Efficient sparse least squares support vector machines for pattern classification

We propose a novel least squares support vector machine, named epsilon-least squares support vector machine (epsilon-LSSVM), for binary classification. By introducing the epsilon-insensitive loss function instead of the quadratic loss function into LSSVM, epsilon-LSSVM has several improved advantages compared with the plain LSSVM. (1) It has the sparseness which is controlled by the parameter epsilon. (2) By weighting different sparseness parameters epsilon for each class, the unbalanced problem can be solved successfully, furthermore, an useful choice of the parameter epsilon is proposed. (3) It is actually a kind of epsilon-support vector regression (epsilon-SVR), the only difference here is that it takes the binary classification problem as a special kind of regression problem. (4) Therefore it can be implemented efficiently by the sequential minimization optimization (SMO) method for large scale problems. Experimental results on several benchmark datasets show the effectiveness of our method in sparseness, balance performance and classification accuracy, and therefore confirm the above conclusion further. (C) 2013 Elsevier Ltd. All rights reserved.