Complete Model Identification Using Independent Vector Analysis: Application to the Fusion of Task FMRI Data

Linear latent variable models have proven effective for data fusion using joint decomposition of multiple matrices. Identification of the dependence structure of the latent variables—components—across multiple datasets is key to this success as this helps explain the underlying relationship across the datasets, and allows the design of a joint decomposition model that best fits the properties of the problem. However, identification of the complete dependence structure across more than two datasets is a difficult problem due to large number of possible dependence scenarios. In this paper, we address this problem, i.e., the estimation of not only the number of components that are dependent across N ≥ 2 datasets but also their complete dependence structure, i.e., the index of datasets across which they are dependent. The method, complete model identification using IVA (CMI-IVA), builds on the well-structured formulation of independent vector analysis (IVA), which generalizes multiset canonical correlation analysis, and provides a key step in facilitating this difficult problem. Properties of CMI-IVA are established and its performance is first verified using simulations. We then apply the method to real functional magnetic resonance (fMRI) data and demonstrate that CMI-IVA provides meaningful interpretation of the data in terms of number of components dependent across datasets and the associated components.