一种新的加权Spearman步距
A New Weighted Spearman's Footrule as A Measure of Distance between Rankings
摘要：
许多应用激发了排名之间的距离度量，例如比较前k列表和排名聚合以进行投票，并引起了研究人员的极大兴趣。例如，对于搜索引擎，使用不同的排名算法可以返回不同的排名列表。排名算法的效果可以通过计算其返回的结果排名与人们期望的适当排名之间的距离（相似度）来估计。人们可能只对结果排名的前几个项目感兴趣，因此用于测量距离的度量应该强调位置较高的项目。此外，在极端情况下，如果结果排名是预期排名的总逆，则认为它是具有最大距离的最差排名。因此，需要一个度量，它可以满足这两个直觉。为了解决这个问题，我们提出了一个加权度量的基础上经典斯皮尔曼的foottrule度量来衡量两个排列的n个对象之间的距离。该度量可以应用于秩聚集问题的多项式时间算法，并产生2-近似采用加权肯德尔的tau距离由Farnoud等人提出的。
英文摘要：
Many applications motivate the distance measure between rankings, such as comparing top-k lists and rank aggregation for voting, and intrigue great interest to researchers. For example, for a search engine, the use of different ranking algorithms may return different ranking lists. The effect of a ranking algorithm can be estimated by computing the distance (similarity) between the result ranking it returns and the appropriate ranking people expect. People may be interested in only the first few items of result ranking, therefore the metric for measuring the distance should emphasize on the items in higher positions. Besides, in an extreme case, if a result ranking is the total reverse of the expected ranking, then it is considered to be the worst ranking with the maximum distance. Therefore, a metric is called for, which can satisfy both of the two intuitions. To address this problem, we present a weighted metric based on the classical Spearman's footrule metric to measure the distance between two permutations of n objects. This metric can be applied in rank aggregation problem with a polynomial time algorithm, and produces a 2-approximation for adopting the weighted Kendall's tau distance proposed by Farnoud et al.
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