  With increasing availability of high dimensional, multi-source data, the
identification of joint and data specific patterns of variability has become a
subject of interest in many research areas. Several matrix decomposition
methods have been formulated for this purpose, for example JIVE (Joint and
Individual Variation Explained), and its angle based variation, aJIVE. Although
the effect of data contamination on the estimated joint and individual
components has not been considered in the literature, gross errors and outliers
in the data can cause instability in such methods, and lead to incorrect
estimation of joint and individual variance components. We focus on the aJIVE
factorization method and provide a thorough analysis of the effect outliers on
the resulting variation decomposition. After showing that such effect is not
negligible when all data-sources are contaminated, we propose a robust
extension of aJIVE (RaJIVE) that integrates a robust formulation of the
singular value decomposition into the aJIVE approach. The proposed RaJIVE is
shown to provide correct decompositions even in the presence of outliers and
improves the performance of aJIVE. We use extensive simulation studies with
different levels of data contamination to compare the two methods. Finally, we
describe an application of RaJIVE to a multi-omics breast cancer dataset from
The Cancer Genome Atlas. We provide the R package RaJIVE with a ready-to-use
implementation of the methods and documentation of code and examples.
