Data fusion—the joint analysis of multiple datasets—through coupled factorizations has the promise to enable enhanced knowledge discovery, and hence is an active area. Various formulations of coupled matrix factorizations have been proposed, each with its own modeling assumptions. In this paper, we study two such methods, namely Independent Vector Analysis (IVA), i.e., extension of Independent Component Analysis (ICA) to multiple datasets, and PARAFAC2, a tensor factorization approach. We

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... trate the modeling assumptions of IVA and PARAFAC2 using simulations, revealing that both methods can accurately capture the latent components, albeit with certain differences in capturing the corresponding subject scores. By making use of a rich multi-task functional Magnetic Resonance Imaging (fMRI) dataset, we show how the two methods can be used for achieving two important goals at once, namely capturing group differences between patients with schizophrenia and healthy controls with interpretable components, as well as understanding the relationship across multiple tasks. This is achieved through the definition of source component vectors across datasets.