Twin LSSVM Incremental Learning And Sparse Algorithm Research

Least square twin support vector machine(LSTSVM)is a variant of twin support vector machine(TSVM),which is widely used in classification and regression problems.In solving quadratic programming problem,LSTSVM can be transformed into a solution of the linear equations compared to TSVM.LSTSVM improves the training speed,but loses its sparseness,resulting in slow test speed.LSTSVM is not suitable for large-scale data sets,thus it's important to sparse the solution of it.This paper is mainly based on the LSTSVM put forward two improved incremental learning algorithm and sparse algorithm,the main work of this paper includes two aspects as follow.On the one hand,in order to solve the problem of solving the non-full rank matrix when solving the twin LSSVM objective function,this paper proposes an improved twin LSSVM(ILSTSVM),which uses the principle of minimizing empirical risk to avoid the generation of ill-posed solutions.In the training process,the inverse of the matrix is decomposed by the Sherman-Morrison theorem,and then the inverse of the matrix is reorganized to obtain an iterative solution algorithm with a relatively simple structure and a small amount of calculation,and because incremental learning reduces the time and space.Requirements,so this paper proposes a ILSTSVM algorithm based on Sherman-Morrison theorem and incremental learning,namely SMI-ILSTSVM algorithm.This method controls the test accuracy and training time with the number of iterations by selecting different sample subset sizes.Finally,experiments on UCI datasets show that the SMI-ILSTSVM incremental learning algorithm proposed in this paper can achieve high-precision and high-efficiency classification results,and is suitable for the cross-sample set classification with noise.On the other hand,based on the method of removing some vectors that are approximately linearly related in the feature space,that is,by subtracting the training samples,some components of the approximately linear correlation in the classification discriminant function are eliminated.And because the sparse representation of the discriminant function can be derived by using the representation theorem,a sparse least squares twin support vector machine classification algorithm,namely S-LSTSVM,is proposed in this paper.This method can control the accuracy of the algorithm by controlling the different values of sparsity parameters.When the value is,each data set can reach or approach the best classification accuracy.Finally,the effectiveness of the algorithm S-LSTSVM is illustrated by the experiments of linear classification and nonlinear classification.