Jointly Modeling and Clustering Tensors in High Dimensions

Biao Cai, Jingfei Zhang*, Will Wei Sun

*Corresponding author for this work

    Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

    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. © 2024 INFORMS
    Original languageEnglish
    Pages (from-to)1320-1335
    JournalOperations Research
    Volume73
    Issue number3
    Online published27 Dec 2024
    DOIs
    Publication statusPublished - May 2025

    Research Keywords

    • expectation conditional maximization
    • computational and statistical errors
    • tensor clustering
    • tensor decomposition
    • unsupervised learning

    Fingerprint

    Dive into the research topics of 'Jointly Modeling and Clustering Tensors in High Dimensions'. Together they form a unique fingerprint.

    Cite this