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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.

Identification of homogeneous subgroups of subjects plays a key role in the study of precision medicine. While there are a number of approaches based on the clustering of low-level features such as behavioral variables, work that makes use of fully multivariate nature of medical imaging data is very limited. Given that the individual variability in brain functional networks obtained from functional magnetic resonance imaging (fMRI) data is noted as being both significant and consistent like fingerprints, its use provides a particularly appealing approach to this challenging problem. We present a completely data-driven approach, subgroup identification using independent vector analysis (SI-IVA), which leverages the desirable properties of IVA to uncover the relationship across subjects along with the discovery of subgroup structures revealed by Gershgorin disc theorem. We show that SI-IVA outperforms an eigenanalysisbased approach by simulations. We then apply the method to real fMRI data obtained from patients of during resting state to identify group differences in multiple relevant brain regions including primary somatosensory and motor cortex, which demonstrates that SI-IVA provides interpretable and meaningful results.

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