Finding outlying items in sets of partial rankings

Abstract

Partial rankings are totally ordered subsets of a set of items. For example, the sequence in which a user browses through different parts of a website is a partial ranking. We consider the following problem. Given a set D of partial rankings, find items that have strongly different status in different parts of D. To do this, we first compute a clustering of D and then look at items whose average rank in the cluster substantially deviates from its average rank in D. Such items can be seen as those that contribute the most to the differences between the clusters. To test the statistical significance of the found items, we propose a method that is based on a MCMC algorithm for sampling random sets of partial rankings with exactly the same statistics as D. We also demonstrate the method on movie rankings and gene expression data. © Springer-Verlag Berlin Heidelberg 2007.