Data-driven methods have been very attractive for fusion of both multiset and multimodal data, in particular using matrix factorizations based on independent component analysis (ICA) and its extension to multiple datasets, independent vector analysis (IVA). This is primarily due to the fact that independence enables (essentially) unique decompositions under very general conditions and for a large class of signals, and independent components lend themselves to easier interpretation. In this paper, we first present a framework that provides a common umbrella to previously introduced fusion methods based on ICA and IVA, and allows us to clearly demonstrate the tradeoffs involved in the design of these approaches. This then motivates the introduction of a new approach for fusion, that of disjoint subspaces (DS). We demonstrate the desired performance of DS using ICA through simulations as well as application to real data, for fusion of multi-modal medical imaging data-functional magnetic resonance imaging (fMRI),and electroencephalography (EEG) data collected from a group of healthy controls and patients with schizophrenia performing an auditory oddball task.
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