Sparse support vector machine with pinball loss

Abstract

Abstract The standard support vector machine (SVM) with a hinge loss function suffers from feature noise sensitivity and instability. Employing a pinball loss function instead of a hinge loss function in SVMs provides noise insensitivity to the model as it maximizes the quantile distance. However, the pinball loss function simultaneously causes the model to lose sparsity by penalizing correctly classified samples. To overcome the aforementioned shortcomings, we propose a novel sparse SVM with pinball loss (Pin‐SSVM) for solving classification problems. The proposed Pin‐SSVM employs L1‐norm in the SVM classifier with the pinball loss (Pin‐SVM), which ensures the robustness, sparseness, and noise insensitivity of the model. The proposed Pin‐SSVM eradicates the need to solve the dual as we simply obtain its solution by solving a linear programming problem (LPP). The proposed Pin‐SSVM does not spend more computational time as that of Pin‐SVM. Hence, solving an LPP with two linear inequality constraints does not affect the computational complexity. The numerical experiments on several real‐world benchmark noise corrupted and imbalanced UCI datasets demonstrate that the proposed Pin‐SSVM is suitable for noisy and imbalanced data sets, and in most cases, outperforms the results of the baseline models.