IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i1d10.1007_s13171-021-00255-2.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-021-00255-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-021-00255-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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).
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Wang, Lei & Zhang, Jing & Li, Bo & Liu, Xiaohui, 2022. "Quantile trace regression via nuclear norm regularization," Statistics & Probability Letters, Elsevier, vol. 182(C).
    3. Xiaoshan Li & Da Xu & Hua Zhou & Lexin Li, 2018. "Tucker Tensor Regression and Neuroimaging Analysis," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 520-545, December.
    4. 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).
    5. Inkoo Lee & Debajyoti Sinha & Qing Mai & Xin Zhang & Dipankar Bandyopadhyay, 2023. "Bayesian regression analysis of skewed tensor responses," Biometrics, The International Biometric Society, vol. 79(3), pages 1814-1825, September.
    6. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    7. Zhao, Junlong & Niu, Lu & Zhan, Shushi, 2017. "Trace regression model with simultaneously low rank and row(column) sparse parameter," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 1-18.
    8. Yaeji Lim & Hee-Seok Oh & Ying Kuen Cheung, 2019. "Multiscale Clustering for Functional Data," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 368-391, July.
    9. Yujia Li & Xiangrui Zeng & Chien‐Wei Lin & George C. Tseng, 2022. "Simultaneous estimation of cluster number and feature sparsity in high‐dimensional cluster analysis," Biometrics, The International Biometric Society, vol. 78(2), pages 574-585, June.
    10. Dong Liu & Changwei Zhao & Yong He & Lei Liu & Ying Guo & Xinsheng Zhang, 2023. "Simultaneous cluster structure learning and estimation of heterogeneous graphs for matrix‐variate fMRI data," Biometrics, The International Biometric Society, vol. 79(3), pages 2246-2259, September.
    11. Jeffrey Andrews & Paul McNicholas, 2014. "Variable Selection for Clustering and Classification," Journal of Classification, Springer;The Classification Society, vol. 31(2), pages 136-153, July.
    12. Hung Hung & Su‐Yun Huang, 2019. "Sufficient dimension reduction via random‐partitions for the large‐p‐small‐n problem," Biometrics, The International Biometric Society, vol. 75(1), pages 245-255, March.
    13. Hayato Maki & Sakriani Sakti & Hiroki Tanaka & Satoshi Nakamura, 2018. "Quality prediction of synthesized speech based on tensor structured EEG signals," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-13, June.
    14. Chelsey Hill & James Li & Matthew J. Schneider & Martin T. Wells, 2021. "The tensor auto‐regressive model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 636-652, July.
    15. Luo, Chongliang & Liang, Jian & Li, Gen & Wang, Fei & Zhang, Changshui & Dey, Dipak K. & Chen, Kun, 2018. "Leveraging mixed and incomplete outcomes via reduced-rank modeling," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 378-394.
    16. Lan Liu & Wei Li & Zhihua Su & Dennis Cook & Luca Vizioli & Essa Yacoub, 2022. "Efficient estimation via envelope chain in magnetic resonance imaging‐based studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 481-501, June.
    17. J. Fernando Vera & Rodrigo Macías, 2021. "On the Behaviour of K-Means Clustering of a Dissimilarity Matrix by Means of Full Multidimensional Scaling," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 489-513, June.
    18. Feiyang Han & Yimin Wei & Pengpeng Xie, 2024. "Regularized and Structured Tensor Total Least Squares Methods with Applications," Journal of Optimization Theory and Applications, Springer, vol. 202(3), pages 1101-1136, September.
    19. Kenneth W. Latimer & David J. Freedman, 2023. "Low-dimensional encoding of decisions in parietal cortex reflects long-term training history," Nature Communications, Nature, vol. 14(1), pages 1-24, December.
    20. Daniel Spencer & Rajarshi Guhaniyogi & Raquel Prado, 2020. "Joint Bayesian Estimation of Voxel Activation and Inter-regional Connectivity in fMRI Experiments," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 845-869, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00255-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.