aNy-way ICA and its application to estimate cortico-thalamo-cerebellar functional links in schizophrenia.

Multimodal data collected by international and national biobanking efforts have distinct scales and model orders and provide unique and complementary insights into disease mechanisms. We propose a novel, flexible and efficient data fusion approach-aNy-way independent component analysis (aNy-way ICA). aNy-way ICA fuses N-way multimodal or multidomain data by optimizing the entire loading correlation structure of linked components via Gaussian independent vector analysis (IVA-G) and simultaneously optimizing independence via separate ICAs. This allows for distinct model orders for different modalities/domains and multiple linked sources detection across any number of modalities or domains without requiring orthogonality constraints on sources. Simulation results demonstrate that aNy-way ICA identifies the designed sources and loadings, as well as the true covariance patterns, with improved accuracy compared to other approaches, especially under noisy conditions. Applying aNy-way ICA to fuse 4D multi-domain fMRI data in schizophrenia, we identified a cortico-thalamo-cerebellar circuit, highlighting the functional linkages among higher order thalamic nuclei, the visual cortex, default mode network, and the posterior lobe of cerebellum. Their function links were replicated in two independent datasets. The connection among higher order thalamic nuclei, the visual cortex, and default mode network discriminates schizophrenia from controls and this aberrant connection is related to multiple cognitive deficits in both discovery and replication datasets, indicating the identified cortico-thalamo-cerebellar circuit may underlie "cognitive dysmetria" in schizophrenia.