{"id":2367,"date":"2024-10-29T20:39:21","date_gmt":"2024-10-29T12:39:21","guid":{"rendered":"https:\/\/www.gnn.club\/?p=2367"},"modified":"2024-11-01T17:22:27","modified_gmt":"2024-11-01T09:22:27","slug":"spherenet","status":"publish","type":"post","link":"http:\/\/gnn.club\/?p=2367","title":{"rendered":"SphereNet"},"content":{"rendered":"\n<p>\u4e3a\u4e86\u66f4\u597d\u7684\u63cf\u8ff0\u89e3\u91caSphereNet\u7684\u4e8c\u9762\u89d2\u8ba1\u7b97\u65b9\u5f0f\uff0c\u6211\u4eec\u9996\u5148\u6b63\u5f0f\u5b9a\u4e49\u4e00\u4e2a\u4e09\u7ef4\u5206\u5b50\u56fe\uff0c\u901a\u5e38\u8868\u793a\u4e3a\u4e00\u4e2a\u56db\u5143\u7ec4\\(G=(u,V,E,P)\\)\u3002\u5176\u4e2d\\(u\\in R^{d_{u}}\\)\u662f\u5206\u5b50\u56fe\u7684\u5168\u5c40\u7279\u5f81\u5411\u91cf\u3002$ V=\\left\\{\\boldsymbol{v}_{i}\\right\\}_{i=1}^{n} $\u662f\u539f\u5b50\u7279\u5f81\u96c6\uff0c\u5176\u4e2d\u6bcf\u4e2a\\(v_{i}\\in R^{d_{\\nu}}\\)\u662f\u539f\u5b50<em>i<\/em>\u7684\u7279\u5f81\u5411\u91cf\u3002$E = \\left\\{ (e_k, r_k, s_k)\\right\\}_{k=1}^{m}$\u662f\u8fb9\u96c6\uff0c\u5176\u4e2d\u6bcf\u4e2a\\(e_k\\in\\mathbb{R}^{d_c}\\)\u662f\u7279\u5f81\u5411\u91cf\uff0c\\(r_{k}\\)\u662f\u63a5\u6536\u539f\u5b50\u7684\u7d22\u5f15\uff0c\u800c\\({s_{k}}\\)\u662f\u53d1\u9001\u8fb9<em>k<\/em>\u7684\u539f\u5b50\u7684\u7d22\u5f15\u3002$P= \\left\\{ p_h\\right\\}_{h=1}^{n}$\u662f\u5305\u542b\u6bcf\u4e2a\u539f\u5b50\u4e09\u7ef4\u7a7a\u95f4\u4fe1\u606f\u7684\u4e09\u7ef4\u7b1b\u5361\u5c14\u5750\u6807\u96c6\u3002\u53e6\u5916\uff0c\u6211\u4eec\u4f7f\u7528$E = \\left\\{ (e_k, r_k, s_k)\\right\\}_{k=1}^{m}$\u8868\u793a\u6307\u5411\u539f\u5b50<em>i<\/em>\u7684\u8fb9\u96c6\uff0c\\(N_{i}\\)\u8868\u793a\u8fdb\u5165\u539f\u5b50<em>i <\/em>\u7684\u8282\u70b9\u7684\u7d22\u5f15\u96c6\u3002\u4fe1\u606f\u4f20\u9012\u8fc7\u7a0b\u540e\u7684\u8f93\u51fa\u5305\u62ec\u66f4\u65b0\u7684\u5168\u5c40\u7279\u5f81\u5411\u91cf\\(u^{^{\\prime}}\\in R^{d_u}\\)\u3001\u66f4\u65b0\u7684\u539f\u5b50\u7279\u5f81$V' = \\{ v_i' \\}_{i=1}^{n}$\u548c\u66f4\u65b0\u7684\u8fb9$\\boldsymbol{E}' = \\{ (\\boldsymbol{e}_k', r_k', s_k') \\}_{k=1}^{m}$\uff0cSphereNet\u7684\u4e8c\u9762\u89d2\u8ba1\u7b97\u65b9\u5f0f\u5982\u56fe1\u6240\u793a\u3002<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"361\" src=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/10\/20241029200556942-1024x361.png\" alt=\"\" class=\"wp-image-2368\" srcset=\"https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/10\/20241029200556942-1024x361.png 1024w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/10\/20241029200556942-300x106.png 300w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/10\/20241029200556942-768x271.png 768w, https:\/\/gnnclub-1311496010.cos.ap-beijing.myqcloud.com\/wp-content\/uploads\/2024\/10\/20241029200556942.png 1070w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">\u56fe1 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