期刊
KNOWLEDGE-BASED SYSTEMS
卷 52, 期 -, 页码 223-235出版社
ELSEVIER
DOI: 10.1016/j.knosys.2013.08.008
关键词
1-Norm SVM; Linear programming; Column generation; Newton algorithm; Kernel function
资金
- National Natural Science Foundation of China [61373093, 61033013]
- Natural Science Foundation of the Jiangsu Higher Education Institutions of China [13KJA520001]
- Natural Science Foundation of Jiangsu Province of China [BK2011284, BK201222725]
- Natural Science Pre-research Project of Soochow University [SDY2011B09]
- Qing Lan Project
This paper presents a fast algorithm called Column Generation Newton (CGN) for kernel 1-norm support vector machines (SVMs). CGN combines the Column Generation (CG) algorithm and the Newton Linear Programming SVM (NLPSVM) method. NLPSVM was proposed for solving 1-norm SVM, and CG is frequently used in large-scale integer and linear programming algorithms. In each iteration of the kernel 1-norm SVM, NLPSVM has a time complexity of O(l(3)), where l is the sample number, and CG has a time complexity between O(l(3)) and O(n'(3)), where n' is the number of columns of the coefficient matrix in the subproblem. CGN uses CG to generate a sequence of subproblems containing only active constraints and then NLPSVM to solve each subproblem. Since the subproblem in each iteration only consists of n' unbound constraints, CGN thus has a time complexity of O(n'(3)), which is smaller than that of NLPSVM and CG. Also, CGN is faster than CG when the solution to 1-norm SVM is sparse. A theorem is given to show a finite step convergence of CGN. Experimental results on the Ringnorm and UCI data sets demonstrate the efficiency of CGN to solve the kernel 1-norm SVM. (C) 2013 Elsevier B.V. All rights reserved.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据