Regularized linear discriminant analysis based on generalized capped l-norm

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

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 \(l_{2,q}\)-norm (GCLDA). Compared to CLDA, there are two improvements in GCLDA. Firstly, GCLDA uses the capped \(l_{2,q}\)-norm rather than the capped \(l_{2,1}\)-norm to measure the within-class and between-class distances for arbitrary \(q>0\). 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.