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Multi-way data extend two-way matrices into higher-dimensional tensors, oftenexplored through dimensional reduction techniques. In this paper, we study theParallel Factor Analysis (PARAFAC) model for handling multi-way data,representing it more compactly through a concise set of loading matrices andscores. We assume that the data may be incomplete and could contain bothrowwise and cellwise outliers, signifying cases that deviate from the majorityand outlying cells dispersed throughout the data array. To address thesechallenges, we present a novel algorithm designed to robustly estimate bothloadings and scores. Additionally, we introduce an enhanced outlier map todistinguish various patterns of outlying behavior. Through simulations and theanalysis of fluorescence Excitation-Emission Matrix (EEM) data, we demonstratethe robustness of our approach. Our results underscore the effectiveness ofdiagnostic tools in identifying and interpreting unusual patterns within thedata.

MacroPARAFAC for handling rowwise and cellwise outliers in incomplete multi-way data