A Penalized Wishart Mixture Model for Clustering Covariance Matrices

A Penalized Wishart Mixture Model for Clustering Covariance Matrices 

Andrea Cappozzo, Cattolica University Milan. 

16th of September 2025

Abstract: 

Covariance matrices capture linear relationships among variables and are fundamental in fields such as finance, genomics, and neuroscience. In brain imaging, for instance, they reveal functional connectivity between regions, offering valuable insights into neural dynamics. This talk introduces a model-based approach for clustering high-dimensional sample covariance matrices. Traditional methods, such as Wishart mixture models, face significant scalability issues due to the quadratic growth in the number of parameters with increasing dimensionality. To address this, we propose a sparse Wishart mixture model that incorporates cluster-specific sparsity in the scale matrices. Estimation is performed via penalized likelihood, using a graphical lasso penalty within a customized EM algorithm. This regularization enhances both interpretability and computational efficiency by shrinking weak or spurious associations toward zero, thereby emphasizing the most salient variable interactions within each cluster. We demonstrate the effectiveness of our method on functional magnetic resonance imaging (fMRI) data. The model successfully clusters individuals based on their functional brain connectivity, uncovering meaningful patterns of neural interaction and providing insights into potential neurological differences. The imposed sparsity also facilitates clearer visualization and interpretation of connectivity structures within and across clusters.  This is joint work with Alessandro Casa.