Twin SVM for conditional probability estimation in binary and multiclass classification

In this paper, we estimate the conditional probability function by presenting a new twin SVM model (CPTWSVM) in binary and multiclass classification problems. The motivation of CPTWSVM is to imple-ment the empirical risk minimization on training data, which is hard to realize in traditional twin SVMs. In each subproblem of CPTWSVM, it measures the empirical risk and outputs the corresponding proba-bility estimate of each class, which eliminates the problems of inconsistent measurement in twin SVMs. Though an additional discriminant objective function is introduced, the optimization problem size of each subproblem is smaller than conditional probability SVM, and is solved by block decomposition algorithm efficiently. In addition, we extend CPTWSVM to multiclass classification by estimating the conditional probability of each class, and maintaining the above properties. Numerical experiments on benchmark and real application datasets demonstrate that CPTWSVM outputs the estimate of probability and the data projection well, resulting in better generalization ability than some leading TWSVMs communities, in terms of binary and multiclass classification. (c) 2022 Elsevier Ltd. All rights reserved.