Joint matrix decompositions are widely used to extract useful features from multiple datasets. Multiset Canonical Correlation Analysis (mCCA) is one of the oldest and most established methods among those. Prior work claimed that Independent Vector Analysis (IVA), an extension of Independent Component Analysis (ICA) to multiple datasets, generalizes mCCA and that, under the assumption of orthogonality, the objective function of IVA with a Gaussian model (IVA-G) coincides with that of mCCA using the genvar criterion. We revisit this connection and demonstrate that the main difference between these methods is in fact not orthogonality but deflation, which is inherent to most mCCA objective functions, including genvar. To show this, we introduce orthogonal IVA-G (o-IVA-G) and deflationary orthogonal IVA-G (d-o-IVA-G) and compare them with IVA-G and mCCA-genvar in simulations inspired by the functional Magnetic Resonance Imaging (fMRI) subgroup identification problem. Our results suggest that the all-at-once methods can successfully perform Joint Blind Source Separation (JBSS) in more difficult scenarios and are more statistically efficient than deflationary methods.
Lehmann et al. (Fri,) studied this question.