Double weighted least square support vector machines

Support vector machines (SVM) is widely used in pattern recognition and artificial intelligence domain in recent years for its efficiency in classification and regression. Least squares version of SVM (LSSVM) is very popular for its optimization problem can be solved in a simple linear system. However, its generalization performance is sensitive to noise points and outliers that are often existent in training dataset. Additionally, the effect caused by SVM is assumed to be uniform over all the bands, which is not necessarily true. Under this condition, a double weighting method is proposed for LSSVM. First, the relaxation variable corresponding to each sample is weighted according to the distance between the sample and its corresponding class center. Second, each band is weighted in agreement with its significance by introducing a weighting matrix into training samples. Additionally, sequential minimal optimization (SMO) algorithm is also extended to the new method for its efficient implementation. Comparison experiments show superiority of the new method in terms of generalization performance, robust property and sparse approximation.