A novel kernel-free least squares twin support vector machine for fast and accurate multi-class classification

Abstract

Multi-class classification is an important and challenging research topic with many real-life applications. The problem is much harder than the classical binary classification, especially when the given data set is imbalanced. Hidden nonlinear patterns in the data set can further complicate the task of multi-class classification. In this paper, we propose a kernel-free least squares twin support vector machine for multi-class classification. The proposed model employs a special fourth order polynomial surface, namely the double well potential surface, and adopts the ”one-verses-all” classification strategy. An ℓ2 regularization term is added to accommodate data sets with different levels of nonlinearity. We provide some theoretical analysis of the proposed model. Computational results using artificial data sets and public benchmarks clearly show the superior performance of the proposed model over other well-known multi-class classification methods, in particular for imbalanced data sets.