期刊
IEEE TRANSACTIONS ON NEURAL NETWORKS
卷 13, 期 5, 页码 1045-1052出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNN.2002.1031937
关键词
asymptotic convergence; decomposition methods; stopping criteria; support vector machines (SVMs)
In a previous paper, we proved the convergence of a commonly used decomposition method for support vector machines (SVMs). However, there is no theoretical justification about its stopping criterion, which is based on the gap of the violation of the optimality condition. It is essential to have the gap asymptotically approach zero, so we are sure that existing implementations stop in a finite number of iterations after reaching a specified tolerance. Here, we prove this result and illustrate it by two extensions: nu-SVM and a multiclass SVM by Crammer and,Singer. A further result shows that, in final iterations of the decomposition method, only a particular set of variables are still being modified. This supports the use of the shrinking and caching techniques in some existing implementations. Finally, we prove the asymptotic convergence of a decomposition method for this multiclass SVM. Discussions on the difference between this convergence proof and the one in another paper by Lin are also included.
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