Decremental Learning Algorithms for Nonlinear Langrangian and Least Squares Support Vector Machines

Langrangian Support Vector Machine (LSVM) and Least Squares Support Vector Machine (LSSVM) are two quick and effective classification methods. In this paper, we first introduce the mathematical models for LSVM and LSSVM and analyze their properties. In the nonlinear case, Sherman-Morrison-Woodbury identity is not used to compute the inversion of a matrix. According to block computation of a matrix and properties of a symmetric and positive-definite matrix, an approach to compute the inversion of a matrix is obtained and applied in the decremental learning algorithms for nonlinear LSVM and LSSVM. The online and batch decremental learning algorithms for nonlinear LSVM and LSSVM are presented, respectively, in which it is not necessary to relearn since the inversion of matrix after decrement is solved based on the former information. Thus, the computation time can be reduced. Through experiments, it is shown that the algorithms proposed in this paper can reduce the computation time.