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

Chun-Na Li (), Pei-Wei Ren (), Yan-Ru Guo (), Ya-Fen Ye () and Yuan-Hai Shao ()
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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

Annals of Operations Research, 2024, vol. 339, issue 3, No 13, 1433-1459

Abstract: 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.

Keywords: Linear discriminant analysis; Capped norm; Generalized capped norm; Capped norm linear discriminant analysis; Dimensionality reduction (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10479-022-04959-y

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