Decremental Learning Algorithms for Nonlinear Langrangian and Least Squares Support Vector Machines
作者单位：Department of MathematicsShanghai Jiaotong University College of Information Science and EngineeringShandong University of Science and Technology
会议名称：《第一届最优化与系统生物学国际研讨会》
会议日期：2007年
学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 0835[工学-软件工程] 070102[理学-计算数学] 0811[工学-控制科学与工程] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）]
基 金：supported partially by national science foundation of China (10571109 and 60603090)
摘 要：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.