Efficient sparse least squares support vector machines for pattern classification

We propose a novel least squares support vector machine, named εε-least squares support vector machine (εε-LSSVM), for binary classification. By introducing the εε-insensitive loss function instead of the quadratic loss function into LSSVM, εε-LSSVM has several improved advantages compared with the plain LSSVM. (1) It has the sparseness which is controlled by the parameter εε. (2) By weighting different sparseness parameters εε for each class, the unbalanced problem can be solved successfully, furthermore, an useful choice of the parameter εε is proposed. (3) It is actually a kind of εε-support vector regression (εε-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.