2025/08/05 by Zaccaria, Giorgia, Benzakour, Lorenzo, García-Escudero, Luis A. +2 · 1 citation
#FOS: Computer and information sciences #Methodology (stat.ME)
paper · doi:10.48550/arxiv.2508.03310
In a data matrix, it can be distinguished between observations, each represented by a full row vector for an individual, and cells, which correspond to single entries of that matrix. Recent developments in robust statistics have introduced the cellwise contamination paradigm, which assumes contamination on cells rather than on entire observations. This approach becomes particularly relevant as the number of variables increases. Indeed, discarding or downweighting entire observations because of a few anomalous values in them, as done by traditional (casewise) robust methods, can result in substantial information loss, since the non-contaminated (or reliable) cells can still be highly informative. This philosophy can also be considered in fuzzy clustering, by assuming that reliable cells within an observation may still provide useful information for determining fuzzy memberships. A robust fuzzy clustering proposal is thus introduced in this work, combining the advantages of dealing with outlying cells and simultaneously controlling the degrees of fuzziness of observation assignments. The cluster-specific relationships among variables, detected by the fuzzy clustering approach, are also key to better identifying outlying cells. The strengths of the proposed methodology are illustrated through a simulation study and two real-world applications. The effects of the model's tuning parameters are explored, and some guidance for users on how to set them suitably is provided.