Consecutive Independence and Correlation Transform for Multimodal Data Fusion: Discovery of One-to-Many Associations in Structural and Functional Imaging Data

Brain signals can be measured using multiple imaging modalities, such as magnetic resonance imaging (MRI)-based techniques. Different modalities convey distinct yet complementary information; thus, their joint analyses can provide valuable insight into how the brain functions in both healthy and diseased conditions. Data-driven approaches have proven most useful for multimodal fusion as they minimize assumptions imposed on the data, and there are a number of methods that have been developed to uncover relationships across modalities. However, none of these methods, to the best of our knowledge, can discover "one-to-many associations", meaning one component from one modality is linked with more than one component from another modality. However, such "one-to-many associations" are likely to exist, since the same brain region can be involved in multiple neurological processes. Additionally, most existing data fusion methods require the signal subspace order to be identical for all modalities-a severe restriction for real-world data of different modalities. Here, we propose a new fusion technique-the consecutive independence and correlation transform (C-ICT) model-which successively performs independent component analysis and independent vector analysis and is uniquely flexible in terms of the number of datasets, signal subspace order, and the opportunity to find "one-to-many associations". We apply C-ICT to fuse diffusion MRI, structural MRI, and functional MRI datasets collected from healthy controls (HCs) and patients with schizophrenia (SZs). We identify six interpretable triplets of components, each of which consists of three associated components from the three modalities. Besides, components from these triplets that show significant group differences between the HCs and SZs are identified, which could be seen as putative biomarkers in schizophrenia.