\u8ba1\u7b97Gram\u77e9\u9635<\/strong><\/h2>\nG = linear_kernel(X)<\/p>\n
print("Gram \u77e9\u9635:\\n", G)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u5728\u8fd9\u4e2a\u4f8b\u5b50\u4e2d\uff0clinear_kernel<\/code> \u51fd\u6570\u7528\u4e8e\u8ba1\u7b97\u6837\u672c\u4e4b\u95f4\u7684\u7ebf\u6027\u6838\uff0c\u5373Gram\u77e9\u9635\u3002<\/p>\n<\/p>\n\u516d\u3001GRAM\u77e9\u9635\u7684\u6027\u8d28\u548c\u9a8c\u8bc1<\/p>\n<\/p>\n
\n- \n
\u5bf9\u79f0\u6027<\/strong>\uff1aGram\u77e9\u9635\u662f\u5bf9\u79f0\u7684\uff0c\u5373 ( G_{ij} = G_{ji} )\u3002\u8fd9\u610f\u5473\u7740\u77e9\u9635\u5173\u4e8e\u4e3b\u5bf9\u89d2\u7ebf\u662f\u5bf9\u79f0\u7684\u3002<\/p>\n<\/p>\n<\/li>\n- \n
\u534a\u6b63\u5b9a\u6027<\/strong>\uff1aGram\u77e9\u9635\u662f\u534a\u6b63\u5b9a\u7684\uff0c\u5176\u7279\u5f81\u503c\u5e94\u5f53\u4e3a\u975e\u8d1f\u503c\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528NumPy\u7684 np.linalg.eigvals()<\/code> \u51fd\u6570\u6765\u8ba1\u7b97\u7279\u5f81\u503c\uff0c\u5e76\u9a8c\u8bc1\u5176\u975e\u8d1f\u6027\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n# \u8ba1\u7b97\u7279\u5f81\u503c<\/p>\neigenvalues = np.linalg.eigvals(G)<\/p>\n
\u9a8c\u8bc1\u7279\u5f81\u503c\u975e\u8d1f\u6027<\/strong><\/h2>\nis_semidefinite = np.all(eigenvalues >= 0)<\/p>\n
print("Gram \u77e9\u9635\u662f\u534a\u6b63\u5b9a\u7684:", is_semidefinite)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u4e03\u3001GRAM\u77e9\u9635\u7684\u4f18\u5316<\/p>\n<\/p>\n
\u5728\u5904\u7406\u5927\u578b\u6570\u636e\u96c6\u65f6\uff0cGram\u77e9\u9635\u7684\u8ba1\u7b97\u53ef\u80fd\u4f1a\u53d8\u5f97\u975e\u5e38\u8017\u65f6\u548c\u5360\u7528\u5185\u5b58\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u4f18\u5316\u6280\u5de7\uff1a<\/p>\n<\/p>\n
\n- \n
\u7a00\u758f\u77e9\u9635\u8868\u793a<\/strong>\uff1a\u5bf9\u4e8e\u7a00\u758f\u6570\u636e\u96c6\uff0c\u53ef\u4ee5\u4f7f\u7528SciPy\u5e93\u4e2d\u7684\u7a00\u758f\u77e9\u9635\u8868\u793a\uff0c\u4ee5\u8282\u7701\u5185\u5b58\u548c\u8ba1\u7b97\u65f6\u95f4\u3002<\/p>\n<\/p>\n<\/li>\n- \n
\u5206\u5757\u8ba1\u7b97<\/strong>\uff1a\u5982\u679c\u6570\u636e\u96c6\u592a\u5927\uff0c\u53ef\u4ee5\u5c06\u6570\u636e\u5206\u6210\u5757\uff0c\u5206\u522b\u8ba1\u7b97\u6bcf\u4e2a\u5757\u7684Gram\u77e9\u9635\uff0c\u7136\u540e\u7ec4\u5408\u7ed3\u679c\u3002<\/p>\n<\/p>\n<\/li>\n- \n
\u5e76\u884c\u8ba1\u7b97<\/strong>\uff1a\u5229\u7528\u591a\u6838\u5904\u7406\u5668\u548c\u5e76\u884c\u8ba1\u7b97\u6280\u672f\uff0c\u52a0\u901fGram\u77e9\u9635\u7684\u8ba1\u7b97\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\n\u516b\u3001\u5e94\u7528\u5b9e\u4f8b\uff1aGRAM\u77e9\u9635\u5728\u56fe\u50cf\u5904\u7406\u4e2d<\/p>\n<\/p>\n
\u5728\u56fe\u50cf\u5904\u7406\u4e2d\uff0cGram\u77e9\u9635\u53ef\u4ee5\u7528\u4e8e\u98ce\u683c\u8f6c\u6362\u7b97\u6cd5\u4e2d\u3002\u901a\u8fc7\u8ba1\u7b97\u5185\u5bb9\u56fe\u50cf\u548c\u98ce\u683c\u56fe\u50cf\u7684Gram\u77e9\u9635\uff0c\u53ef\u4ee5\u5b9e\u73b0\u56fe\u50cf\u98ce\u683c\u7684\u8fc1\u79fb\u548c\u878d\u5408\u3002<\/p>\n<\/p>\n
\n- \n
\u63d0\u53d6\u56fe\u50cf\u7279\u5f81<\/strong>\uff1a\u9996\u5148\u9700\u8981\u63d0\u53d6\u56fe\u50cf\u7684\u5377\u79ef\u7279\u5f81\u3002\u53ef\u4ee5\u4f7f\u7528\u6df1\u5ea6\u5b66\u4e60\u6846\u67b6\uff08\u5982TensorFlow\u6216PyTorch\uff09\u4e2d\u7684\u9884\u8bad\u7ec3\u6a21\u578b\uff08\u5982VGG16\uff09\u6765\u63d0\u53d6\u7279\u5f81\u3002<\/p>\n<\/p>\n<\/li>\n- \n
\u8ba1\u7b97GRAM\u77e9\u9635<\/strong>\uff1a\u5bf9\u4e8e\u63d0\u53d6\u7684\u7279\u5f81\uff0c\u8ba1\u7b97\u5176Gram\u77e9\u9635\uff0c\u4ee5\u6355\u6349\u56fe\u50cf\u4e2d\u7684\u98ce\u683c\u4fe1\u606f\u3002<\/p>\n<\/p>\n<\/li>\n- \n
\u5b9e\u73b0\u98ce\u683c\u8fc1\u79fb<\/strong>\uff1a\u901a\u8fc7\u6700\u5c0f\u5316\u5408\u6210\u56fe\u50cf\u4e0e\u76ee\u6807\u98ce\u683c\u56fe\u50cf\u7684Gram\u77e9\u9635\u4e4b\u95f4\u7684\u5dee\u5f02\uff0c\u5b9e\u73b0\u98ce\u683c\u8fc1\u79fb\u3002<\/p>\n<\/p>\n<\/li>\n<\/ol>\nimport torch<\/p>\nimport torchvision.models as models<\/p>\n
\u52a0\u8f7d\u9884\u8bad\u7ec3\u7684VGG16\u6a21\u578b<\/strong><\/h2>\nvgg = models.vgg16(pretrained=True).features<\/p>\n
\u63d0\u53d6\u7279\u5f81<\/strong><\/h2>\nfeatures = vgg(image)<\/p>\n
\u8ba1\u7b97Gram\u77e9\u9635<\/strong><\/h2>\ndef gram_matrix(tensor):<\/p>\n
b, c, h, w = tensor.size()<\/p>\n
features = tensor.view(b, c, h * w)<\/p>\n
G = torch.bmm(features, features.transpose(1, 2))<\/p>\n
return G<\/p>\n
\u8ba1\u7b97\u56fe\u50cf\u7684Gram\u77e9\u9635<\/strong><\/h2>\ngram = gram_matrix(features)<\/p>\n
<\/code><\/pre>\n<\/p>\n
\u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u53ef\u4ee5\u5b9e\u73b0\u56fe\u50cf\u98ce\u683c\u7684\u8f6c\u6362\u548c\u878d\u5408\u3002Gram\u77e9\u9635\u5728\u6355\u6349\u56fe\u50cf\u98ce\u683c\u65b9\u9762\u63d0\u4f9b\u4e86\u4e00\u79cd\u6709\u6548\u7684\u6570\u5b66\u5de5\u5177\u3002<\/p>\n<\/p>\n
\u4e5d\u3001\u603b\u7ed3<\/p>\n<\/p>\n
\u521b\u5efa\u548c\u4f7f\u7528Gram\u77e9\u9635\u5728\u673a\u5668\u5b66\u4e60\u548c\u6570\u636e\u79d1\u5b66\u4e2d\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u4ece\u7406\u8bba\u5b9a\u4e49\u5230\u5b9e\u9645\u8ba1\u7b97\uff0c\u518d\u5230\u5e94\u7528\u6848\u4f8b\uff0c\u672c\u6587\u8be6\u7ec6\u4ecb\u7ecd\u4e86\u5982\u4f55\u5728Python\u4e2d\u521b\u5efa\u548c\u4f7f\u7528Gram\u77e9\u9635\u3002\u901a\u8fc7NumPy\u3001Pandas\u3001Scikit-learn\u7b49\u5e93\uff0c\u53ef\u4ee5\u9ad8\u6548\u5730\u8ba1\u7b97Gram\u77e9\u9635\uff0c\u5e76\u5c06\u5176\u5e94\u7528\u4e8e\u652f\u6301\u5411\u91cf\u673a\u3001\u6838\u5cad\u56de\u5f52\u3001\u56fe\u50cf\u98ce\u683c\u8f6c\u6362\u7b49\u9886\u57df\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u8fd8\u9700\u8981\u8003\u8651\u8ba1\u7b97\u4f18\u5316\u548c\u77e9\u9635\u6027\u8d28\u9a8c\u8bc1\uff0c\u4ee5\u786e\u4fdd\u7ed3\u679c\u7684\u6b63\u786e\u6027\u548c\u8ba1\u7b97\u7684\u9ad8\u6548\u6027\u3002<\/p>\n<\/p>\n
\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n \u5982\u4f55\u5728Python\u4e2d\u521b\u5efaGram\u77e9\u9635\uff1f<\/strong>
\u5728Python\u4e2d\u521b\u5efaGram\u77e9\u9635\u901a\u5e38\u6d89\u53ca\u4f7f\u7528NumPy\u5e93\u3002Gram\u77e9\u9635\u662f\u4e00\u4e2a\u5bf9\u79f0\u77e9\u9635\uff0c\u5305\u542b\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u5185\u79ef\u3002\u53ef\u4ee5\u901a\u8fc7\u5c06\u6570\u636e\u96c6\u7684\u8f6c\u7f6e\u4e0e\u81ea\u8eab\u76f8\u4e58\u6765\u8ba1\u7b97\u3002\u4ee5\u4e0b\u662f\u4e00\u4e2a\u7b80\u5355\u7684\u793a\u4f8b\u4ee3\u7801\uff1a <\/p>\nimport numpy as np\n\n# \u793a\u4f8b\u6570\u636e\ndata = np.array([[1, 2], [3, 4], [5, 6]])\n\n# \u521b\u5efaGram\u77e9\u9635\ngram_matrix = np.dot(data, data.T)\nprint(gram_matrix)\n<\/code><\/pre>\n\u8fd9\u6bb5\u4ee3\u7801\u5c06\u8f93\u51fa\u4e00\u4e2aGram\u77e9\u9635\uff0c\u5305\u542b\u6bcf\u5bf9\u6570\u636e\u70b9\u7684\u5185\u79ef\u3002<\/p>\n
\u4f7f\u7528\u54ea\u4e9b\u5e93\u53ef\u4ee5\u66f4\u65b9\u4fbf\u5730\u8ba1\u7b97Gram\u77e9\u9635\uff1f<\/strong>
\u9664\u4e86NumPy\uff0cScikit-learn\u4e5f\u662f\u4e00\u4e2a\u975e\u5e38\u5b9e\u7528\u7684\u5e93\uff0c\u7279\u522b\u662f\u5728\u5904\u7406\u673a\u5668\u5b66\u4e60\u76f8\u5173\u4efb\u52a1\u65f6\u3002Scikit-learn\u63d0\u4f9b\u4e86\u4e00\u4e9b\u51fd\u6570\u6765\u7b80\u5316\u6570\u636e\u5904\u7406\u548c\u8ba1\u7b97\uff0c\u4f8b\u5982pairwise<\/code>\u6a21\u5757\uff0c\u5b83\u53ef\u4ee5\u76f4\u63a5\u8ba1\u7b97Gram\u77e9\u9635\u3002\u4f7f\u7528\u8fd9\u4e9b\u5e93\u53ef\u4ee5\u63d0\u9ad8\u5f00\u53d1\u6548\u7387\uff0c\u907f\u514d\u91cd\u590d\u5b9e\u73b0\u5e38\u7528\u7b97\u6cd5\u3002<\/p>\nGram\u77e9\u9635\u7684\u5e94\u7528\u573a\u666f\u6709\u54ea\u4e9b\uff1f<\/strong>
Gram\u77e9\u9635\u5e7f\u6cdb\u5e94\u7528\u4e8e\u673a\u5668\u5b66\u4e60\u548c\u7edf\u8ba1\u5b66\u4e2d\uff0c\u7279\u522b\u662f\u5728\u652f\u6301\u5411\u91cf\u673a\uff08SVM\uff09\u3001\u4e3b\u6210\u5206\u5206\u6790\uff08PCA\uff09\u548c\u6838\u65b9\u6cd5\u4e2d\u3002\u5b83\u80fd\u591f\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u6570\u636e\u70b9\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\uff0c\u5e76\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u8fdb\u884c\u6709\u6548\u7684\u8fd0\u7b97\u3002\u901a\u8fc7\u8ba1\u7b97Gram\u77e9\u9635\uff0c\u6a21\u578b\u53ef\u4ee5\u66f4\u597d\u5730\u6355\u6349\u6570\u636e\u7684\u7ed3\u6784\u7279\u5f81\uff0c\u63d0\u9ad8\u9884\u6d4b\u6027\u80fd\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u521b\u5efaGram\u77e9\u9635\u662f\u4e00\u4e2a\u5e38\u89c1\u7684\u4efb\u52a1\uff0c\u5c24\u5176\u662f\u5728\u673a\u5668\u5b66\u4e60\u548c\u6570\u636e\u79d1\u5b66\u4e2d\u3002\u8981\u5728Python\u4e2d\u521b\u5efaGram\u77e9\u9635\uff0c\u4e3b\u8981\u6b65\u9aa4\u5305 […]","protected":false},"author":3,"featured_media":1018361,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1018350"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=1018350"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1018350\/revisions"}],"predecessor-version":[{"id":1018364,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1018350\/revisions\/1018364"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1018361"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1018350"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1018350"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1018350"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
![\"python\u5982\u4f55\u521b\u5efagram\u77e9\u9635\"](\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25161000\/17abf432-e6fa-42cc-b2c4-4e7564f0cd40.webp\")
<\/p>\n