Capped L1-Norm Proximal Support Vector Machine

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 L1-norm into the generalized eigenvalue proximal support vector machine, which employs nonsquared L1-norm and “capped†operation, and further proposes a novel capped L1-norm proximal support vector machine, called CPSVM. Due to the use of capped L1-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.