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A Portmanteau Local Feature Discrimination Approach to the Classification with High-dimensional Matrix-variate Data

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  • Zengchao Xu

    (Shanghai Jiao Tong University)

  • Shan Luo

    (Shanghai Jiao Tong University)

  • Zehua Chen

    (National University of Singapore)

Abstract

Matrix-variate data arise in many scientific fields such as face recognition, medical imaging, etc. Matrix data contain important structure information which can be ruined by vectorization. Methods incorporating the structure information into analysis have significant advantages over vectorization approaches. In this article, we consider the problem of two-class classification with high-dimensional matrix-variate data, and propose a novel portmanteau-local-feature discrimination (PLFD) method. This method first identifies local discrimination features of the matrix variate and then pools them together to construct a discrimination rule. We investigated the theoretical properties of the PLFD method and established its asymptotic optimality. We carried out extensive numerical studies including simulation and real data analysis to compare this method with other methods available in the literature, which demonstrate that the PLFD method has a great advantage over the other methods in terms of misclassification rate.

Suggested Citation

  • Zengchao Xu & Shan Luo & Zehua Chen, 2023. "A Portmanteau Local Feature Discrimination Approach to the Classification with High-dimensional Matrix-variate Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 441-467, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00255-2
    DOI: 10.1007/s13171-021-00255-2
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    References listed on IDEAS

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    1. Luo, Shan & Chen, Zehua, 2020. "A procedure of linear discrimination analysis with detected sparsity structure for high-dimensional multi-class classification," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    2. Hua Zhou & Lexin Li, 2014. "Regularized matrix regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 463-483, March.
    3. Yuqing Pan & Qing Mai & Xin Zhang, 2019. "Covariate-Adjusted Tensor Classification in High Dimensions," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(527), pages 1305-1319, July.
    4. Hua Zhou & Lexin Li & Hongtu Zhu, 2013. "Tensor Regression with Applications in Neuroimaging Data Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 540-552, June.
    5. Witten, Daniela M. & Tibshirani, Robert, 2010. "A Framework for Feature Selection in Clustering," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 713-726.
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