Wavelet transform-based weighted $$\nu$$-twin support vector regression

Abstract

In this paper, an efficient wavelet transform-based weighted $$\nu$$-twin support vector regression (WTWTSVR) is proposed, inspired by twin support vector regression (TSVR) and $$\nu$$-twin support vector machine-based regression. TSVR and its improved models work faster than support vector regression because they solve a pair of smaller-sized quadratic programming problems. However, they give the same emphasis to the training samples, i.e., all of the training samples share the same weights, and prior information is not used, which leads to the degradation of performance. Motivated by this, samples in different positions in the proposed WTWTSVR model are given different penalty weights determined by the wavelet transform. The weights are applied to both the quadratic empirical risk term and the first-degree empirical risk term to reduce the influence of outliers. The final regressor can avoid the overfitting problem to a certain extent and yield great generalization ability. Numerical experiments on artificial datasets and benchmark datasets demonstrate the feasibility and validity of our proposed algorithm.