{"id":698,"date":"2024-03-15T14:23:27","date_gmt":"2024-03-15T06:23:27","guid":{"rendered":"http:\/\/lingbo.online\/?p=698"},"modified":"2024-03-19T13:56:35","modified_gmt":"2024-03-19T05:56:35","slug":"bm25","status":"publish","type":"post","link":"https:\/\/lingbo.online\/index.php\/algorithm_learning\/bm25\/","title":{"rendered":"BM25\u7b97\u6cd5\u8be6\u89e3"},"content":{"rendered":"

\u7b80\u4ecb<\/h1>\n

BM25\u662f\u4e00\u79cd\u7528\u4e8e\u4fe1\u606f\u68c0\u7d22\u7684\u7b97\u6cd5\uff0c\u53ef\u4ee5\u7528\u4e8e\u8861\u91cf\u6587\u6863\u7684\u76f8\u5173\u6027\u3002\u8be5\u7b97\u6cd5\u6700\u65e9\u7531Robertson\u7b49\u4eba\u4e8e1995\u5e74\u63d0\u51fa\uff0c\u662f\u57fa\u4e8eOkapi TF-IDF\u7b97\u6cd5\u7684\u6539\u8fdb\u7248\u672c\uff0c\u65e8\u5728\u89e3\u51b3Okapi TF-IDF\u7b97\u6cd5\u7684\u4e00\u4e9b\u4e0d\u8db3\u3002\u5176\u88ab\u5e7f\u6cdb\u5e94\u7528\u4e8e\u4fe1\u606f\u68c0\u7d22\u9886\u57df\u7684\u6392\u540d\u51fd\u6570\uff0c\u7528\u4e8e\u4f30\u8ba1\u6587\u6863D<\/span>\u548c\u7528\u6237\u67e5\u8be2Q<\/span>\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u3002\u4ed6\u662f\u4e00\u79cd\u57fa\u4e8e\u6982\u7387\u68c0\u7d22\u6846\u67b6\u7684\u6539\u8fdb\u3002\u7279\u522b\u662f\u5728\u5904\u7406\u957f\u6587\u6863\u548c\u77ed\u67e5\u8be2\u65f6\u8868\u73b0\u51fa\u8272\u3002BM25\u7684\u6838\u5fc3\u601d\u60f3\u662f\u57fa\u4e8e\u8bcd\u9891\uff08TF\uff09\u548c\u9006\u6587\u6863\u9891\u7387\uff08IDF\uff09\uff0c\u540c\u65f6\u8fd8\u5f15\u5165\u4e86\u6587\u6863\u7684\u957f\u5ea6\u4fe1\u606f\u6765\u8ba1\u7b97\u6587\u6863D<\/span>\u548c\u67e5\u8be2Q<\/span>\u4e4b\u95f4\u7684\u76f8\u5173\u6027\u3002\u76ee\u524d\u88ab\u5e7f\u6cdb\u7528\u4e8e\u7684\u641c\u7d22\u5f15\u64ceES\u5c31\u5185\u7f6e\u4e86BM25\u7b97\u6cd5\u8fdb\u884c\u5168\u6587\u68c0\u7d22\u3002<\/p>\n

\u57fa\u672c\u516c\u5f0f<\/h1>\n

BM25\u7b97\u6cd5\u7684\u57fa\u672c\u516c\u5f0f\u5982\u4e0b\uff1a
\n\"\"<\/p>\n

\u5176\u4e2d\uff1a<\/p>\n

\n

Score(D,Q)<\/span>\u662f\u6587\u6863D<\/span>\u548c\u67e5\u8be2Q<\/span>\u7684\u76f8\u5173\u6027\u5f97\u5206\u3002
\nq_i<\/span>\u662f\u67e5\u8be2\u4e2d\u7684\u7b2ci<\/span>\u4e2a\u8bcd\u3002
\nf(q_i,D)<\/span>\u662f\u8bcdq_i<\/span>\u5728\u6587\u6863D\u4e2d\u7684\u9891\u7387\u3002
\nIDF(q_i)<\/span>\u662f\u8bcdq_i<\/span>\u7684\u9006\u6587\u6863\u9891\u7387\u3002
\n|D|<\/span>\u662f\u6587\u6863|D|<\/span>\u7684\u957f\u5ea6\u3002
\navgdl<\/span>\u662f\u6240\u6709\u6587\u6863\u7684\u5e73\u5747\u957f\u5ea6
\nk_1<\/span>\u548cb<\/span>\u662f\u53ef\u8c03\u7684\u53c2\u6570\uff0c\u901a\u5e38k_1<\/span>\u57281.2\u52302\u4e4b\u95f4\uff0cb<\/span>\u901a\u5e38\u8bbe\u7f6e\u4e3a0.75\u3002<\/p>\n<\/blockquote>\n

IDF\u7684\u8ba1\u7b97\u65b9\u6cd5\u4e3a\uff1a
\n\"\"<\/p>\n

\n

N<\/span>\u662f\u6587\u6863\u96c6\u5408\u4e2d\u7684\u6587\u6863\u603b\u6570
\nn(q_i)<\/span>\u662f\u5305\u542b\u8bcdq_i<\/span>\u7684\u6587\u6863\u6570<\/p>\n<\/blockquote>\n

\u516c\u5f0f\u89e3\u91ca<\/h1>\n
    \n
  • \u8bcd\u9891\uff08f(q_i,D)<\/span>\uff09:<\/strong>\u8fd9\u662f\u67e5\u8be2\u4e2d\u7684\u8bcdq_i<\/span>\u5728\u6587\u6863D<\/span>\u4e2d\u51fa\u73b0\u7684\u9891\u7387\u3002\u8bcd\u9891\u662f\u5f88\u4eae\u4e00\u4e2a\u8bcd\u5728\u6587\u6863\u4e2d\u91cd\u8981\u6027\u7684\u57fa\u672c\u6307\u6807\u3002\u8bcd\u9891\u8d8a\u9ad8\uff0c\u8fd9\u4e2a\u8bcd\u5728\u6587\u6863\u7684\u91cd\u8981\u6027\u901a\u5e38\u8d8a\u5927\u3002<\/li>\n
  • \u9006\u6587\u6863\u9891\u7387\uff08IDF(q_i)<\/span>\uff09:<\/strong>\u9006\u6587\u6863\u9891\u7387\u662f\u8861\u91cf\u4e00\u4e2a\u8bcd\u5bf9\u4e8e\u6574\u4e2a\u6587\u6863\u96c6\u5408\u7684\u72ec\u7279\u6027\u6216\u4fe1\u606f\u91cf\u7684\u6307\u6807\u3002\u5b83\u662f\u7531\u6574\u4e2a\u6587\u6863\u96c6\u5408\u4e2d\u5305\u542b\u8be5\u8bcd\u7684\u6587\u6863\u6570\u91cf\u51b3\u5b9a\u7684\u3002\u4e00\u4e2a\u8bcd\u5728\u5f88\u591a\u6587\u6863\u4e2d\u51fa\u73b0\uff0c\u5176IDF\u503c\u5c31\u4f1a\u4f4e\uff0c\u53cd\u4e4b\u5219\u9ad8\u3002\u8fd9\u610f\u5473\u7740\u7f55\u89c1\u7684\u8bcd\u901a\u5e38\u6709\u66f4\u9ad8\u7684IDF\u503c\uff0c\u4ece\u800c\u5728\u76f8\u5173\u6027\u8bc4\u5206\u4e2d\u62e5\u6709\u66f4\u5927\u7684\u6743\u91cd\u3002<\/li>\n
  • \u6587\u6863\u957f\u5ea6(|D|<\/span>)\uff1a<\/strong>\u8fd9\u662f\u6587\u6863D<\/span>\u4e2d\u7684\u8bcd\u6c47\u6570\u91cf\u3002\u6587\u6863\u957f\u5ea6\u7528\u4e8e\u8c03\u6574\u8bcd\u9891\u7684\u5f71\u54cd\uff0c\u56e0\u4e3a\u8f83\u957f\u7684\u6587\u6863\u53ef\u80fd\u4ec5\u56e0\u4e3a\u4ed6\u4eec\u7684\u957f\u5ea6\u5c31\u6709\u66f4\u9ad8\u7684\u8bcd\u9891<\/li>\n
  • \u5e73\u5747\u6587\u6863\u957f\u5ea6\uff08avgdl<\/span>\uff09\uff1a<\/strong>\u8fd9\u662f\u6574\u4e2a\u6587\u6863\u96c6\u5408\u4e2d\u6240\u6709\u6587\u6863\u957f\u5ea6\u7684\u5e73\u5747\u503c\u3002\u5b83\u7528\u4e8e\u6807\u51c6\u5316\u4e0d\u540c\u6587\u6863\u7684\u957f\u5ea6\uff0c\u53ef\u4ee5\u516c\u5e73\u6bd4\u8f83\u4e0d\u540c\u957f\u5ea6\u7684\u6587\u6863\u3002<\/li>\n
  • \u53ef\u8c03\u53c2\u6570(k1\u548cb)<\/strong>\uff1a\n
      \n
    • k_1<\/span>\u662f\u4e00\u4e2a\u6b63\u7cfb\u6570\uff0c\u7528\u4e8e\u63a7\u5236\u8bcd\u9891\u7684\u9971\u548c\u5ea6\u3002\u8f83\u9ad8\u7684k_1<\/span>\u503c\u610f\u5473\u7740\u8bcd\u9891\u5bf9\u8bc4\u5206\u7684\u5f71\u54cd\u66f4\u5927\u3002<\/li>\n
    • b<\/span>\u7528\u4e8e\u63a7\u5236\u6587\u6863\u957f\u5ea6\u5bf9\u8bc4\u5206\u5f71\u54cd\u7684\u53c2\u6570\uff0c\u53d6\u503c\u57280\u52301\u4e4b\u95f4\u3002\u5f53b=1<\/span>\u65f6\uff0c\u6587\u6863\u957f\u5ea6\u7684\u5f71\u54cd\u6700\u5927\uff1b\u5f53b=0<\/span>\u65f6\uff0c\u6587\u6863\u957f\u5ea6\u4e0d\u5f71\u54cd\u8bc4\u5206\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n

      BM25\u7b97\u6cd5\u4f18\u7f3a\u70b9<\/h1>\n

      \u4f18\u70b9<\/h2>\n
        \n
      • \u4e0e\u4f20\u7edf\u7684TF-IDF\u7b97\u6cd5\u76f8\u6bd4\uff0cBM25\u7b97\u6cd5\u53ef\u4ee5\u8003\u8651\u6587\u6863\u957f\u5ea6\uff0c\u6709\u6548\u907f\u514d\u6587\u6863\u957f\u5ea6\u7684\u5f71\u54cd\u3002<\/li>\n
      • BM25\u7b97\u6cd5\u7684\u5e38\u6570k_1<\/span>\u548cb<\/span>\u53ef\u4ee5\u6839\u636e\u4e0d\u540c\u9886\u57df\u7684\u6570\u636e\u8fdb\u884c\u8c03\u6574\uff0c\u4ee5\u5f97\u5230\u6700\u4f73\u6027\u80fd\u3002\u8fd9\u4e5f\u4f7f\u5f97BM25\u7b97\u6cd5\u80fd\u591f\u9002\u7528\u4e8e\u4e0d\u540c\u9886\u57df\u7684\u6570\u636e\u3002<\/li>\n<\/ul>\n

        \u7f3a\u70b9<\/h2>\n
          \n
        • \u5bf9\u6570\u636e\u8d28\u91cf\u8981\u6c42\u8f83\u9ad8\uff1aBM25\u7b97\u6cd5\u9700\u8981\u5e72\u51c0\u3001\u9ad8\u8d28\u91cf\u7684\u6570\u636e\uff0c\u56e0\u4e3a\u5b83\u9700\u8981\u51c6\u786e\u7684\u68c0\u6d4b\u67e5\u8be2\u9879\uff0c\u5e76\u8ba1\u7b97\u6587\u6863\u548c\u67e5\u8be2\u6761\u4ef6\u4e4b\u95f4\u7684\u5339\u914d\u7a0b\u5ea6\u3002<\/li>\n
        • BM25\u7b97\u6cd5\u6548\u679c\u53d7\u5230k_1<\/span>\u548cb<\/span>\u7684\u5f71\u54cd\u3002\u8fd9\u4e9b\u53c2\u6570\u5fc5\u987b\u7ecf\u8fc7\u8c03\u6574\u624d\u80fd\u83b7\u5f97\u6700\u4f73\u6027\u80fd\uff0c\u4f46\u662f\u8fd9\u4e5f\u610f\u5473\u7740BM25\u7b97\u6cd5\u5bf9\u53c2\u6570\u654f\u611f\u3002<\/li>\n<\/ul>\n

          \u793a\u4f8b\u4ee3\u7801<\/h1>\n
          import math\nfrom collections import Counter\n\nclass BM25:\n    def __init__(self,docs,k1=1.5,b=0.75):\n        """\n        BM\u7b97\u6cd5\u6784\u9020\u5668\n        :param docs:\u5206\u8bcd\u540e\u7684\u6587\u6863\u5217\u8868\uff0c\u6bcf\u4e00\u4e2a\u6587\u6863\u662f\u4e00\u4e2a\u5305\u542b\u8bcd\u6c47\u7684\u5217\u8868\n        :param k1:BM25\u7b97\u6cd5\u4e2d\u7684\u8c03\u8282\u53c2\u6570k1\n        :param b:BM25\u7b97\u6cd5\u4e2d\u7684\u8c03\u8282\u53c2\u6570b\n        """\n\n        self.docs = docs\n        self.k1 = k1\n        self.b = b\n        self.doc_len = [len(doc) for doc in docs] #\u8ba1\u7b97\u6bcf\u4e2a\u6587\u6863\u7684\u957f\u5ea6\n        self.avgdl=sum(self.doc_len)\/len(docs) #\u8ba1\u7b97\u6240\u6709\u6587\u6863\u7684\u5e73\u5747\u957f\u5ea6\n        self.doc_freqs=[] #\u5b58\u50a8\u6bcf\u4e2a\u6587\u6863\u7684\u8bcd\u9891\n        self.idf={} #\u5b58\u50a8\u6bcf\u4e2a\u8bcd\u7684\u9006\u6587\u6863\u9891\u7387\n        self.initialize()\n\n    def initialize(self):\n        """\n        \u521d\u59cb\u5316\u65b9\u6cd5\uff0c\u8ba1\u7b97\u6240\u6709\u8bcd\u7684\u9006\u6587\u6863\u9891\u7387\n        """\n        df = {} #\u7528\u4e8e\u5b58\u50a8\u6bcf\u4e2a\u8bcd\u5728\u4e0d\u540c\u6587\u6863\u4e2d\u51fa\u73b0\u7684\u9891\u7387\n\n        for doc in self.docs:\n            #\u4e3a\u6bcf\u4e2a\u6587\u6863\u521b\u5efa\u4e00\u4e2a\u8bcd\u9891\u7edf\u8ba1\n            self.doc_freqs.append(Counter(doc))\n            #\u66f4\u65b0df\u503c\n            for word in set(doc):\n                df[word] = df.get(word,0)+1\n        # \u8ba1\u7b97\u6bcf\u4e2a\u8bcd\u7684IDF\u503c\n        for word,freq in df.items():\n            self.idf[word] = math.log((len(self.docs) - freq + 0.5) \/ (freq + 0.5) + 1)\n\n    def score(self,doc,query):\n    """\n    \u8ba1\u7b97\u6587\u6863\u4e0e\u67e5\u8be2\u7684BM25\u5f97\u5206\n    :param doc: \u6587\u6863\u7684\u7d22\u5f15\n    :param query: \u67e5\u8be2\u8bcd\u5217\u8868\n    :return: \u8be5\u6587\u6863\u4e0e\u67e5\u8be2\u7684\u76f8\u5173\u6027\u5f97\u5206\n    """\n    score=0,0\n\n    for word in query:\n        if word in self.doc_freqs[doc]:\n            freq=self.doc_freqs[doc][word] #\u8bcd\u5728\u6587\u6863\u4e2d\u7684\u9891\u7387\n            # \u5e94\u7528BM25\u8ba1\u7b97\u516c\u5f0f\n            score += (self.idf[word] * freq * (self.k1 + 1)) \/ (freq + self.k1 * (1 - self.b + self.b * self.doc_len[doc] \/ self.avgdl))\n    return score\n\n# \u793a\u4f8b\u6587\u6863\u96c6\u548c\u67e5\u8be2\ndocs = [["the", "quick", "brown", "fox"],\n        ["the", "lazy", "dog"],\n        ["the", "quick", "dog"],\n        ["the", "quick", "brown", "brown", "fox"]]\nquery = ["quick", "brown"]\n\n# \u521d\u59cb\u5316BM25\u6a21\u578b\u5e76\u8ba1\u7b97\u5f97\u5206\nbm25 = BM25(docs)\nscores = [bm25.score(i, query) for i in range(len(docs))]\n\n## query\u548c\u6587\u6863\u7684\u76f8\u5173\u6027\u5f97\u5206\uff1a\n## sores = [1.0192447810666774, 0.0, 0.3919504878447609, 1.2045355839511414]\n<\/code><\/pre>\n","protected":false},"excerpt":{"rendered":"
          \u7b80\u4ecb BM25\u662f\u4e00\u79cd\u7528\u4e8e\u4fe1\u606f\u68c0\u7d22\u7684\u7b97\u6cd5\uff0c\u53ef\u4ee5\u7528\u4e8e\u8861\u91cf\u6587\u6863\u7684\u76f8\u5173\u6027\u3002\u8be5\u7b97\u6cd5\u6700\u65e9\u7531Robertson\u7b49\u4eba\u4e8e1995\u5e74\u63d0\u51fa\uff0c\u662f\u57fa\u4e8eOka …<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[45,2],"tags":[],"class_list":["post-698","post","type-post","status-publish","format-standard","hentry","category-llms","category-algorithm_learning"],"_links":{"self":[{"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/posts\/698","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/comments?post=698"}],"version-history":[{"count":4,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/posts\/698\/revisions"}],"predecessor-version":[{"id":704,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/posts\/698\/revisions\/704"}],"wp:attachment":[{"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/media?parent=698"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/categories?post=698"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lingbo.online\/index.php\/wp-json\/wp\/v2\/tags?post=698"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}