Sparse outlier-robust PCA for multi-source data

Abstract

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 data set whereas multi-source data—i.e. multiple related data sets requiring joint analysis—arise across many scientific areas. We introduce a novel PCAmethodologythatsimultaneously(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 an outlier-robust covariance estimator, namely the ssMRCD, is used as plug-in to permit joint, robust analysis across multiple data sources. We provide an efficient implementation of our proposal via the alternating direction method of multipliers and illustrate its practical advantages in simulations and in applications.