Improvements on least squares twin multi-class classification support vector machine

Recently, least squares twin multi-class support vector machine (LSTKSVC) was proposed as a least squares version of twin multi-class classification support vector machine (Twin-KSVC), both based on twin support vector machine (TWSVM). In this paper, we propose a novel multi-class classifier termed as Improvements on least squares twin multi-class classification support vector machine that is motivated by LSTKSVC and Twin-KSVC. Similarly to LSTKSVC that evaluates all the training data into a ``1−versus−1−versus−rest″ structure, the algorithm here proposed generates ternary output {−1,0,+1}. Whereas Twin-KSVC needs to solve two quadratic programming problems (QPPs), the solution of the two modified primal problems for our algorithm is reduced to two systems of linear equations. Besides that, in our algorithm the structural risk minimization (SRM) principle is implemented by introducing a regularization term, along with minimizing the empirical risk. To test the efficacy and validity of the proposed method, numerical experiments on ten UCI benchmark data sets are performed. The results obtained further corroborate the effectiveness of the proposed algorithm.