Large-Scale Independent Vector Analysis (IVA-G) via Coresets

Abstract

Joint blind source separation (JBSS) involves the factorization of multiple matrices, i.e. “datasets”, into “sources” that are statistically dependent across datasets and independent within datasets. Despite this usefulness for analyzing multiple datasets, JBSS methods suffer from considerable computational costs and are typically intractable for hundreds or thousands of datasets. To address this issue, we present a methodology for how a subset of the datasets can be used to perform efficient JBSS over the full set. We motivate two such methods: a numerical extension of independent vector analysis (IVA) with the multivariate Gaussian model (IVA-G), and a recently proposed analytic method resembling generalized joint diagonalization (GJD). We derive nonidentifiability conditions for both methods, and then demonstrate how one can significantly improve these methods’ generalizability by an efficient representative subset selection method. This involves selecting a coreset (a weighted subset) that minimizes a measure of discrepancy between the statistics of the coreset and the full set. Using simulated and real functional magnetic resonance imaging (fMRI) data, we demonstrate significant scalability and source separation advantages of our “coreIVA-G” method vs. other JBSS methods.