Abstract
Covariance matrices capture complex interactions between variables, but traditional clustering methods often overlook this information, focusing primarily on mean levels. Recently, model-based approaches using Wishart mixture models have been explored to cluster covariance matrices directly. However, these models struggle in large-dimensional settings, as the number of parameters grows quadratically with the number of variables. To overcome this, we propose a sparse Wishart mixture model with cluster-specific sparsity in the component scale matrices. Estimation is performed via penalized maximum likelihood, applying a covariance graphical lasso penalty to shrink small coefficients to zero. This reduces overfitting, improves interpretability, and emphasizes the most relevant relationships between variables. We validate our method on real neuroimaging data, clustering subjects based on brain region connectivity patterns.