Jointly Modeling and Clustering Tensors in High Dimensions

Tackling High-Dimensional Tensor Clustering In the paper “Jointly Modeling and Clustering Tensors in High Dimensions,” Cai, Zhang, and Sun address the challenge of jointly modeling and clustering tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. The proposed mixture model exploits the intrinsic structures of tensor data. The authors develop a computationally efficient high-dimensional expectation conditional maximization (HECM) algorithm and show that the HECM iterates, with an appropriate initialization, converge geometrically to a neighborhood that is within statistical precision of the true parameter. The theoretical analysis is nontrivial because of the dual nonconvexity arising from both the expectation maximization-type estimation and the nonconvex objective function in the M step. They also study the convergence rate of the algorithm when the number of clusters is overspecified and when the signal-to-noise ratio diminishes with sample size. The efficacy of the proposed method is demonstrated through numerical experiments and a real-world medical data application.