Robust Least Squares Projection Twin SVM and its Sparse Solution

Least squares projection twin support vector machine(LSPTSVM) has faster computing speed than classical least squares support vector machine(LSSVM). However, LSPTSVM is sensitive to outliers and its solution lacks sparsity. Therefore, it is difficult for LSPTSVM to process large-scale datasets with outliers. In this paper, we propose a robust LSPTSVM model(called R-LSPTSVM) by applying truncated least squares loss function. The robustness of R-LSPTSVM is proved from a weighted perspective. Furthermore, we obtain the sparse solu-tion of R-LSPTSVM by using the pivoting Cholesky factorization method in primal space. Finally, the sparse R-LSPTSVM algo-rithm(SR-LSPTSVM) is proposed. Experimental results show that SR-LSPTSVM is insensitive to outliers and can deal with large-scale datasets fastly.