Capped $L_1$-Norm Proximal Support Vector Machine

Abstract

Compared to the standard support vector machine, the generalized eigenvalue proximal support vector machine coped well with the “Xor” problem. However, it was based on the squared Frobenius norm and hence was sensitive to outliers and noise. To improve the robustness, this paper introduces capped L 1 -norm into the generalized eigenvalue proximal support vector machine, which employs nonsquared L 1 -norm and “capped” operation, and further proposes a novel capped L 1 -norm proximal support vector machine, called CPSVM. Due to the use of capped L 1 -norm, CPSVM can effectively remove extreme outliers and suppress the effect of noise data. CPSVM can also be viewed as a weighted generalized eigenvalue proximal support vector machine and is solved through a series of generalized eigenvalue problems. The experimental results on an artificial dataset, some UCI datasets, and an image dataset demonstrate the effectiveness of CPSVM.