Improvement over Pinball Loss Support Vector Machine

Recently, there have been several papers that discuss the extension of the Pinball loss Support Vector Machine (Pin-SVM) model, originally proposed by Huang et al.,[1][2]. Pin-SVM classifier deals with the pinball loss function, which has been defined in terms of the parameter τ. The parameter τ can take values in [ -1,1]. The existing Pin-SVM model requires to solve the same optimization problem for all values of τ in [ -1,1]. In this paper, we improve the existing Pin-SVM model for the binary classification task. At first, we note that there is major difficulty in Pin-SVM model (Huang et al. [1]) for -1 ≤ τ < 0. Specifically, we show that the Pin-SVM model requires the solution of different optimization problem for -1 ≤ τ < 0. We further propose a unified model termed as Unified Pin-SVM which results in a QPP valid for all -1≤ τ ≤ 1 and hence more convenient to use. The proposed Unified Pin-SVM model can obtain a significant improvement in accuracy over the existing Pin-SVM model which has also been empirically justified by extensive numerical experiments with real-world datasets.