Parsimonious Clustering of Covariance Matrices

Functional connectivity (FC) derived from functional magnetic resonance imaging (fMRI) data offers vital insights for understanding brain function and neurological and psychiatric disorders. Unsupervised clustering methods are desired to group individuals based on shared features, facilitating clinical diagnosis. In this study, a parsimonious clustering model is proposed, which integrates the Mixture-of-Experts (MoE) and covariance regression framework, to cluster individuals based on FC captured by data covariance matrices in resting-state fMRI studies. The model assumes common linear projections across covariance matrices and a generalized linear model with covariates, allowing for flexible yet interpretable projection-specific clustering solutions. To evaluate the performance of the proposed framework, extensive simulation studies are conducted to assess clustering accuracy and robustness. The approach is applied to resting-state fMRI data from the Alzheimer's Disease Neuroimaging Initiative (ADNI). Subgroups are identified based on brain coherence and simultaneously uncover the association with demographic factors and cognitive functions.