Least squares twin multi-class classification support vector machine

• The multi-class classification method based on TWSVM is proposed.
• We formulate a least squares version of Twin K-class support vector machine.
• We just solve two systems of linear equations.
• Our method evaluates all the training data into a “1-v-1-v-rest” structure.
• It generates ternary output {−1, 0, +1}.

Twin K-class support vector classification (Twin-KSVC) is a novel multi-class method based on twin support vector machine (TWSVM). In this paper, we formulate a least squares version of Twin-KSVC called as LST-KSVC. This formulation leads to extremely simple and fast algorithm. LST-KSVC, same as the Twin-KSVC, evaluates all the training data into a “1-versus-1-versus-rest” structure, so it generates ternary output {−1, 0, +1}. In LST-KSVC, the solution of the two modified primal problems is reduced to solving only two systems of linear equations whereas Twin-KSVC needs to solve two quadratic programming problems (QPPs) along with two systems of linear equations. Our experiments on UCI and face datasets indicate that the proposed method has comparable accuracy in classification to that of Twin-KSVC but with remarkably less computational time. Also, because of the structure “1-versus-1-versus-rest”, the classification accuracy of LST-KSVC is higher than typical multi-class method based on SVMs.