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Dynamic Tensor Clustering

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  • Will Wei Sun
  • Lexin Li

Abstract

Dynamic tensor data are becoming prevalent in numerous applications. Existing tensor clustering methods either fail to account for the dynamic nature of the data, or are inapplicable to a general-order tensor. There is also a gap between statistical guarantee and computational efficiency for existing tensor clustering solutions. In this article, we propose a new dynamic tensor clustering method that works for a general-order dynamic tensor, and enjoys both strong statistical guarantee and high computational efficiency. Our proposal is based on a new structured tensor factorization that encourages both sparsity and smoothness in parameters along the specified tensor modes. Computationally, we develop a highly efficient optimization algorithm that benefits from substantial dimension reduction. Theoretically, we first establish a nonasymptotic error bound for the estimator from the structured tensor factorization. Built upon this error bound, we then derive the rate of convergence of the estimated cluster centers, and show that the estimated clusters recover the true cluster structures with high probability. Moreover, our proposed method can be naturally extended to co-clustering of multiple modes of the tensor data. The efficacy of our method is illustrated through simulations and a brain dynamic functional connectivity analysis from an autism spectrum disorder study. Supplementary materials for this article are available online.

Suggested Citation

  • Will Wei Sun & Lexin Li, 2019. "Dynamic Tensor Clustering," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1894-1907, October.
  • Handle: RePEc:taf:jnlasa:v:114:y:2019:i:528:p:1894-1907
    DOI: 10.1080/01621459.2018.1527701
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    Cited by:

    1. Xianpeng Mao & Yuning Yang, 2022. "Several approximation algorithms for sparse best rank-1 approximation to higher-order tensors," Journal of Global Optimization, Springer, vol. 84(1), pages 229-253, September.
    2. Mao, Xianpeng & Yang, Yuning, 2022. "Best sparse rank-1 approximation to higher-order tensors via a truncated exponential induced regularizer," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    3. Lu, Wenqi & Zhu, Zhongyi & Li, Rui & Lian, Heng, 2024. "Statistical performance of quantile tensor regression with convex regularization," Journal of Multivariate Analysis, Elsevier, vol. 200(C).
    4. Kai Deng & Xin Zhang, 2022. "Tensor envelope mixture model for simultaneous clustering and multiway dimension reduction," Biometrics, The International Biometric Society, vol. 78(3), pages 1067-1079, September.

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