u7406\u5de5\u540e\uff0c\u4ee5\u52a9\u7406\u6559\u6388\u8eab\u4efd\u52a0\u76df\u5317\u4f0a\u5229\u8bfa\u4f0a\u5927\u5b66\u3002\u4ed6\u7684\u7814\u7a76\u5174\u8da3\u5e7f\u6cdb\u8986\u76d6\u673a\u5668\u5b66\u4e60\u548c\u6570\u636e\u6316\u6398\u8303\u7574\uff0c\u5c24\u5176\u805a\u7126\u4e8e\u56fe\u795e\u7ecf\u7f51\u7edc\u3001\u56fe\u7ed3\u6784\u5b66\u4e60\u3001\u53cc\u5c42\u4f18\u5316\u3001\u795e\u7ecf\u67b6\u6784\u641c\u7d22\u4ee5\u53ca\u793e\u4ea4\u7f51\u7edc\u6316\u6398\u7b49\u65b9\u9762\u3002\u5728 AAAI\u3001ICDM \u7b49\u9876\u7ea7\u4f1a\u8bae\u4e0a\u53d1\u8868\u591a\u7bc7\u8bba\u6587\uff0c\u5e76\u4e8e 2023 \u5e74\u590f\u5b63\u65a9\u83b7\u5f17\u5409\u5c3c\u4e9a\u7406\u5de5\u5927\u5b66\u7684 Cunningham Fellowship\u3002<\/strong><\/p>\n<p><strong>\u8d75\u4eae\u535a\u58eb\uff1a\u8eab\u4e3a\u57c3\u9ed8\u91cc\u5927\u5b66\u8ba1\u7b97\u673a\u7cfb\u526f\u6559\u6388\uff0c\u4ed6\u7684\u7814\u7a76\u9886\u57df\u6a2a\u8de8\u6570\u636e\u6316\u6398\u3001\u4eba\u5de5\u667a\u80fd\u7b49\u591a\u5b66\u79d1\uff0c\u5728\u56fe\u5b66\u4e60\u9886\u57df\u6210\u679c\u6590\u7136\u3002\u5728 KDD\u3001NeurIPS\u3001AAAI\u3001IJCAI\u3001WWW \u7b49\u4f17\u591a\u9876\u7ea7\u4f1a\u8bae\u53ca\u671f\u520a\u4e0a\u53d1\u8868\u8d85\u767e\u7bc7\u8bba\u6587\uff0c\u5c61\u83b7\u6b8a\u8363\uff0c\u5982 NSF CAREER \u5956\u3001Meta Research \u5956\u3001Amazon Research \u5956\u7b49\uff0c\u8fd8\u8363\u83b7 ICDM 2022 \u6700\u4f73\u8bba\u6587\u5956\u3001ACM SIGPSATIAL 2022 \u6700\u4f73\u8bba\u6587\u5956\u4ee5\u53ca WWW 2023 \u6700\u4f73\u8bba\u6587\u63d0\u540d\u7b49\u3002<\/strong><\/p>\n<p>\u56fe\u6570\u636e\u5b66\u4e60\u5728\u8fc7\u53bb\u51e0\u5e74\u4e2d\u53d6\u5f97\u4e86\u663e\u8457\u7684\u8fdb\u5c55\uff0c\u56fe\u795e\u7ecf\u7f51\u7edc\uff08GNN\uff09\u5728\u6b64\u8fc7\u7a0b\u4e2d\u8d77\u5230\u4e86\u6838\u5fc3\u4f5c\u7528\u3002\u7136\u800c\uff0c\u4e0d\u540c\u7684 GNN \u65b9\u6cd5\u5728\u6982\u5ff5\u548c\u5b9e\u73b0\u4e0a\u7684\u5dee\u5f02\uff0c\u5bf9\u7406\u89e3\u548c\u5e94\u7528\u56fe\u5b66\u4e60\u7b97\u6cd5\u6784\u6210\u4e86\u6311\u6218\u3002<\/p>\n<p>\u9488\u5bf9\u8fd9\u4e00\u95ee\u9898\uff0c\u6765\u81ea\u5bc6\u897f\u897f\u6bd4\u5dde\u7acb\u5927\u5b66\uff0c\u5317\u4f0a\u5229\u8bfa\u4f0a\u5927\u5b66\u548c\u57c3\u9ed8\u91cc\u5927\u5b66\u7684\u5b66\u8005\u901a\u8fc7\u4e00\u7cfb\u5217\u6559\u7a0b\u5bf9\u6b64\u95ee\u9898\u5c55\u5f00\u4e86\u8ba8\u8bba\uff0c\u8fd9\u4e9b\u6559\u7a0b\u5c55\u793a\u5728 CVPR 2024\u3001CIKM 2024\u3001SIAM Math and Data Science 2024\uff0c\u4ee5\u53ca\u53d1\u8868\u5728 Computing Surveys \u7684\u4e00\u7bc7\u8bba\u6587: \u300aBridging the Gap between Spatial and Spectral Domains: A Unified Framework for Graph Neural Networks\u300b\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-a6eeeb44de352266f460b713ab10ec12.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-a6eeeb44de352266f460b713ab10ec12.png\"><\/a><\/p>\n<p>\u8bba\u6587\u5730\u5740\uff1ahttps:\/\/dl.acm.org\/doi\/10.1145\/3627816<\/p>\n<p><strong>\u95ee\u9898\uff1a\u7edf\u4e00\u6846\u67b6\u7684\u7a81\u7834\u610f\u4e49\u4f55\u5728\uff1f<\/strong><\/p>\n<p>\u5c3d\u7ba1\u56fe\u795e\u7ecf\u7f51\u7edc\u5df2\u7ecf\u5728\u591a\u4e2a\u9886\u57df\u5c55\u793a\u51fa\u4e86\u5353\u8d8a\u7684\u6027\u80fd\uff0c\u4ece\u5316\u5b66\u5206\u5b50\u8bc6\u522b\u5230\u793e\u4ea4\u7f51\u7edc\u5206\u6790\uff0c\u4ece\u4ea4\u901a\u7f51\u7edc\u5230\u8f93\u7535\u7f51\u7edc\uff0c\u518d\u5230\u5927\u8111\u7f51\u7edc\u3002GNN \u4e5f\u5728\u4e0d\u540c\u7684\u573a\u666f\u4e0b\uff0c\u7528\u4e0d\u540c\u7684\u7406\u8bba\u548c\u673a\u5236\u6765\u8bbe\u8ba1\u65b0\u7684\u56fe\u795e\u7ecf\u7f51\u7edc\uff0c\u4f8b\u5982 Heat diffusion, page rank, random walk, attention model, ARMA, low-pass filtering\u3002\u867d\u7136\u5c55\u73b0\u4e86 GNN \u548c\u5f88\u591a\u4e0d\u540c\u7406\u8bba\u5de5\u5177\u7684\u8fde\u63a5\u6027\uff0c\u4f46\u8fd9\u4e5f\u52a0\u5267\u4e86 GNN \u9886\u57df\u7684\u5206\u88c2\u3002\u8fd9\u4e9b\u65b9\u6cd5\u56e0\u4e3a\u6025\u4e8e\u4e0d\u540c\u7406\u8bba\uff0c\u65e0\u6cd5\u8fdb\u884c\u7406\u8bba\u4e0a\u76f4\u63a5\u7684\u6bd4\u8f83\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-24dd7c1f8a069d06363d9561ad33ef58.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-24dd7c1f8a069d06363d9561ad33ef58.png\"><\/a><\/p>\n<p><strong>Part 1: \u56fe\u5b66\u4e60\u7406\u8bba\u6846\u67b6\u7684\u73b0\u72b6<\/strong><\/p>\n<p>\u76ee\u524d\uff0c\u56fe\u795e\u7ecf\u7f51\u7edc\uff08GNN\uff09\u6db5\u76d6\u4e86\u591a\u79cd\u6a21\u578b\u548c\u5c42\u7684\u7c7b\u578b\uff0c\u4f46\u603b\u4f53\u53ef\u4ee5\u5206\u4e3a\u7a7a\u57df\uff08spatial\uff09\u56fe\u6a21\u578b\u548c\u9891\u57df\uff08spectral\uff09\u56fe\u6a21\u578b\u3002\u9488\u5bf9\u8fd9\u4e9b\u6a21\u578b\uff0c\u4e0d\u5c11\u7814\u7a76\u8005\u5c1d\u8bd5\u63d0\u51fa\u901a\u7528\u6846\u67b6\uff0c\u4ee5\u4fbf\u5728\u540c\u4e00\u6846\u67b6\u4e0b\u5bf9\u4e0d\u540c\u6a21\u578b\u8fdb\u884c\u5206\u6790\u548c\u6bd4\u8f83\u3002\u7136\u800c\uff0c\u8fd9\u4e9b\u6846\u67b6\u4e3b\u8981\u96c6\u4e2d\u4e8e\u7a7a\u57df\u56fe\u6a21\u578b\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u6709\u4e00\u7c7b\u7814\u7a76\u4ece\u7edf\u4e00\u7684\u51fa\u53d1\u70b9 \u2014\u2014 \u5373\u6a21\u578b\u7684\u8868\u8fbe\u80fd\u529b\uff08Expressive Power\uff09\u2014\u2014 \u5bf9\u7a7a\u57df\u548c\u9891\u57df\u56fe\u6a21\u578b\u8fdb\u884c\u4e86\u5206\u6790\u3002\u5c3d\u7ba1\u5982\u6b64\uff0c\u7a7a\u57df\u548c\u9891\u57df\u56fe\u6a21\u578b\u5728\u8868\u8fbe\u80fd\u529b\u7684\u5b9a\u4e49\u4e0a\u5b58\u5728\u5dee\u5f02\uff0c\u5176\u5206\u6790\u7ed3\u8bba\u548c\u8bbe\u8ba1\u5efa\u8bae\u65e2\u6709\u5171\u901a\u4e4b\u5904\uff0c\u4e5f\u5404\u6709\u4e0d\u540c\uff0c\u540c\u65f6\u4e24\u8005\u5747\u5b58\u5728\u4e00\u5b9a\u7684\u5c40\u9650\u6027\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-6e1aac633cbc28cfa97971a24b024888.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-6e1aac633cbc28cfa97971a24b024888.png\"><\/a><\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-f47eb6c71a07125cba9dfe58149c3a6d.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-f47eb6c71a07125cba9dfe58149c3a6d.png\"><\/a><\/p>\n<p><strong>Part 2: \u56fe\u5377\u79ef<\/strong><\/p>\n<p>\u56fe\u5377\u79ef\u53ef\u4ee5\u901a\u8fc7\u8c31\u56fe\u7406\u8bba\uff08Spectral Graph Theory\uff09\u4e2d\u7684\u56fe\u5085\u91cc\u53f6\u53d8\u6362\uff08Graph Fourier Transform\uff09\u548c\u5377\u79ef\u5b9a\u7406\uff08Convolution Theorem\uff09\u6765\u7406\u89e3\u3002<\/p>\n<p>\u56fe\u5085\u7acb\u53f6\u53d8\u6362\uff1a\u56fe\u7684\u7ed3\u6784\u901a\u8fc7\u56fe\u62c9\u666e\u62c9\u65af\u77e9\u9635\uff08Graph Laplacian\uff09\u6765\u8868\u793a\u3002\u62c9\u666e\u62c9\u65af\u77e9\u9635 L \u53ef\u4ee5\u8fdb\u884c\u7279\u5f81\u503c\u5206\u89e3\uff1a<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-18a617895a262e604bf200108b8d5454.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-18a617895a262e604bf200108b8d5454.png\"><\/a>\uff0c\u5176\u4e2d U \u662f\u7279\u5f81\u5411\u91cf\u77e9\u9635\uff0c\u2227 \u662f\u7279\u5f81\u503c\u7684\u5bf9\u89d2\u77e9\u9635\u3002\u56fe\u5085\u91cc\u53f6\u53d8\u6362\u5c31\u662f\u5c06\u56fe\u4fe1\u53f7<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-7bfee33f595d83e9389c6b3f440213b3.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-7bfee33f595d83e9389c6b3f440213b3.png\"><\/a>\u8f6c\u6362\u5230\u9891\u57df\uff1a<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-be06c7c07a646a14472c84bc8eb5f659.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-be06c7c07a646a14472c84bc8eb5f659.png\"><\/a>\u3002\u5176\u9006\u53d8\u6362\u4e3a<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-987ea8d40656196f33e0ed16d0989fc8.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-987ea8d40656196f33e0ed16d0989fc8.png\"><\/a>\u3002\u901a\u8fc7\u8fd9\u79cd\u53d8\u6362\uff0c\u7814\u7a76\u8005\u53ef\u4ee5\u5728\u9891\u57df\u4e2d\u5904\u7406\u548c\u5206\u6790\u56fe\u4fe1\u53f7\u3002<\/p>\n<p>\u5377\u79ef\u5b9a\u7406\uff1a\u5728\u4f20\u7edf\u4fe1\u53f7\u5904\u7406\u4e2d\uff0c\u65f6\u57df\u7684\u5377\u79ef\u7b49\u4ef7\u4e8e\u9891\u57df\u7684\u9010\u70b9\u76f8\u4e58\u3002\u5bf9\u4e8e\u56fe\u4fe1\u53f7\uff0c\u540c\u6837\u6210\u7acb\uff1a\u8bbe\u4e24\u4e2a\u56fe\u4fe1\u53f7 X\uff08\u8f93\u5165\u7279\u5f81\uff09\u548c g\uff08\u6ee4\u6ce2\u5668\uff09\uff0c\u5b83\u4eec\u7684\u56fe\u5377\u79ef\u5b9a\u4e49\u4e3a\uff1a<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-e544ce3c27ce6225e9fdb18d29ecfda6.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-e544ce3c27ce6225e9fdb18d29ecfda6.png\"><\/a>\u3002\u5176\u4e2d\uff0c\u2299 \u8868\u793a\u9891\u57df\u7684\u9010\u70b9\u76f8\u4e58\uff0cg \u8868\u793a\u9891\u57df\u6ee4\u6ce2\u5668\u3002\u8fd9\u8868\u660e\u56fe\u5377\u79ef\u53ef\u4ee5\u901a\u8fc7\u9891\u57df\u64cd\u4f5c\u5b9e\u73b0\u3002\u4e3a\u4e86\u5728\u56fe\u795e\u7ecf\u7f51\u7edc\u4e2d\u5b9e\u73b0\u5377\u79ef\uff0c\u6ee4\u6ce2\u5668 g \u88ab\u53c2\u6570\u5316\u4e3a<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-3f117fef3c03ccee4826b192bf647fda.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-3f117fef3c03ccee4826b192bf647fda.png\"><\/a>\uff0c\u5b83\u662f\u7279\u5f81\u503c \u2227 \u7684\u51fd\u6570\uff1a<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-fb11245a2d58b8e2932339527d3f118a.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-fb11245a2d58b8e2932339527d3f118a.png\"><\/a>\uff0c\u5176\u4e2d \u03b8 \u662f\u53ef\u8bad\u7ec3\u7684\u53c2\u6570\u5411\u91cf\u3002\u5377\u79ef\u64cd\u4f5c\u53ef\u4ee5\u5199\u4e3a\uff1a<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-4e182fa5333ed2b44e007b766ca3c04a.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-4e182fa5333ed2b44e007b766ca3c04a.png\"><\/a>\u3002<\/p>\n<p>\u56fe\u5377\u79ef\u7f51\u7edc\uff08GCN\uff09\u5728\u9891\u57df\u548c\u7a7a\u57df\u7684\u89e3\u91ca\uff1a\u5728\u9891\u57df\u56fe\u6a21\u578b\u4e2d\uff0cGCN \u4f7f\u7528\u7684\u662f<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-fae23491ed17c5858ac0ce673dfd9800.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-fae23491ed17c5858ac0ce673dfd9800.png\"><\/a>\u7684\u4e00\u9636\u8fd1\u4f3c\uff0c\u5176\u4e2d<a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-01392aad25997b1e65c8546b53c88055.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-01392aad25997b1e65c8546b53c88055.png\"><\/a>\u3002\u8fd9\u79cd\u64cd\u4f5c\u672c\u8d28\u4e0a\u662f\u4e00\u79cd\u56fa\u5b9a\u7684\u5377\u79ef\u64cd\u4f5c\uff0c\u6ca1\u6709\u53ef\u5b66\u4e60\u53c2\u6570\u3002\u7531\u4e8e\u5f52\u4e00\u5316\u4e4b\u540e\u7684\u62c9\u666e\u62c9\u65af\u77e9\u9635\u7684\u7279\u5f81\u503c\u8303\u56f4\u4e3a 0 \u5230 2 \u4e4b\u95f4\uff0c2-\u03b8 \u7684\u6ee4\u6ce2\u5668\u5b9e\u9645\u4e0a\u662f\u4e00\u4e2a\u4f4e\u901a\u6ee4\u6ce2\u5668\uff1a\u653e\u5927\u4f4e\u9891\u5e73\u6ed1\u4fe1\u53f7\uff0c\u51cf\u5f31\u9ad8\u9891\u4fe1\u53f7\u3002\u5728\u7a7a\u57df\u56fe\u6a21\u578b\u4e2d\uff0c GCN \u7684\u64cd\u4f5c\u53ef\u4ee5\u7406\u89e3\u4e3a\u5bf9\u6bcf\u4e2a\u8282\u70b9\u7684\u90bb\u5c45\u8282\u70b9\u7684\u7279\u5f81\u503c\u8fdb\u884c\u6c42\u548c\uff0c\u7136\u540e\u53d6\u5e73\u5747\u503c\u3002\u8fd9\u662f\u4e00\u79cd\u57fa\u4e8e\u90bb\u5c45\u7279\u5f81\u805a\u5408\u7684\u65b9\u5f0f\u3002GCN \u7684\u9891\u57df\u548c\u7a7a\u57df\u89c6\u89d2\u662f\u7b49\u4ef7\u7684\uff0c\u4f46\u5404\u6709\u4fa7\u91cd\u3002\u9891\u57df\u89e3\u91ca\u66f4\u504f\u5411\u7406\u8bba\u4e0a\u7684\u4fe1\u53f7\u5904\u7406\u672c\u8d28\uff0c\u800c\u7a7a\u57df\u89e3\u91ca\u66f4\u8d34\u8fd1\u5de5\u7a0b\u5b9e\u73b0\u548c\u76f4\u89c2\u7406\u89e3\u3002\u5bf9\u4e8e\u7814\u7a76\u8005\u800c\u8a00\uff0c\u8fd9\u4e24\u79cd\u89c6\u89d2\u662f\u76f8\u8f85\u76f8\u6210\u7684\uff0c\u7ed3\u5408\u4f7f\u7528\u53ef\u4ee5\u66f4\u5168\u9762\u5730\u7406\u89e3\u548c\u6539\u8fdb GCN\u3002<\/p>\n<p><strong>Part 3: \u65b0\u7684\u7edf\u4e00\u6846\u67b6\uff1a\u8fde\u63a5\u7a7a\u57df\u548c\u9891\u57df<\/strong><\/p>\n<p>\u6559\u7a0b\u4e2d\u63d0\u51fa\u7684\u6846\u67b6\u57fa\u4e8e\u4e00\u4e2a\u6838\u5fc3\u5047\u8bbe\uff1a\u7a7a\u95f4\u57df\u548c\u9891\u8c31\u57df\u7684\u56fe\u8868\u793a\u5b66\u4e60\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e2a\u5171\u540c\u7684\u6570\u5b66\u8bed\u8a00\u8fdb\u884c\u63cf\u8ff0\u3002\u7814\u7a76\u4eba\u5458\u5f15\u5165\u4e86\u4e00\u79cd\u65b0\u7684\u56fe\u5d4c\u5165\u65b9\u6cd5\uff0c\u8be5\u65b9\u6cd5\u7ed3\u5408\u4e86\u56fe\u7684\u7a7a\u95f4\u8fde\u63a5\u6027\u548c\u8282\u70b9\u7279\u5f81\uff0c\u80fd\u591f\u66f4\u52a0\u7cbe\u51c6\u5730\u6355\u6349\u548c\u8868\u793a\u56fe\u6570\u636e\u7684\u590d\u6742\u6027\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-8bb4ac2725e6b2644e812abaf2b79389.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-8bb4ac2725e6b2644e812abaf2b79389.png\"><\/a><\/p>\n<p><strong>\u5176\u4ed6\u9886\u57df\u91cc\u9891\u57df\u548c\u7a7a\u57df\u7684\u7814\u7a76<\/strong><\/p>\n<p>\u5728\u5df2\u5b58\u5728\u7684\u7814\u7a76\u91cc\uff0c\u8fd9\u79cd\u7a7a\u57df\u548c\u9891\u57df\u76f8\u4e92\u8fde\u63a5\u89c6\u89d2\u5e76\u4e0d\u5c11\u89c1\u3002\u7814\u7a76\u8005\u7528\u4e24\u4e2a\u4f8b\u5b50\u6765\u8bf4\u660e\uff1a<\/p>\n<p>\uff081\uff09\u8c31\u805a\u7c7b\uff1a\u4ece\u8c31\u57df\u7684\u89c6\u89d2\u770b\u8c31\u805a\u7c7b\u662f\u4f7f\u7528\u8c31\u5206\u89e3 (spectral decomposition) \u6216\u5219\u8bf4\u7279\u5f81\u5206\u89e3\uff08eigen-decomposition\uff09\uff0c\u7136\u540e\u4f7f\u7528\u5206\u89e3\u7ed3\u679c\u4e2d\u7279\u5f81\u503c\u54cd\u4eae\u7684\u4f4e\u9891\u4fe1\u53f7\u6765\u4f5c\u4e3a\u65b0\u7684\u8868\u8fbe\uff0c\u7136\u540e\u4f7f\u7528\u8f83\u4e3a\u7b80\u5355\u5feb\u901f\u7684 Kmeans \u5f97\u5230\u805a\u7c7b\u7ed3\u679c\u3002\u800c\u53e6\u5916\u4e00\u4e2a\u65b0\u7684\u5b9e\u73b0\uff0cSpectralNet\uff0c\u8bbe\u8ba1\u4e86\u4e00\u4e2a\u7279\u522b loss\uff0c\u4f7f\u7528\u795e\u7ecf\u7f51\u7edc\u6765\u5f97\u5230\u51e0\u4e4e\u4e00\u6837\u7684\u7ed3\u679c\u3002\u5355\u795e\u7ecf\u7f51\u7edc\u662f\u4e00\u79cd\u4ee5\u964d\u4f4e loss \u4e3a\u5bfc\u5411\u7684\u8fed\u4ee3\u7b97\u6cd5\uff0c\u6240\u4ee5\u53ef\u4ee5\u89c6\u4e3a\u4e00\u79cd\u8fd1\u4f3c\u8c31\u805a\u7c7b\u7684\u7b97\u6cd5\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-71cee77d7d1c3e6591e56e8c2c5409d7.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-71cee77d7d1c3e6591e56e8c2c5409d7.png\"><\/a><\/p>\n<p>\uff082\uff09\u53e6\u5916\u4e00\u4e2a\u4f8b\u5b50\u662f\u8457\u540d\u7684 Word2Vec \u7b97\u6cd5\u3002\u4ee5 Skip-gram \u4e3a\u4f8b\uff0c\u6bcf\u4e2a\u5355\u8bcd\u90fd\u8981\u76f8\u4f3c\u4e8e\u5b83\u7684\u4e0a\u4e0b\u6587\u7684\u73af\u5883\u91cc\u5176\u4ed6\u5355\u8bcd\u3002\u6240\u4ee5 Word2Vec \u662f\u4e00\u4e2a\u8fed\u4ee3\u7b97\u6cd5\u3002\u5728\u540e\u6765\u7684\u7814\u7a76\u4e2d\uff0cLevy \u63d0\u51fa\u4e86\u4e00\u4e9b\u5206\u6790\uff0c\u53d1\u73b0\u4f7f\u7528 Word2Vec \u7684\u7ed3\u679c\u91cc\u7684\u77e9\u9635\uff0c\u80fd\u591f\u51e0\u4e4e\u5b8c\u6574\u7684\u8fd8\u539f\u5355\u8bcd\u7684\u5171\u73b0\u77e9\u9635\uff08PPMI\uff09\u3002\u4e5f\u5c31\u662f\u8bf4 Word2Vec \u53ef\u4ee5\u770b\u4f5c\u662f\u77e9\u9635\u5206\u89e3\u7b97\u6cd5\u7684\u4e00\u79cd\u8fd1\u4f3c\u7b97\u6cd5\u3002<\/p>\n<p><a href=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-6604bc16544337204a4438446e0cecfe.png\" data-fancybox=\"images\" data-fancybox=\"gallery\"><img decoding=\"async\" src=\"https:\/\/17aitech.com\/wp-content\/uploads\/2024\/12\/frc-6604bc16544337204a4438446e0cecfe.png\"><\/a><\/p>\n<p>\u5728\u8fd9\u4e24\u4e2a\u4f8b\u5b50\u4e2d\uff0c\u7814\u7a76\u8005\u53d1\u73b0\u8fd9\u79cd\u6bd4\u8f83\u4e2d\uff0c\u6709\u7c7b\u4f3c\u4e8e\u8be5\u7814\u7a76\u63d0\u51fa\u7684\u8c31\u57df\u548c\u7a7a\u57df\u65b9\u6cd5\u533a\u522b\u3002\u5373\uff0c\u4e00\u79cd\u65b9\u6cd5\u4fa7\u91cd\u77e9\u9635\u5206\u89e3\uff0c\u800c\u53e6\u5916\u4e00\u79cd\u4fa7\u91cd\u4e8e\u8fed\u4ee3\u8fd1\u4f3c\u3002<\/p>\n<p><strong>Part 4: \u672a\u6765\u65b9\u5411\u5c55\u671b<\/strong><\/p>\n<p>\u8fd9\u9879\u7814\u7a76\u5f00\u8f9f\u4e86\u56fe\u7ed3\u6784\u5b66\u4e60\u9886\u57df\u7684\u65b0\u65b9\u5411\uff0c\u672a\u6765\u7684\u7814\u7a76\u53ef\u4ee5\u57fa\u4e8e\u6b64\u6846\u67b6\u8fdb\u4e00\u6b65\u63a2\u7d22\uff1a<\/p>\n<ul>\n<li>\n<p>\u8ba1\u7b97\u6548\u7387\uff1a\u5982\u4f55\u8fdb\u4e00\u6b65\u4f18\u5316\u7edf\u4e00\u6846\u67b6\u4ee5\u5904\u7406\u5927\u89c4\u6a21\u56fe\u6570\u636e\uff0c\u5728\u8c31\u8bba\u8868\u8fbe\u4e0b\uff0c\u56fe\u7684\u4fe1\u606f\u91cf\u4f9d\u7136\u5de8\u5927\uff0c\u5bf9\u8ba1\u7b97\u4ecd\u7136\u662f\u4e00\u4e2a\u6311\u6218\u3002<\/p>\n<\/li>\n<li>\n<p>\u7edf\u4e00\u7684\u8c31\u8bba\uff1a\u76ee\u524d\u8c31\u8bba\u4e3b\u8981\u5e94\u7528\u4e8e\u9759\u6001\u56fe\u7ed3\u6784\uff0c\u800c\u4e14\u662f\u7b80\u5355\u56fe\uff08\u5373\u65e0\u5411\uff0c\u8fb9\u53ea\u8fde\u63a5\u4e24\u4e2a\u8282\u70b9\uff09\u3002\u7136\u540e\u56fe\u8bba\u4e2d\u4ecd\u7136\u6709\u5927\u91cf\u7684\u4e0d\u540c\u7c7b\u578b\u7684\u56fe\uff0c\u7f3a\u5c11\u8c31\u8bba\u7684\u8868\u8fbe\uff0c\u4f8b\u5982\u6709\u5411\u56fe\uff0c\u8d85\u56fe\uff0c\u6216\u5219\u52a8\u6001\u56fe\u3002<\/p>\n<\/li>\n<li>\n<p>\u5e94\u7528\u6269\u5c55\uff1a\u5c06\u7edf\u4e00\u6846\u67b6\u5e94\u7528\u5230\u66f4\u591a\u5b9e\u9645\u95ee\u9898\u4e2d\uff0c\u5982\u751f\u7269\u4fe1\u606f\u5b66\u548c\u793e\u4f1a\u7f51\u7edc\u5206\u6790\uff0c\u5982\u4f55\u89e3\u91ca\u8c31\u8bba\u89c6\u89d2\u4e0b\u771f\u5b9e\u5e94\u7528\u7684\u89c4\u5f8b\uff0c\u662f\u4e00\u4e2a\u503c\u5f97\u63a2\u7d22\u7684\u9886\u57df\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u6587\u7ae0\u6765\u6e90\u4e8e\u4e92\u8054\u7f51:<a 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