Model-Based Clustering of Inhomogeneous Paired Comparison Data

This paper demonstrates the derivation of a clustering model for paired comparison data. Similarities for non-Euclidean, ordinal data are handled in the model such that it is capable of performing an integrated analysis on real-world data with different patterns of missings. Rank-based pairwise comparison matrices with missing entries can be described and compared by means of a probabilistic mixture model defined on the symmetric group. Our EM-method offers two advantages compared to models for pairwise comparison rank data available in the literature: (i) it identifies groups in the pairwise choices based on similarity (ii) it provides the ability to analyze a data set of heterogeneous character w.r.t. to the structural properties of individal data samples. Furthermore, we devise an active learning strategy for selecting paired comparisons that are highly informative to extract the underlying ranking of the objects. The model can be employed to predict pairwise choice probabilities for individuals and, therefore, it can be used for preference modeling.