Efficient sparse least squares support vector machines for pattern classification

• Published in: Computers & mathematics with applications (1987) Vol. 66; no. 10; pp. 1935 - 1947
• Main Authors: Tian, Yingjie, Ju, Xuchan, Qi, Zhiquan, Shi, Yong
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.12.2013
• Subjects: Classification; Least squares support vector machine; Loss function; Regression; Sparseness; Regression; Loss function; Least squares support vector machine; Classification; Sparseness
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2013.06.028

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