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Regularized linear discriminant analysis based on generalized capped $$l_{2,q}$$ l 2 , q -norm

Author

Listed:
  • Chun-Na Li

    (Hainan University)

  • Pei-Wei Ren

    (Hainan University)

  • Yan-Ru Guo

    (Zhejiang University of Science and Technology)

  • Ya-Fen Ye

    (Zhejiang University of Technology)

  • Yuan-Hai Shao

    (Hainan University)

Abstract

Aiming to improve the robustness and adaptiveness of the recently investigated capped norm linear discriminant analysis (CLDA), this paper proposes a regularized linear discriminant analysis based on the generalized capped $$l_{2,q}$$ l 2 , q -norm (GCLDA). Compared to CLDA, there are two improvements in GCLDA. Firstly, GCLDA uses the capped $$l_{2,q}$$ l 2 , q -norm rather than the capped $$l_{2,1}$$ l 2 , 1 -norm to measure the within-class and between-class distances for arbitrary $$q>0$$ q > 0 . By selecting an appropriate q, GCLDA is adaptive to different data, and also removes extreme outliers and suppresses the effect of noise more effectively. Secondly, by taking into account a regularization term, GCLDA not only improves its generalization ability but also avoids singularity. GCLDA is solved through a series of generalized eigenvalue problems. Experiments on an artificial dataset, some real world datasets and a high-dimensional dataset demonstrate the effectiveness of GCLDA.

Suggested Citation

  • Chun-Na Li & Pei-Wei Ren & Yan-Ru Guo & Ya-Fen Ye & Yuan-Hai Shao, 2024. "Regularized linear discriminant analysis based on generalized capped $$l_{2,q}$$ l 2 , q -norm," Annals of Operations Research, Springer, vol. 339(3), pages 1433-1459, August.
    • Handle: RePEc:spr:annopr:v:339:y:2024:i:3:d:10.1007_s10479-022-04959-y
    DOI: 10.1007/s10479-022-04959-y
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    References listed on IDEAS

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