We propose a novel regularized mixture model for clustering matrix-valued data. The proposed method assumes a separable covariance structure for each cluster and imposes a sparsity structure (e.g., low rankness, spatial sparsity) for the mean signal of each cluster. We formulate the problem as a finite mixture model of matrix-normal distributions with regularization terms, and then develop an EM-type of algorithm for efficient computation. In theory, we show that the proposed estimators are strongly consistent for various choices of penalty functions. Simulation and two applications on brain signal studies confirm the excellent performance of the proposed method including a better prediction accuracy than the competitors and the scientific interpretability of the solution.
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The authors thank the editor, the associate editor and two referees for their constructive and helpful comments on the earlier version of this paper. Shen’s research was partially supported by the Simons Foundation Award 512620 and the NSF Grant DMS 1509023. Hu’s eﬀort was partially supported by the National Institute of Health Grants R01AI143886, R01CA219896,and CCSG P30 CA013696. Fortin’s research was supported by NIH grant R01-MH115697,NSF awards IOS-1150292 and BCS-1439267, and Whitehall Foundation award 2010-05-84.Frostig’s research was partially supported by the Leducq Foundation.