Cell-TRICC: A Model-Based Approach to Cellwise-Trimmed Co-Clustering

Co-clustering consists of simultaneously partitioning the rows and columns of a data matrix. It is an unsupervised technique well suited to explore and extract patterns from high-dimensional data. It is often the case that real data contain outliers: such anomalous values could impair standard statistical methods, while being interesting pieces of information. Despite this fact and the wide applicability of co-clustering, very little literature is concerned with outlier-robust co-clustering approaches. Building on the well-known framework of Latent Block Models, we propose a novel co-clustering method that can deal with cellwise contaminated matrices. We focus on count data modeled by Poisson distributions, but the main ideas are general. Robustness is sought through cellwise trimming, implemented as an additional step in a stochastic EM-like algorithm. Model selection is performed by using novel Bayesian criteria to select the number of groups and the trimming level simultaneously. Finally, our approach is tested and compared to existing methods through extensive simulations, and showcased on a fully fledged application to a trade monitoring problem. The real-data analysis shows the potential of the proposed methodology both as a data exploration and anomaly detection tool, and is further enriched by insights drawn from original visualizations and diagnostic plots.