A projection wavelet weighted twin support vector regression and its primal solution

Abstract

In this paper, an efficient projection wavelet weighted twin support vector regression (PWWTSVR) algorithm is proposed. PWWTSVR determines the regression function by solving a pair of smaller unconstrained minimization problems in primal space, which can reduce computational costs. Classical SVR algorithms give the same emphasis to all training samples, which degrades performance. PWWTSVR gives samples penalty weights determined by wavelet transforms. These are applied to both the quadratic empirical risks term and the first-degree empirical risks term to reduce the influence of outliers. A projection axis in each objective function is sought to minimize the variance of the projected points due to the utilization of a priori information of training data. Therefore, data structure terms are added to the penalty functions. The final regressor can avoid the overfitting problem to a certain extent, and yields great generalization ability. Numerical experiments on artificial and benchmark datasets demonstrate the feasibility and validity of the proposed algorithm.