Clustering permutations by Exponential Blurring Mean-Shift algorithm

Suppose that a sample of people independently examine a fixed set of k items and then rank these items according to personal judgment. Whatever the nature of these items, each person produces a ranking. This paper aims at clustering people into different groups according to their preferences. We propose the exponential blurring mean-shift (EBMS) algorithm which shifts the rankings to new locations obtained by a locally weighted combination of all the data. The number of clusters does not need to be specified in advance and outliers can be detected. Our experiments show that the EBMS algorithm can be succesfully applied in clustering the ranking data. The algorithm generalizes to partial orderings when only the top-t ranks are observed.