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Ensemble LDA via the modified Cholesky decomposition

Author

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  • Gao, Zhenguo
  • Wang, Xinye
  • Kang, Xiaoning

Abstract

A binary classification problem in the high-dimensional settings is studied via the ensemble learning with each base classifier constructed from the linear discriminant analysis (LDA), and these base classifiers are integrated by the weighted voting. The precision matrix in the LDA rule is estimated by the modified Cholesky decomposition (MCD), which is able to provide us with a set of precision estimates by considering multiple variable orderings, and hence yield a group of different LDA classifiers. Such available LDA classifiers are then integrated to improve the classification performance. The simulation and the application studies are conducted to demonstrate the merits of the proposed method.

Suggested Citation

  • Gao, Zhenguo & Wang, Xinye & Kang, Xiaoning, 2023. "Ensemble LDA via the modified Cholesky decomposition," Computational Statistics & Data Analysis, Elsevier, vol. 188(C).
  • Handle: RePEc:eee:csdana:v:188:y:2023:i:c:s0167947323001342
    DOI: 10.1016/j.csda.2023.107823
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    References listed on IDEAS

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    1. Rajaratnam, Bala & Salzman, Julia, 2013. "Best permutation analysis," Journal of Multivariate Analysis, Elsevier, vol. 121(C), pages 193-223.
    2. Kang, Xiaoning & Wang, Mingqiu, 2021. "Ensemble sparse estimation of covariance structure for exploring genetic disease data," Computational Statistics & Data Analysis, Elsevier, vol. 159(C).
    3. Xiaoning Kang & Xinwei Deng & Kam‐Wah Tsui & Mohsen Pourahmadi, 2020. "On variable ordination of modified Cholesky decomposition for estimating time‐varying covariance matrices," International Statistical Review, International Statistical Institute, vol. 88(3), pages 616-641, December.
    4. Qing Mai & Hui Zou & Ming Yuan, 2012. "A direct approach to sparse discriminant analysis in ultra-high dimensions," Biometrika, Biometrika Trust, vol. 99(1), pages 29-42.
    5. Liu, Jianyu & Yu, Guan & Liu, Yufeng, 2019. "Graph-based sparse linear discriminant analysis for high-dimensional classification," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 250-269.
    6. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
    7. Hao Zheng & Kam-Wah Tsui & Xiaoning Kang & Xinwei Deng, 2017. "Cholesky-based model averaging for covariance matrix estimation," Statistical Theory and Related Fields, Taylor & Francis Journals, vol. 1(1), pages 48-58, January.
    8. Enrico Glaab & Jaume Bacardit & Jonathan M Garibaldi & Natalio Krasnogor, 2012. "Using Rule-Based Machine Learning for Candidate Disease Gene Prioritization and Sample Classification of Cancer Gene Expression Data," PLOS ONE, Public Library of Science, vol. 7(7), pages 1-18, July.
    9. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    10. Jianhua Z. Huang & Naiping Liu & Mohsen Pourahmadi & Linxu Liu, 2006. "Covariance matrix selection and estimation via penalised normal likelihood," Biometrika, Biometrika Trust, vol. 93(1), pages 85-98, March.
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