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With increasing availability of high dimensional, multi-source data, theidentification of joint and data specific patterns of variability has become asubject of interest in many research areas. Several matrix decompositionmethods have been formulated for this purpose, for example JIVE (Joint andIndividual Variation Explained), and its angle based variation, aJIVE. Althoughthe effect of data contamination on the estimated joint and individualcomponents has not been considered in the literature, gross errors and outliersin the data can cause instability in such methods, and lead to incorrectestimation of joint and individual variance components. We focus on the aJIVEfactorization method and provide a thorough analysis of the effect outliers onthe resulting variation decomposition. After showing that such effect is notnegligible when all data-sources are contaminated, we propose a robustextension of aJIVE (RaJIVE) that integrates a robust formulation of thesingular value decomposition into the aJIVE approach. The proposed RaJIVE isshown to provide correct decompositions even in the presence of outliers andimproves the performance of aJIVE. We use extensive simulation studies withdifferent levels of data contamination to compare the two methods. Finally, wedescribe an application of RaJIVE to a multi-omics breast cancer dataset fromThe Cancer Genome Atlas. We provide the R package RaJIVE with a ready-to-useimplementation of the methods and documentation of code and examples.

RaJIVE: Robust Angle Based JIVE for Integrating Noisy Multi-Source Data