User Clustering for Pairwise Comparison with Missing Values Using Bradley-Terry Model and Consensus Clustering

As a method of evaluating user preferences for items such as products and designs, the pairwise comparison method, where the user chooses which of two items is preferable, is often employed. Since the preference for items varies among users, clustering methods such as k-means can be applied to capture these tendencies. However, as the number of items increases, the number of comparisons also increases. Therefore, missing values occur when users do not answer due to fatigue, or when experimenters reduce the number of comparisons in advance. The net-win vector, which counts the number of wins for each item against others, has robustness for clustering with missing values. In this paper, we propose a multiple imputation method for clustering pairwise comparison data. Our approach combines the net-win vector with missing-value imputation using the Bradley-Terry model and consensus clustering to integrate multiple clustering results. Furthermore, we attempt to improve performance by iteration between missing value imputation and clustering. The effectiveness of the proposed method is demonstrated through synthetic and benchmark problems.