Jointly Modeling and Clustering Tensors in High Dimensions

Biao Cai (), Jingfei Zhang () and Will Wei Sun ()
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Biao Cai: Department of Management Sciences, City University of Hong Kong, Hong Kong, China
Jingfei Zhang: Goizueta Business School, Emory University, Atlanta, Georgia 30322
Will Wei Sun: Daniels School of Business, Purdue University, West Lafayette, Indiana 47907

Operations Research, 2025, vol. 73, issue 3, 1320-1335

Abstract: We consider the problem of jointly modeling and clustering populations of tensors by introducing a high-dimensional tensor mixture model with heterogeneous covariances. To effectively tackle the high dimensionality of tensor objects, we employ plausible dimension reduction assumptions that exploit the intrinsic structures of tensors, such as low rankness in the mean and separability in the covariance. In estimation, we develop an efficient high-dimensional expectation conditional maximization ( HECM ) algorithm that breaks the intractable optimization in the M step into a sequence of much simpler conditional optimization problems, each of which is convex, admits regularization, and has closed-form updating formulas. Our theoretical analysis is challenged by both the nonconvexity in the expectation maximization-type estimation and having access to only the solutions of conditional maximizations in the M step, leading to the notion of dual nonconvexity. We demonstrate that the proposed HECM algorithm, with an appropriate initialization, converges geometrically to a neighborhood that is within statistical precision of the true parameter. The efficacy of our proposed method is demonstrated through comparative numerical experiments and an application to a medical study, where our proposal achieves an improved clustering accuracy over existing benchmarking methods.

Keywords: Machine Learning and Data Science; expectation conditional maximization; computational and statistical errors; tensor clustering; tensor decomposition; unsupervised learning (search for similar items in EconPapers)
Date: 2025
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