Robust non-convex least squares loss function for regression with outliers

Abstract

In this paper, we propose a robust scheme for least squares support vector regression (LS-SVR), termed as RLS-SVR, which employs non-convex least squares loss function to overcome the limitation of LS-SVR that it is sensitive to outliers. Non-convex loss gives a constant penalty for any large outliers. The proposed loss function can be expressed by a difference of convex functions (DC). The resultant optimization is a DC program. It can be solved by utilizing the Concave–Convex Procedure (CCCP). RLS-SVR iteratively builds the regression function by solving a set of linear equations at one time. The proposed RLS-SVR includes the classical LS-SVR as its special case. Numerical experiments on both artificial datasets and benchmark datasets confirm the promising results of the proposed algorithm.