{"id":33,"date":"2025-10-12T23:59:41","date_gmt":"2025-10-12T15:59:41","guid":{"rendered":"https:\/\/www.yiersan79.com\/?p=33"},"modified":"2025-10-13T00:30:52","modified_gmt":"2025-10-12T16:30:52","slug":"%e8%81%9a%e7%b1%bb%e7%ae%97%e6%b3%951-dbscan","status":"publish","type":"post","link":"https:\/\/www.yiersan79.com\/index.php\/2025\/10\/12\/%e8%81%9a%e7%b1%bb%e7%ae%97%e6%b3%951-dbscan\/","title":{"rendered":"\u805a\u7c7b\u7b97\u6cd51: DBSCAN"},"content":{"rendered":"\n<h1 class=\"wp-block-heading\">\u7b80\u4ecb<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">DBSCAN \u7b97\u6cd5\u7684\u5168\u79f0\u662f \u201cDensity-Based Spatial Clustering of Applications with Noise\u201d\uff0c\u4e2d\u6587\u610f\u4e3a \u201c\u57fa\u4e8e\u5bc6\u5ea6\u7684\u5e26\u6709\u566a\u58f0\u7684\u7a7a\u95f4\u805a\u7c7b\u5e94\u7528\u201d\u3002DBSCAN\u662f\u4e00\u79cd\u57fa\u4e8e\u5bc6\u5ea6\u7684\u805a\u7c7b\u7b97\u6cd5\uff0c\u6838\u5fc3\u662f\u5c06 \u201c\u5bc6\u5ea6\u76f8\u8fde\u201d \u7684\u6837\u672c\u805a\u6210\u4e00\u7c7b\uff0c\u80fd\u81ea\u52a8\u8bc6\u522b\u4efb\u610f\u5f62\u72b6\u7684\u7c07\u5e76\u6807\u8bb0\u566a\u58f0\u70b9\u3002<\/p>\n\n\n\n<h1 class=\"wp-block-heading\">\u76f8\u5173\u6982\u5ff5<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u03b5\uff08Epsilon\uff09<\/strong>\uff1a\u5b9a\u4e49 \u201c\u6837\u672c\u7684\u90bb\u57df\u8303\u56f4\u201d\uff0c\u5373\u67d0\u4e2a\u6837\u672c\u5468\u56f4\u591a\u5927\u8303\u56f4\u5185\u7684\u5176\u4ed6\u6837\u672c\u4f1a\u88ab\u89c6\u4e3a \u201c\u90bb\u5c45\u201d\u3002<\/li>\n\n\n\n<li><strong>MinPts\uff08Minimum Points\uff09<\/strong>\uff1a\u5b9a\u4e49 \u201c\u5bc6\u96c6\u7684\u6807\u51c6\u201d\uff0c\u5373\u4e00\u4e2a\u90bb\u57df\u5185\u81f3\u5c11\u5305\u542b\u591a\u5c11\u4e2a\u6837\u672c\uff0c\u624d\u80fd\u88ab\u5224\u5b9a\u4e3a \u201c\u5bc6\u96c6\u533a\u57df\u201d<\/li>\n\n\n\n<li><strong>\u5bc6\u5ea6\u53ef\u8fbe<\/strong>\uff1a\u901a\u8fc7\u6838\u5fc3\u70b9\u7684 \u03b5 \u90bb\u57df\u95f4\u63a5\u8fde\u63a5\u7684\u6837\u672c<\/li>\n\n\n\n<li><strong>\u4e09\u79cd\u7c7b\u578b\u7684\u70b9<\/strong>\uff1a\n<ul class=\"wp-block-list\">\n<li><strong>\u6838\u5fc3\u70b9<\/strong>\uff1a\u82e5\u4e00\u4e2a\u6837\u672c\u7684 \u03b5 \u90bb\u57df\u5185\uff0c\u5305\u542b\u7684\u6837\u672c\u6570 \u2265 MinPts\uff0c\u5219\u8be5\u6837\u672c\u4e3a\u6838\u5fc3\u70b9\uff08\u5bc6\u96c6\u533a\u57df\u7684\u4e2d\u5fc3\uff09\u3002<\/li>\n\n\n\n<li><strong>\u8fb9\u754c\u70b9<\/strong>\uff1a\u82e5\u4e00\u4e2a\u6837\u672c\u7684 \u03b5 \u90bb\u57df\u5185\uff0c\u6837\u672c\u6570 &lt; MinPts\uff0c\u4f46\u8be5\u6837\u672c\u843d\u5728\u67d0\u4e2a\u6838\u5fc3\u70b9\u7684 \u03b5 \u90bb\u57df\u5185\uff0c\u5219\u4e3a\u8fb9\u754c\u70b9\uff08\u5bc6\u96c6\u533a\u57df\u7684\u8fb9\u7f18\uff09\u3002<\/li>\n\n\n\n<li><strong>\u566a\u58f0\u70b9<\/strong>\uff1a\u65e2\u4e0d\u662f\u6838\u5fc3\u70b9\uff0c\u4e5f\u4e0d\u5728\u4efb\u4f55\u6838\u5fc3\u70b9\u7684 \u03b5 \u90bb\u57df\u5185\uff0c\u6700\u7ec8\u4f1a\u88ab\u6392\u9664\u5728\u6240\u6709\u7c07\u4e4b\u5916\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">\u7b97\u6cd5\u6d41\u7a0b<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u6b65\u9aa4 1\uff1a\u521d\u59cb\u5316\u6807\u8bb0\uff0c\u904d\u5386\u672a\u5904\u7406\u6837\u672c<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7ed9\u6240\u6709\u6837\u672c\u6253\u4e0a \u201c\u672a\u8bbf\u95ee\u201d \u6807\u8bb0\uff0c\u786e\u4fdd\u6bcf\u4e2a\u6837\u672c\u90fd\u4f1a\u88ab\u68c0\u67e5\uff1b<\/li>\n\n\n\n<li>\u4ece\u7b2c\u4e00\u4e2a \u201c\u672a\u8bbf\u95ee\u201d \u7684\u6837\u672c\u5f00\u59cb\uff0c\u8fdb\u5165\u540e\u7eed\u5224\u65ad\uff1b\u5904\u7406\u5b8c\u4e00\u4e2a\u6837\u672c\u540e\uff0c\u7ee7\u7eed\u904d\u5386\u4e0b\u4e00\u4e2a \u201c\u672a\u8bbf\u95ee\u201d \u6837\u672c\uff0c\u76f4\u5230\u6240\u6709\u6837\u672c\u90fd\u88ab\u6807\u8bb0\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u6b65\u9aa4 2\uff1a\u5224\u65ad\u5f53\u524d\u6837\u672c\u7c7b\u578b\uff0c\u533a\u5206\u6838\u5fc3\u70b9\u4e0e\u975e\u6838\u5fc3\u70b9<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8ba1\u7b97\u5f53\u524d \u201c\u672a\u8bbf\u95ee\u201d \u6837\u672c\u7684 \u03b5 \u90bb\u57df\u5185\uff0c\u6240\u6709\u5176\u4ed6\u6837\u672c\u7684\u6570\u91cf\uff08\u5373 \u201c\u90bb\u5c45\u6570\u201d\uff09\u3002<\/li>\n\n\n\n<li>\u82e5\u90bb\u5c45\u6570 \u2265 MinPts\uff1a\u8be5\u6837\u672c\u662f<strong>\u6838\u5fc3\u70b9<\/strong>\uff0c\u8fdb\u5165 \u201c\u6269\u5c55\u7c07\u201d \u6b65\u9aa4\uff1b\u82e5\u90bb\u5c45\u6570 &lt; MinPts\uff1a\u6682\u65f6\u6807\u8bb0\u4e3a \u201c\u672a\u5206\u7c7b\u201d\uff0c\u5148\u8df3\u8fc7\uff0c\u540e\u7eed\u7531\u6838\u5fc3\u70b9\u5224\u65ad\u662f\u5426\u4e3a\u8fb9\u754c\u70b9\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u6b65\u9aa4 3\uff1a\u4ece\u6838\u5fc3\u70b9\u51fa\u53d1\uff0c\u6269\u5c55\u5bc6\u5ea6\u76f8\u8fde\u7684\u7c07<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u8fd9\u662f\u5f62\u6210\u7c07\u7684\u5173\u952e\u6b65\u9aa4\uff0c\u6838\u5fc3\u662f\u628a\u6240\u6709 \u201c\u5bc6\u5ea6\u53ef\u8fbe\u201d \u7684\u6837\u672c\u5f52\u4e3a\u540c\u4e00\u7c07\u3002<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u4ee5\u5f53\u524d\u6838\u5fc3\u70b9\u4e3a\u8d77\u70b9\uff0c\u521b\u5efa\u4e00\u4e2a\u65b0\u7684\u7c07\uff0c\u5e76\u5c06\u8be5\u6838\u5fc3\u70b9\u52a0\u5165\u7c07\u4e2d\uff0c\u540c\u65f6\u6807\u8bb0\u5176\u4e3a \u201c\u5df2\u8bbf\u95ee\u201d\u3002<\/li>\n\n\n\n<li>\u6536\u96c6\u8be5\u6838\u5fc3\u70b9 \u03b5 \u90bb\u57df\u5185\u7684\u6240\u6709\u6837\u672c\uff0c\u4f5c\u4e3a \u201c\u5f85\u68c0\u67e5\u90bb\u5c45\u5217\u8868\u201d\u3002<\/li>\n\n\n\n<li>\u904d\u5386 \u201c\u5f85\u68c0\u67e5\u90bb\u5c45\u5217\u8868\u201d \u4e2d\u7684\u6bcf\u4e2a\u6837\u672c\uff1a\n<ul class=\"wp-block-list\">\n<li>\u82e5\u8be5\u6837\u672c \u201c\u672a\u8bbf\u95ee\u201d\uff1a\u6807\u8bb0\u4e3a \u201c\u5df2\u8bbf\u95ee\u201d\uff0c\u8ba1\u7b97\u5176\u90bb\u5c45\u6570\uff1b\u82e5\u90bb\u5c45\u6570 \u2265 MinPts\uff08\u4e5f\u662f\u6838\u5fc3\u70b9\uff09\uff0c\u5219\u5c06\u5176\u90bb\u57df\u5185\u7684\u6837\u672c\u4e5f\u52a0\u5165 \u201c\u5f85\u68c0\u67e5\u90bb\u5c45\u5217\u8868\u201d\uff0c\u7ee7\u7eed\u6269\u5c55\u3002\u82e5\u90bb\u5c45\u6570 \uff1cMinPts\uff08\u975e\u6838\u5fc3\u70b9\uff09\uff0c\u5219\u4e0d\u9700\u8981\u8be5\u70b9\u7684\u90bb\u57df\u5185\u7684\u6837\u672c\u3002\u56e0\u4e3a\u975e\u6838\u5fc3\u70b9\u53ea\u80fd\u52a0\u5165\u96c6\u7fa4\uff0c\u800c\u4e0d\u80fd\u7528\u4e8e\u8fdb\u4e00\u6b65\u6269\u5c55\u96c6\u7fa4\u3002<\/li>\n\n\n\n<li>\u82e5\u8be5\u6837\u672c \u201c\u672a\u5206\u7c7b\u201d\uff1a\u5c06\u5176\u52a0\u5165\u5f53\u524d\u7c07\uff08\u4f5c\u4e3a\u8fb9\u754c\u70b9\uff09\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u76f4\u5230 \u201c\u5f85\u68c0\u67e5\u90bb\u5c45\u5217\u8868\u201d \u4e3a\u7a7a\uff0c\u5f53\u524d\u7c07\u6269\u5c55\u5b8c\u6210\uff0c\u7c07\u6570\u91cf + 1\u3002<\/li>\n<\/ol>\n\n\n\n<h2 class=\"wp-block-heading\">\u6b65\u9aa4 4\uff1a\u6807\u8bb0\u566a\u58f0\u70b9\uff0c\u5b8c\u6210\u6240\u6709\u805a\u7c7b<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u6240\u6709\u6837\u672c\u904d\u5386\u7ed3\u675f\u540e\uff0c\u672a\u88ab\u52a0\u5165\u4efb\u4f55\u7c07\u7684 \u201c\u672a\u5206\u7c7b\u201d \u6837\u672c\uff0c\u5373\u4e3a<strong>\u566a\u58f0\u70b9<\/strong>\uff0c\u76f4\u63a5\u6807\u8bb0\u4e3a \u201c\u566a\u58f0\u201d\u3002<\/li>\n\n\n\n<li>\u6700\u7ec8\u5c31\u53ef\u4ee5\u5f97\u5230\u6240\u6709\u7c07\uff08\u5305\u542b\u6838\u5fc3\u70b9\u548c\u8fb9\u754c\u70b9\uff09\u548c\u566a\u58f0\u70b9\u7684\u6807\u8bb0\u7ed3\u679c\u3002<\/li>\n<\/ul>\n\n\n\n<h1 class=\"wp-block-heading\">python\u4ee3\u7801\u5b9e\u73b0<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">\u8f93\u5165<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u884c\u8f93\u5165\u4e09\u4e2a\u6570&nbsp;eps\u3001min_samples\u3001x\uff0c\u4ee5\u7a7a\u683c\u9694\u5f00\uff0c\u5206\u522b\u8868\u793a\uff1a\n<ul class=\"wp-block-list\">\n<li>eps\uff1a\u8ba1\u7b97&nbsp;eps&nbsp;\u90bb\u57df\u7684\u534a\u5f84\u503c\uff0c\u53ef\u4e3a\u5c0f\u6570\u3002<\/li>\n\n\n\n<li>min_samples\uff1a\u6838\u5fc3\u70b9\u7684&nbsp;eps&nbsp;\u90bb\u57df\u5185\u6837\u672c\u6570\u91cf\u9608\u503c\uff0c\u6574\u6570\u3002<\/li>\n\n\n\n<li>x\uff1a\u6570\u636e\u96c6\u884c\u6570\uff0c\u5373\u6837\u672c\u6570\u91cf\uff0c\u6574\u6570\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u884c\u5f00\u59cb\u4e3a\u8f93\u5165\u7684\u6837\u672c\u6570\u636e\uff0c\u6570\u503c\u4e4b\u95f4\u7528\u7a7a\u683c\u9694\u5f00\uff0c\u5171\u8f93\u5165&nbsp;x&nbsp;\u884c\uff0c\u6bcf\u884c\u8f93\u5165\u7684\u6570\u503c\u6570\u91cf\u4e3a&nbsp;y&nbsp;\u4e2a\uff0c\u4e14\u6ee1\u8db3&nbsp;2\u2264y\u22643\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u8f93\u51fa<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u8f93\u51fa\u4e24\u4e2a\u503c\uff0c\u7528\u7a7a\u683c\u9694\u5f00\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7b2c\u4e00\u4e2a\u503c\uff1a\u5f97\u5230\u7684\u7c07\u7684\u4e2a\u6570\u3002<\/li>\n\n\n\n<li>\u7b2c\u4e8c\u4e2a\u503c\uff1a\u8bc6\u522b\u5230\u7684\u566a\u58f0\u70b9\u7684\u4e2a\u6570\u3002<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">\u793a\u4f8b<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8f93\u5165\u793a\u4f8b1\uff1a<\/strong><\/p>\n\n\n\n<div class=\"wp-block-urvanov-syntax-highlighter-code-block\"><\/div>\n\n\n\n<div class=\"wp-block-urvanov-syntax-highlighter-code-block\"><pre class=\"lang:default decode:true \">2 2 10\n0 0\n3 3\n6 6\n9 9\n12 12\n2 6\n6 2\n9 5\n5 9\n10 2<\/pre><\/div>\n\n\n\n<p class=\"wp-block-paragraph\">eps\u4e3a2\uff0cmin_samples\u4e3a2\uff0c\u517110\u4e2a\u70b9\u3002<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>\u8f93\u51fa\u793a\u4f8b1\uff1a<\/strong><\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>0 10<\/code><\/pre>\n\n\n\n<p class=\"wp-block-paragraph\">0\u4e2a\u7c07\uff0c10\u4e2a\u566a\u58f0\u70b9\u3002<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">\u5b8c\u6574\u4ee3\u7801<\/h2>\n\n\n\n<div class=\"wp-block-urvanov-syntax-highlighter-code-block\"><pre class=\"theme:obsidian-light lang:default decode:true \" >def read_input():\n    # \u8bfb\u53d6\u7528\u6237\u8f93\u5165\u7684\u4e00\u884c\u5b57\u7b26\u4e32\n    eps, min_samples, x = map(float, input().split())\n    min_samples = int(min_samples)\n    x = int(x)\n    samples = []\n    for _ in range(x):\n        # \u8bfb\u53d6\u7528\u6237\u8f93\u5165\u7684\u4e0b\u4e00\u884c\u5b57\u7b26\u4e32\n        samples.append(list(map(float, input().split())))\n    return eps, min_samples, x, samples\n\n\ndef distance(sample_a, sample_b):\n    return sum([(ai - bi) ** 2 for ai, bi in zip(sample_a, sample_b)])\n\n\ndef get_cluster(i, eps, samples, visited):\n    neighbors = []\n    for j in range(len(samples)):\n        if visited[j]:\n            continue\n        if distance(samples[i], samples[j]) &lt;= eps * eps:\n            neighbors.append(j)\n            visited[j] = True\n    return neighbors\n\n\ndef dbscan(eps, min_samples, x, samples):\n    clusters_num = 0\n    visited = [False] * x\n    noise = [True] * x\n    for i in range(x):\n        if visited[i]:\n            continue\n        cluster = get_cluster(i, eps, samples, visited)\n        samples_in_cluster = []\n        while cluster:\n            j = cluster.pop()\n            samples_in_cluster.append(j)\n            cluster.extend(get_cluster(j, eps, samples, visited))\n        if len(samples_in_cluster) &gt;= min_samples:\n            clusters_num += 1\n            for p in samples_in_cluster:\n                noise[p] = False\n    return clusters_num, sum(noise)\n\n\nif __name__ == '__main__':\n    eps, min_samples, x, samples = read_input()\n    clusters_num, noise_num = dbscan(eps, min_samples, x, samples)\n    print(clusters_num, noise_num)<\/pre><\/div>\n\n\n\n<h1 class=\"wp-block-heading\">\u53c2\u8003<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>https:\/\/zhuanlan.zhihu.com\/p\/1925351611942809908<\/li>\n\n\n\n<li>sklearn\u5b98\u65b9\u6587\u6863<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">\u200b<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u7b80\u4ecb DBSCAN \u7b97\u6cd5\u7684\u5168\u79f0\u662f \u201cDensity-Ba\u2026<\/p>\n","protected":false},"author":2,"featured_media":49,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[5],"tags":[],"class_list":["post-33","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-5"],"jetpack_featured_media_url":"https:\/\/www.yiersan79.com\/wp-content\/uploads\/2025\/10\/\u7ed8\u5236-DBSCAN-\u56fe-e1760286141668.png","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/posts\/33","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/comments?post=33"}],"version-history":[{"count":14,"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/posts\/33\/revisions"}],"predecessor-version":[{"id":71,"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/posts\/33\/revisions\/71"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/media\/49"}],"wp:attachment":[{"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/media?parent=33"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/categories?post=33"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.yiersan79.com\/index.php\/wp-json\/wp\/v2\/tags?post=33"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}