MacroPARAFAC for handling rowwise and cellwise outliers in incomplete multiway data

Multiway data extend two-way matrices into higher-dimensional tensors, often explored through dimensional reduction techniques. In this paper, we study the Parallel Factor Analysis (PARAFAC) model for handling multiway data, representing it more compactly through a concise set of loading matrices and scores. We assume that the data may be incomplete and could contain both rowwise and cellwise outliers, signifying cases that deviate from the majority and outlying cells dispersed throughout the data array. To address these challenges, we present a novel algorithm designed to robustly estimate both loadings and scores. Additionally, we introduce an enhanced outlier map to distinguish various patterns of outlying behavior. Through simulations and the analysis of fluorescence Excitation-Emission Matrix (EEM) data, we demonstrate the robustness of our approach. Our results underscore the effectiveness of diagnostic tools in identifying and interpreting unusual patterns within the data. •A new robust PARAFAC method is proposed.•Simulations show its robustness and efficiency compared to other approaches.•The enhanced outlier map displays various patterns of outlying behavior.•An extensive analysis of the Dorrit EEM data is performed.