广告系统中weak-and算法原理及编码验证

wand(weak and)算法基本思路

　　一般搜索的query比较短，但如果query比较长，如是一段文本，需要搜索相似的文本，这时候一般就需要wand算法，该算法在广告系统中有比较成熟的应

该，主要是adsense场景，需要搜索一个页面内容的相似广告。

　 　Wand方法简单来说，一般我们在计算文本相关性的时候，会通过倒排索引的方式进行查询，通过倒排索引已经要比全量遍历节约大量时间，但是有时候仍

然很慢。

　 　原因是很多时候我们其实只是想要top n个结果，一些结果明显较差的也进行了复杂的相关性计算，而weak-and算法通过计算每个词的贡献上限来估计文档

的相关性上限，从而建立一个阈值对倒排中的结果进行减枝，从而得到提速的效果。

　　 wand算法首先要估计每个词对相关性贡献的上限，最简单的相关性就是TF*IDF，一般query中词的TF均为1，IDF是固定的，因此就是估计一个词在文档中的

词频TF上限，一般TF需要归一化，即除以文档所有词的个数，因此，就是要估算一个词在文档中所能占到的最大比例，这个线下计算即可。

　 　知道了一个词的相关性上界值，就可以知道一个query和一个文档的相关性上限值，显然就是他们共同的词的相关性上限值的和。

　 　这样对于一个query，获得其所有词的相关性贡献上限，然后对一个文档，看其和query中都出现的词，然后求这些词的贡献和即可，然后和一个预设值比

较，如果超过预设值，则进入下一步的计算，否则则丢弃。

　　如果按照这样的方法计算n个最相似文档，就要取出所有的文档，每个文档作预计算，比较threshold，然后决定是否在top-n之列。这样计算当然可行，但

是还是可以优化的。

wand(weak and)算法原理演示

代码实现了主要的算法逻辑以验证算法的有效性，供大家参考，该实现优化了原始算法的一些逻辑尽量减少了无谓的循环：

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www.169it.com #!/usr/bin/python #wangben updated 20130108 class WAND:     '''implement wand algorithm'''     def __init__(self, InvertIndex, last_docid):         self.invert_index = InvertIndex #InvertIndex: term -> docid1, docid2, docid3 ...         self.current_doc = 0         self.current_invert_index = {}         self.query_terms = []         self.threshold = 2         self.sort_terms = []         self.LastID = 2000000000 #big num         self.debug_count = 0         self.last_docid = last_docid     def __InitQuery(self, query_terms):         '''check terms len > 0'''         self.current_doc = -1         self.current_invert_index.clear()         self.query_terms = query_terms         self.sort_terms[:] = []         self.debug_count = 0         for term in query_terms:             #initial start pos from the first position of term's invert_index             self.current_invert_index[term] = [ self.invert_index[term][0], 0 ] #[ docid, index ]                                                                                          def __SortTerms(self):         if len(self.sort_terms) == 0:             for term in self.query_terms:                 if term in self.current_invert_index:                     doc_id = self.current_invert_index[term][0]                     self.sort_terms.append([ int(doc_id), term ])         self.sort_terms.sort()                                                                                                  def __PickTerm(self, pivot_index):         return 0     def __FindPivotTerm(self):         score = 0         for i in range(0, len(self.sort_terms)):             score += 1             if score >= self.threshold:                 return [ self.sort_terms[i][1], i]         return [ None, len(self.sort_terms) ]     def __IteratorInvertIndex(self, change_term, docid, pos):         '''move to doc id > docid'''         doc_list = self.invert_index[change_term]         i = 0         for i in range(pos, len(doc_list)):             if doc_list[i] >= docid:                 pos = i                 docid = doc_list[i]                 break         return [ docid, pos ]     def __AdvanceTerm(self, change_index, docid ):         change_term = self.sort_terms[change_index][1]         pos = self.current_invert_index[change_term][1]         (new_doc, new_pos) = \             self.__IteratorInvertIndex(change_term, docid, pos)                                                                                                  self.current_invert_index[change_term] = \             [ new_doc , new_pos ]         self.sort_terms[change_index][0] = new_doc                                                                                                                                                                                       def __Next(self):         if self.last_docid == self.current_doc:             return None                                                                                                      while True:             self.debug_count += 1             #sort terms by doc id             self.__SortTerms()                                                                                                          #find pivot term > threshold             (pivot_term, pivot_index) = self.__FindPivotTerm()             if pivot_term == None:                 #no more candidate                 return None                                                                                                          #debug_info:             for i in range(0, pivot_index + 1):                 print self.sort_terms[i][0],self.sort_terms[i][1],"|",             print ""                                                                                                              pivot_doc_id = self.current_invert_index[pivot_term][0]             if pivot_doc_id == self.LastID: #!!                 return None             if pivot_doc_id <= self.current_doc:                 change_index = self.__PickTerm(pivot_index)                 self.__AdvanceTerm( change_index, self.current_doc + 1 )             else:                 first_docid = self.sort_terms[0][0]                 if pivot_doc_id == first_docid:                     self.current_doc = pivot_doc_id                     return self.current_doc                 else:                     #pick all preceding term                     for i in range(0, pivot_index):                         change_index = i                         self.__AdvanceTerm( change_index, pivot_doc_id )                                                                                          def DoQuery(self, query_terms):         self.__InitQuery(query_terms)                                                                                                  while True:             candidate_docid = self.__Next()             if candidate_docid == None:                 break             print "candidate_docid:",candidate_docid             #insert candidate_docid to heap             #update threshold         print "debug_count:",self.debug_count                                                                                          if __name__ == "__main__":     testIndex = {}     testIndex["t1"] = [ 0, 1, 2, 3, 6 , 2000000000]     testIndex["t2"] = [ 3, 4, 5, 6, 2000000000 ]     testIndex["t3"] = [ 2, 5, 2000000000 ]     testIndex["t4"] = [ 4, 6, 2000000000 ]     w = WAND(testIndex, 6)     w.DoQuery(["t1", "t2", "t3", "t4"])

输出结果中会展示next中循环的次数，以及最后被选为candidate的docid。  这里省略了建立堆的过程，使用了一个默认阈值2作为doc的删选条件，候选doc和query doc采用重复词的个数计算UB，这里只是一个算法演示，实际使用的时候需要根据自己的相关性公式进行调整

本文来源:广告系统中weak-and算法原理及编码验证