{"id":1121880,"date":"2025-01-08T19:14:32","date_gmt":"2025-01-08T11:14:32","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1121880.html"},"modified":"2025-01-08T19:14:35","modified_gmt":"2025-01-08T11:14:35","slug":"%e5%9c%a8python%e4%b8%ad%e5%a6%82%e4%bd%95%e8%bf%9b%e8%a1%8c%e6%9b%bc%e5%93%88%e9%a1%bf%e8%b7%9d%e7%a6%bb%e8%ae%a1%e7%ae%97","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/1121880.html","title":{"rendered":"\u5728python\u4e2d\u5982\u4f55\u8fdb\u884c\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25083942\/f125a3ab-15a3-4b4c-9a5c-80d93b07a5d3.webp\" alt=\"\u5728python\u4e2d\u5982\u4f55\u8fdb\u884c\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97\" \/><\/p>\n<p><p> <strong>Python\u4e2d\u5982\u4f55\u8fdb\u884c\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97<\/strong><\/p>\n<\/p>\n<p><p>\u5728Python\u4e2d\u8fdb\u884c\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97\uff0c\u6838\u5fc3\u6b65\u9aa4\u662f<strong>\u8ba1\u7b97\u5404\u7ef4\u5ea6\u5750\u6807\u5dee\u7684\u7edd\u5bf9\u503c\u3001\u5c06\u8fd9\u4e9b\u5dee\u503c\u8fdb\u884c\u7d2f\u52a0\u3001\u8fd4\u56de\u7ed3\u679c<\/strong>\u3002\u66fc\u54c8\u987f\u8ddd\u79bb\uff0c\u4e5f\u79f0\u4e3a\u57ce\u5e02\u8857\u533a\u8ddd\u79bb\uff0c\u662f\u4e00\u79cd\u7528\u4e8e\u8861\u91cf\u4e24\u4e2a\u70b9\u5728\u6807\u51c6\u7f51\u683c\u8def\u5f84\u4e0a\u7684\u8ddd\u79bb\u7684\u65b9\u6cd5\u3002\u5b83\u7684\u540d\u79f0\u6765\u6e90\u4e8e\u66fc\u54c8\u987f\u8857\u9053\u5e03\u5c40\u7684\u7279\u70b9\uff0c\u5373\u53ea\u80fd\u6cbf\u7740\u6c34\u5e73\u6216\u5782\u76f4\u65b9\u5411\u79fb\u52a8\u3002\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u516c\u5f0f\u4e3a\uff1a[ D = \\sum |x_i &#8211; y_i| ]\uff0c\u5176\u4e2d ( x_i ) \u548c ( y_i ) \u5206\u522b\u662f\u4e24\u4e2a\u70b9\u5728\u7b2ci\u7ef4\u7684\u5750\u6807\u3002<\/p>\n<\/p>\n<p><p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u4ecb\u7ecd\u5982\u4f55\u5728Python\u4e2d\u5b9e\u73b0\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u8ba1\u7b97\uff0c\u5e76\u8ba8\u8bba\u4e00\u4e9b\u76f8\u5173\u5e94\u7528\u548c\u5b9e\u73b0\u7684\u4f18\u5316\u3002<\/p>\n<\/p>\n<p><h2>\u4e00\u3001\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u57fa\u672c\u6982\u5ff5\u4e0e\u516c\u5f0f<\/h2>\n<\/p>\n<p><p>\u66fc\u54c8\u987f\u8ddd\u79bb\u5728\u6570\u5b66\u4e0a\u662f\u4e00\u79cdL1\u8303\u6570\uff0c\u9002\u7528\u4e8e\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u4e24\u4e2a\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u8ba1\u7b97\u3002\u516c\u5f0f\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p><p>[ D = \\sum_{i=1}^{n} |x_i &#8211; y_i| ]<\/p>\n<\/p>\n<p><p>\u5176\u4e2d\uff1a<\/p>\n<\/p>\n<ul>\n<li>( n ) \u662f\u7ef4\u5ea6\u6570\uff0c<\/li>\n<li>( x_i ) \u548c ( y_i ) \u662f\u4e24\u4e2a\u70b9\u5728\u7b2ci\u7ef4\u7684\u5750\u6807\u3002<\/li>\n<\/ul>\n<p><p>\u8fd9\u4e2a\u516c\u5f0f\u7684\u6838\u5fc3\u601d\u60f3\u662f<strong>\u5bf9\u6bcf\u4e00\u4e2a\u7ef4\u5ea6\u7684\u5750\u6807\u5dee\u503c\u53d6\u7edd\u5bf9\u503c\u5e76\u7d2f\u52a0<\/strong>\uff0c\u5f97\u5230\u7684\u7ed3\u679c\u5373\u4e3a\u66fc\u54c8\u987f\u8ddd\u79bb\u3002<\/p>\n<\/p>\n<p><h2>\u4e8c\u3001Python\u4e2d\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u65b9\u6cd5<\/h2>\n<\/p>\n<p><h3>1\u3001\u624b\u52a8\u5b9e\u73b0\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97<\/h3>\n<\/p>\n<p><p>\u4e0b\u9762\u662f\u4e00\u4e2a\u624b\u52a8\u5b9e\u73b0\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97\u7684\u793a\u4f8b\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def manhattan_distance(point1, point2):<\/p>\n<p>    if len(point1) != len(point2):<\/p>\n<p>        r<a href=\"https:\/\/docs.pingcode.com\/blog\/59162.html\" target=\"_blank\">AI<\/a>se ValueError(&quot;Points must have the same dimension&quot;)<\/p>\n<p>    distance = sum(abs(a - b) for a, b in zip(point1, point2))<\/p>\n<p>    return distance<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>point1 = [1, 2, 3]<\/p>\n<p>point2 = [4, 0, 3]<\/p>\n<p>print(manhattan_distance(point1, point2))  # \u8f93\u51fa: 6<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u5b9e\u73b0\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u68c0\u67e5\u4e24\u4e2a\u70b9\u662f\u5426\u5177\u6709\u76f8\u540c\u7684\u7ef4\u5ea6\uff0c\u7136\u540e\u4f7f\u7528Python\u5185\u7f6e\u7684 <code>zip<\/code> \u51fd\u6570\u5c06\u4e24\u4e2a\u70b9\u7684\u5750\u6807\u4e00\u4e00\u914d\u5bf9\uff0c\u5e76\u5bf9\u6bcf\u5bf9\u5750\u6807\u8ba1\u7b97\u7edd\u5bf9\u5dee\u503c\u7684\u548c\u3002<\/p>\n<\/p>\n<p><h3>2\u3001\u4f7f\u7528NumPy\u5e93\u8fdb\u884c\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97<\/h3>\n<\/p>\n<p><p>NumPy\u662f\u4e00\u4e2a\u5f3a\u5927\u7684\u79d1\u5b66\u8ba1\u7b97\u5e93\uff0c\u53ef\u4ee5\u7b80\u5316\u6570\u7ec4\u64cd\u4f5c\u3002\u4f7f\u7528NumPy\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">import numpy as np<\/p>\n<p>def manhattan_distance_np(point1, point2):<\/p>\n<p>    point1 = np.array(point1)<\/p>\n<p>    point2 = np.array(point2)<\/p>\n<p>    return np.sum(np.abs(point1 - point2))<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>point1 = [1, 2, 3]<\/p>\n<p>point2 = [4, 0, 3]<\/p>\n<p>print(manhattan_distance_np(point1, point2))  # \u8f93\u51fa: 6<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u5b9e\u73b0\u4e2d\uff0c\u6211\u4eec\u9996\u5148\u5c06\u8f93\u5165\u7684\u70b9\u8f6c\u6362\u4e3aNumPy\u6570\u7ec4\uff0c\u7136\u540e\u5229\u7528NumPy\u7684\u5411\u91cf\u5316\u64cd\u4f5c\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u3002<\/p>\n<\/p>\n<p><h3>3\u3001\u4f7f\u7528scipy\u5e93\u8fdb\u884c\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97<\/h3>\n<\/p>\n<p><p>SciPy\u662f\u4e00\u4e2a\u7528\u4e8e\u6570\u5b66\u3001\u79d1\u5b66\u548c\u5de5\u7a0b\u8ba1\u7b97\u7684Python\u5e93\uff0c\u5b83\u63d0\u4f9b\u4e86\u66f4\u9ad8\u7ea7\u7684\u63a5\u53e3\u6765\u8fdb\u884c\u5404\u79cd\u7c7b\u578b\u7684\u8ddd\u79bb\u8ba1\u7b97\uff0c\u5305\u62ec\u66fc\u54c8\u987f\u8ddd\u79bb\u3002<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">from scipy.spatial import distance<\/p>\n<p>def manhattan_distance_scipy(point1, point2):<\/p>\n<p>    return distance.cityblock(point1, point2)<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>point1 = [1, 2, 3]<\/p>\n<p>point2 = [4, 0, 3]<\/p>\n<p>print(manhattan_distance_scipy(point1, point2))  # \u8f93\u51fa: 6<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p>\u5728\u8fd9\u4e2a\u5b9e\u73b0\u4e2d\uff0c\u6211\u4eec\u76f4\u63a5\u4f7f\u7528\u4e86 <code>scipy.spatial.distance<\/code> \u6a21\u5757\u4e2d\u7684 <code>cityblock<\/code> \u51fd\u6570\u6765\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u3002<\/p>\n<\/p>\n<p><h2>\u4e09\u3001\u66fc\u54c8\u987f\u8ddd\u79bb\u5728\u5b9e\u9645\u4e2d\u7684\u5e94\u7528<\/h2>\n<\/p>\n<p><h3>1\u3001\u5728<a href=\"https:\/\/docs.pingcode.com\/ask\/59192.html\" target=\"_blank\">\u673a\u5668\u5b66\u4e60<\/a>\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n<p><p>\u66fc\u54c8\u987f\u8ddd\u79bb\u5728\u673a\u5668\u5b66\u4e60\u4e2d\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\uff0c\u5c24\u5176\u662f\u5728K\u6700\u8fd1\u90bb\uff08K-Nearest Neighbors, KNN\uff09\u7b97\u6cd5\u4e2d\u3002KNN\u7b97\u6cd5\u662f\u4e00\u79cd\u7528\u4e8e\u5206\u7c7b\u548c\u56de\u5f52\u7684\u975e\u53c2\u6570\u65b9\u6cd5\uff0c\u5b83\u901a\u8fc7\u8ba1\u7b97\u6837\u672c\u70b9\u4e0e\u8bad\u7ec3\u96c6\u4e2d\u6240\u6709\u70b9\u7684\u8ddd\u79bb\u6765\u8fdb\u884c\u9884\u6d4b\u3002\u66fc\u54c8\u987f\u8ddd\u79bb\u4f5c\u4e3a\u4e00\u79cd\u8ddd\u79bb\u5ea6\u91cf\u65b9\u5f0f\uff0c\u80fd\u591f\u5f88\u597d\u5730\u5904\u7406\u9ad8\u7ef4\u6570\u636e\u3002<\/p>\n<\/p>\n<p><h3>2\u3001\u5728\u63a8\u8350\u7cfb\u7edf\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n<p><p>\u5728\u63a8\u8350\u7cfb\u7edf\u4e2d\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u53ef\u4ee5\u7528\u4e8e\u8861\u91cf\u7528\u6237\u5174\u8da3\u4e4b\u95f4\u7684\u76f8\u4f3c\u5ea6\u3002\u4f8b\u5982\uff0c\u5728\u7535\u5f71\u63a8\u8350\u7cfb\u7edf\u4e2d\uff0c\u53ef\u4ee5\u7528\u66fc\u54c8\u987f\u8ddd\u79bb\u6765\u8ba1\u7b97\u4e24\u4e2a\u7528\u6237\u7684\u8bc4\u5206\u5411\u91cf\u7684\u76f8\u4f3c\u5ea6\uff0c\u4ece\u800c\u63a8\u8350\u76f8\u4f3c\u7528\u6237\u559c\u6b22\u7684\u7535\u5f71\u3002<\/p>\n<\/p>\n<p><h3>3\u3001\u5728\u56fe\u50cf\u5904\u7406\u4e2d\u7684\u5e94\u7528<\/h3>\n<\/p>\n<p><p>\u5728\u56fe\u50cf\u5904\u7406\u9886\u57df\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u53ef\u4ee5\u7528\u4e8e\u56fe\u50cf\u5206\u5272\u3001\u7279\u5f81\u5339\u914d\u7b49\u4efb\u52a1\u3002\u4f8b\u5982\uff0c\u5728\u56fe\u50cf\u5206\u5272\u4e2d\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u53ef\u4ee5\u5e2e\u52a9\u786e\u5b9a\u50cf\u7d20\u4e4b\u95f4\u7684\u76f8\u4f3c\u5ea6\uff0c\u4ece\u800c\u5b9e\u73b0\u66f4\u7cbe\u786e\u7684\u5206\u5272\u3002<\/p>\n<\/p>\n<p><h2>\u56db\u3001\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u4f18\u5316\u4e0e\u6ce8\u610f\u4e8b\u9879<\/h2>\n<\/p>\n<p><h3>1\u3001\u7ef4\u5ea6\u6570\u8fc7\u5927\u65f6\u7684\u4f18\u5316<\/h3>\n<\/p>\n<p><p>\u5f53\u6570\u636e\u7ef4\u5ea6\u6570\u8f83\u5927\u65f6\uff0c\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u53ef\u80fd\u4f1a\u53d8\u5f97\u8017\u65f6\u3002\u6b64\u65f6\uff0c\u53ef\u4ee5\u8003\u8651\u4f7f\u7528\u4ee5\u4e0b\u4f18\u5316\u7b56\u7565\uff1a<\/p>\n<\/p>\n<ul>\n<li><strong>\u5411\u91cf\u5316\u8ba1\u7b97<\/strong>\uff1a\u5c3d\u91cf\u4f7f\u7528NumPy\u7b49\u5e93\u8fdb\u884c\u5411\u91cf\u5316\u64cd\u4f5c\uff0c\u51cf\u5c11\u5faa\u73af\u6b21\u6570\u3002<\/li>\n<li><strong>\u5e76\u884c\u8ba1\u7b97<\/strong>\uff1a\u5229\u7528\u591a\u7ebf\u7a0b\u6216\u591a\u8fdb\u7a0b\u8fdb\u884c\u5e76\u884c\u8ba1\u7b97\uff0c\u63d0\u5347\u8ba1\u7b97\u901f\u5ea6\u3002<\/li>\n<\/ul>\n<p><h3>2\u3001\u5904\u7406\u7f3a\u5931\u503c<\/h3>\n<\/p>\n<p><p>\u5728\u5b9e\u9645\u6570\u636e\u4e2d\uff0c\u53ef\u80fd\u4f1a\u5b58\u5728\u7f3a\u5931\u503c\u3002\u5bf9\u4e8e\u7f3a\u5931\u503c\u7684\u5904\u7406\uff0c\u53ef\u4ee5\u91c7\u53d6\u4ee5\u4e0b\u7b56\u7565\uff1a<\/p>\n<\/p>\n<ul>\n<li><strong>\u5220\u9664\u7f3a\u5931\u503c<\/strong>\uff1a\u76f4\u63a5\u5220\u9664\u5305\u542b\u7f3a\u5931\u503c\u7684\u6837\u672c\u3002<\/li>\n<li><strong>\u586b\u5145\u7f3a\u5931\u503c<\/strong>\uff1a\u4f7f\u7528\u5747\u503c\u3001\u4e2d\u4f4d\u6570\u6216\u5176\u4ed6\u5408\u7406\u7684\u503c\u586b\u5145\u7f3a\u5931\u503c\u3002<\/li>\n<\/ul>\n<p><h3>3\u3001\u6570\u636e\u6807\u51c6\u5316<\/h3>\n<\/p>\n<p><p>\u5728\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u4e4b\u524d\uff0c\u5bf9\u6570\u636e\u8fdb\u884c\u6807\u51c6\u5316\u5904\u7406\uff0c\u53ef\u4ee5\u907f\u514d\u7531\u4e8e\u4e0d\u540c\u7ef4\u5ea6\u91cf\u7eb2\u4e0d\u540c\u800c\u5bfc\u81f4\u7684\u8ba1\u7b97\u8bef\u5dee\u3002\u5e38\u7528\u7684\u6807\u51c6\u5316\u65b9\u6cd5\u6709\uff1a<\/p>\n<\/p>\n<ul>\n<li><strong>\u6700\u5c0f-\u6700\u5927\u6807\u51c6\u5316<\/strong>\uff1a\u5c06\u6570\u636e\u7f29\u653e\u5230[0, 1]\u533a\u95f4\u3002<\/li>\n<li><strong>\u5747\u503c-\u6807\u51c6\u5dee\u6807\u51c6\u5316<\/strong>\uff1a\u5c06\u6570\u636e\u8f6c\u6362\u4e3a\u5747\u503c\u4e3a0\uff0c\u6807\u51c6\u5dee\u4e3a1\u7684\u6807\u51c6\u6b63\u6001\u5206\u5e03\u3002<\/li>\n<\/ul>\n<p><pre><code class=\"language-python\">from sklearn.preprocessing import StandardScaler<\/p>\n<p>def standardize_data(data):<\/p>\n<p>    scaler = StandardScaler()<\/p>\n<p>    return scaler.fit_transform(data)<\/p>\n<h2><strong>\u793a\u4f8b<\/strong><\/h2>\n<p>data = [[1, 2, 3], [4, 0, 3]]<\/p>\n<p>standardized_data = standardize_data(data)<\/p>\n<p>print(standardized_data)<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><h2>\u4e94\u3001\u66fc\u54c8\u987f\u8ddd\u79bb\u4e0e\u5176\u4ed6\u8ddd\u79bb\u5ea6\u91cf\u7684\u6bd4\u8f83<\/h2>\n<\/p>\n<p><h3>1\u3001\u4e0e\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\u7684\u6bd4\u8f83<\/h3>\n<\/p>\n<p><p>\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\u662f\u6700\u5e38\u7528\u7684\u8ddd\u79bb\u5ea6\u91cf\u4e4b\u4e00\uff0c\u5176\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p><p>[ D = \\sqrt{\\sum_{i=1}^{n} (x_i &#8211; y_i)^2} ]<\/p>\n<\/p>\n<p><p>\u76f8\u6bd4\u4e8e\u66fc\u54c8\u987f\u8ddd\u79bb\uff0c\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\u8003\u8651\u4e86\u5750\u6807\u5dee\u503c\u7684\u5e73\u65b9\u548c\uff0c\u56e0\u6b64\u5bf9\u4e8e\u8f83\u5927\u7684\u5750\u6807\u5dee\u503c\u66f4\u654f\u611f\u3002\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\uff0c\u6b27\u51e0\u91cc\u5f97\u8ddd\u79bb\u53ef\u80fd\u4f1a\u53d7\u5230\u7ef4\u5ea6\u707e\u96be\u7684\u5f71\u54cd\uff0c\u800c\u66fc\u54c8\u987f\u8ddd\u79bb\u5219\u76f8\u5bf9\u7a33\u5b9a\u3002<\/p>\n<\/p>\n<p><h3>2\u3001\u4e0e\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb\u7684\u6bd4\u8f83<\/h3>\n<\/p>\n<p><p>\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb\u662f\u53e6\u4e00\u79cd\u5e38\u89c1\u7684\u8ddd\u79bb\u5ea6\u91cf\uff0c\u5176\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p><p>[ D = \\max_{i} |x_i &#8211; y_i| ]<\/p>\n<\/p>\n<p><p>\u5207\u6bd4\u96ea\u592b\u8ddd\u79bb\u53ea\u5173\u6ce8\u5750\u6807\u5dee\u503c\u7684\u6700\u5927\u503c\uff0c\u800c\u5ffd\u7565\u5176\u4ed6\u7ef4\u5ea6\u7684\u5dee\u503c\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u8003\u8651\u4e86\u6240\u6709\u7ef4\u5ea6\u7684\u5dee\u503c\uff0c\u56e0\u6b64\u80fd\u591f\u66f4\u5168\u9762\u5730\u53cd\u6620\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\u3002<\/p>\n<\/p>\n<p><h3>3\u3001\u4e0e\u4f59\u5f26\u76f8\u4f3c\u5ea6\u7684\u6bd4\u8f83<\/h3>\n<\/p>\n<p><p>\u4f59\u5f26\u76f8\u4f3c\u5ea6\u662f\u4e00\u79cd\u7528\u4e8e\u8861\u91cf\u4e24\u4e2a\u5411\u91cf\u5939\u89d2\u7684\u5ea6\u91cf\u65b9\u6cd5\uff0c\u5176\u516c\u5f0f\u4e3a\uff1a<\/p>\n<\/p>\n<p><p>[ \\text{Cosine Similarity} = \\frac{\\sum_{i=1}^{n} x_i y_i}{\\sqrt{\\sum_{i=1}^{n} x_i^2} \\sqrt{\\sum_{i=1}^{n} y_i^2}} ]<\/p>\n<\/p>\n<p><p>\u4f59\u5f26\u76f8\u4f3c\u5ea6\u4fa7\u91cd\u4e8e\u5411\u91cf\u7684\u65b9\u5411\uff0c\u800c\u4e0d\u662f\u957f\u5ea6\uff0c\u56e0\u6b64\u5728\u9ad8\u7ef4\u7a7a\u95f4\u4e2d\u8868\u73b0\u8f83\u597d\u3002\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u66f4\u5173\u6ce8\u70b9\u4e4b\u95f4\u7684\u5b9e\u9645\u8ddd\u79bb\u3002<\/p>\n<\/p>\n<p><h2>\u516d\u3001\u603b\u7ed3<\/h2>\n<\/p>\n<p><p>\u66fc\u54c8\u987f\u8ddd\u79bb\u4f5c\u4e3a\u4e00\u79cd\u7b80\u5355\u800c\u6709\u6548\u7684\u8ddd\u79bb\u5ea6\u91cf\u65b9\u6cd5\uff0c\u5728\u6570\u5b66\u3001\u673a\u5668\u5b66\u4e60\u3001\u63a8\u8350\u7cfb\u7edf\u548c\u56fe\u50cf\u5904\u7406\u7b49\u9886\u57df\u6709\u7740\u5e7f\u6cdb\u7684\u5e94\u7528\u3002\u901a\u8fc7\u624b\u52a8\u5b9e\u73b0\u3001\u4f7f\u7528NumPy\u5e93\u548cSciPy\u5e93\uff0c\u6211\u4eec\u53ef\u4ee5\u65b9\u4fbf\u5730\u5728Python\u4e2d\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u3002\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u5408\u7406\u9009\u62e9\u8ddd\u79bb\u5ea6\u91cf\u65b9\u6cd5\u5e76\u8fdb\u884c\u9002\u5f53\u7684\u4f18\u5316\uff0c\u53ef\u4ee5\u63d0\u5347\u7b97\u6cd5\u7684\u6027\u80fd\u548c\u51c6\u786e\u6027\u3002<\/p>\n<\/p>\n<p><p>\u901a\u8fc7\u672c\u6587\u7684\u4ecb\u7ecd\uff0c\u5e0c\u671b\u8bfb\u8005\u80fd\u591f\u6df1\u5165\u7406\u89e3\u66fc\u54c8\u987f\u8ddd\u79bb\u7684\u8ba1\u7b97\u65b9\u6cd5\u53ca\u5176\u5e94\u7528\uff0c\u5e76\u5728\u5b9e\u9645\u9879\u76ee\u4e2d\u7075\u6d3b\u8fd0\u7528\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u66fc\u54c8\u987f\u8ddd\u79bb\u662f\u4ec0\u4e48\uff0c\u4e3a\u4ec0\u4e48\u5728Python\u4e2d\u8ba1\u7b97\u5b83\u5f88\u91cd\u8981\uff1f<\/strong><br \/>\u66fc\u54c8\u987f\u8ddd\u79bb\u662f\u6307\u4e24\u4e2a\u70b9\u5728\u5750\u6807\u7cfb\u4e2d\uff0c\u6cbf\u5750\u6807\u8f74\u7684\u7edd\u5bf9\u8ddd\u79bb\u4e4b\u548c\u3002\u5b83\u901a\u5e38\u7528\u4e8e\u5206\u7c7b\u3001\u805a\u7c7b\u7b97\u6cd5\u4ee5\u53ca\u56fe\u5f62\u5904\u7406\u7b49\u9886\u57df\u3002\u5728Python\u4e2d\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u80fd\u591f\u5e2e\u52a9\u5f00\u53d1\u8005\u5728\u6570\u636e\u5206\u6790\u3001\u673a\u5668\u5b66\u4e60\u7b49\u5e94\u7528\u4e2d\u66f4\u597d\u5730\u7406\u89e3\u548c\u5904\u7406\u6570\u636e\u3002<\/p>\n<p><strong>\u5728Python\u4e2d\uff0c\u6709\u54ea\u4e9b\u5e38\u7528\u7684\u65b9\u6cd5\u53ef\u4ee5\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\uff1f<\/strong><br \/>Python\u63d0\u4f9b\u4e86\u591a\u79cd\u65b9\u6cd5\u6765\u8ba1\u7b97\u66fc\u54c8\u987f\u8ddd\u79bb\u3002\u6700\u7b80\u5355\u7684\u65b9\u5f0f\u662f\u4f7f\u7528NumPy\u5e93\uff0c\u901a\u8fc7\u6570\u7ec4\u8fd0\u7b97\u76f4\u63a5\u8ba1\u7b97\u3002\u4e5f\u53ef\u4ee5\u4f7f\u7528SciPy\u5e93\u4e2d\u7684\u8ddd\u79bb\u51fd\u6570\uff0c\u6216\u8005\u624b\u52a8\u7f16\u5199\u51fd\u6570\u6765\u8ba1\u7b97\u3002\u4f8b\u5982\uff1a<\/p>\n<pre><code class=\"language-python\">def manhattan_distance(point1, point2):\n    return sum(abs(a - b) for a, b in zip(point1, point2))\n<\/code><\/pre>\n<p>\u4f7f\u7528\u8fd9\u4e9b\u65b9\u6cd5\u53ef\u4ee5\u65b9\u4fbf\u5730\u5904\u7406\u4e00\u7ef4\u6216\u591a\u7ef4\u6570\u636e\u3002<\/p>\n<p><strong>\u5982\u4f55\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u5229\u7528\u66fc\u54c8\u987f\u8ddd\u79bb\u8fdb\u884c\u6570\u636e\u5206\u6790\uff1f<\/strong><br \/>\u5728\u6570\u636e\u5206\u6790\u4e2d\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u5e38\u7528\u4e8e\u805a\u7c7b\u548c\u5206\u7c7b\u4efb\u52a1\u3002\u4f8b\u5982\uff0c\u5728K\u5747\u503c\u805a\u7c7b\u4e2d\uff0c\u53ef\u4ee5\u4f7f\u7528\u66fc\u54c8\u987f\u8ddd\u79bb\u6765\u5224\u65ad\u6837\u672c\u4e4b\u95f4\u7684\u76f8\u4f3c\u5ea6\u3002\u901a\u8fc7\u8ba1\u7b97\u6837\u672c\u4e0e\u805a\u7c7b\u4e2d\u5fc3\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u5c06\u6837\u672c\u5206\u914d\u5230\u6700\u8fd1\u7684\u805a\u7c7b\u4e2d\u3002\u6b64\u5916\uff0c\u66fc\u54c8\u987f\u8ddd\u79bb\u8fd8\u53ef\u4ee5\u7528\u4e8e\u63a8\u8350\u7cfb\u7edf\uff0c\u4ee5\u8861\u91cf\u7528\u6237\u4e4b\u95f4\u7684\u76f8\u4f3c\u6027\u5e76\u63d0\u4f9b\u4e2a\u6027\u5316\u7684\u63a8\u8350\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"Python\u4e2d\u5982\u4f55\u8fdb\u884c\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97 \u5728Python\u4e2d\u8fdb\u884c\u66fc\u54c8\u987f\u8ddd\u79bb\u8ba1\u7b97\uff0c\u6838\u5fc3\u6b65\u9aa4\u662f\u8ba1\u7b97\u5404\u7ef4\u5ea6\u5750\u6807\u5dee\u7684\u7edd\u5bf9\u503c\u3001 [&hellip;]","protected":false},"author":3,"featured_media":1121886,"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\/1121880"}],"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=1121880"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1121880\/revisions"}],"predecessor-version":[{"id":1121888,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/1121880\/revisions\/1121888"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/1121886"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=1121880"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=1121880"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=1121880"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}