Robustness enhancement for proximal support vector machines

Proximal support vector machine (PSVM) is a new version of SVM, which involves equality instead of inequality constraints, and works with a square error function. In this way, the solution follows from a linear Karush-Kuhn-Tucker system instead of a quadratic programming problem. The linear PSVM can easily solve the classification problems of extremely large datasets. However, according to the experiments below, PSVM is sensitive to noise. To overcome the drawback, this note proposes a weighted version of PSVM. The distance between each point and the center of corresponding class is used to calculate the weight value associated with the related point. In this way, the effect of noise is reduced greatly. The experiments indicate that the new SVM, weighted proximal support vector machine (WPSVM), is much more robust to noise than PSVM without loss of computationally attractive feature of PSVM.