Sparse outlier-robust PCA for multi-source data

Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring joint analysis-arise across many scientific areas. We introduce a novel PCA methodology that simultaneously (i) selects important features, (ii) allows for the detection of global sparse patterns across multiple data sources as well as local source-specific patterns, and (iii) is resistant to outliers. To this end, we develop a regularization problem with a penalty that accommodates global-local structured sparsity patterns, and where the ssMRCD estimator is used as plug-in to permit joint outlier-robust analysis across multiple data sources. We provide an efficient implementation of our proposal via the Alternating Direction Method of Multiplier and illustrate its practical advantages in simulation and in applications.