Robust Least Squares Support Vector Machine

The least squares support vector machine(LS-SVM) is a widely applicable and useful machine learning technique for classification and regression analysis. LS-SVM is an SVM(support vector machine) version which involves equality constraints instead of inequality constraints and works with a squared loss function, which leads the solution to be obtained from a linear Karush-Kuhn-Tucker conditions instead of a quadratic programming problem. A drawback of LS-SVM is that the estimates is less robust due to the assumption of the errors and the use of a squared loss function. In this paper we propose a robust LS-SVM which imposes the robustness on the estimation of LS-SVM by eliminating the candidates of outliers. The proposed method are also applied to pruning support vectors in the LS-SVM case. In the numerical studies, the performance of the robust LS-SVM is shown and compared with the ordinary LS-SVM via FVU.