A novel least squares twin parametric insensitive support vector regression

Abstract

The recently proposed twin parametric insensitive support vector regression, denoted by TPISVR, gets perforce regression performance and is suitable for many cases, especially when the noise is heteroscedastic. However, in the TPISVR, it solves two dual quadratic programming problems (QPPs). Moreover, compared with support vector regression (SVR), TPISVR has at least four regularisation parameters that need regulating, which would affect its practical applications. In this paper, we increase the efficiency of TPISVR from two aspects. First, by introducing the least squares method, we propose a novel least squares twin parametric insensitive support vector regression, called LSTPISVR for short. LSTPISVR attempts to solve two modified primal problems of TPISVR, instead of two dual problems usually solved. Compared with the traditional solution method, LSTPISVR can improve the training speed without loss of generalisation. Second, a discrete binary particle swarm optimisation (BPSO) algorithm is introduced to do the parameter selection. Computational results on several synthetic as well as benchmark datasets confirm the great improvements on the training process of our LSTPISVR.