A general soft method for learning SVM classifiers with L1-norm penalty
A general soft method for learning SVM classifiers with L1-norm penalty
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DOI：
10.1016/j.patcog.2007.08.004
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发表时间：
2008-03-01
影响因子：
8
通讯作者：
Wang, Jue
中科院分区：
文献类型：
--
作者：
Tao, Qing;Wu, Gao-Wei;Wang, Jue
基于支持向量机（SVM）的几何解释，提出了一种通用的技术，该技术允许几乎所有现有的基于L-2范数惩罚的几何算法，包括吉尔伯特算法、Schlesinger-Kozinec（SK）算法和Mitchell-Dem'yanov-Malozemov（MDM）算法，被软化以实现相应的学习L-1-SVM分类器。本质上，所得到的软算法是寻找两个软凸包之间的E-最优最近点。理论分析表明，我们提出的软算法本质上是相应的现有的硬算法的推广，因此，它们具有相同的收敛性和几乎相同的计算成本。作为一个具体的例子，研究了软MDM算法求解nu-SVMs的问题，并给出了相应的求解过程。为了验证通用软技术，我们用所提出的基于L-1范数的MDM算法进行了几个真实的分类实验，数值结果表明，它们的性能与相应的基于L-2范数的算法（如SK和MDM算法）相当。(C)2007模式识别学会。由爱思唯尔有限公司出版。保留所有权利。
Based on the geometric interpretation of support vector machines (SVMs), this paper presents a general technique that allows almost all the existing L-2-norm penalty based geometric algorithms, including Gilbert's algorithm, Schlesinger-Kozinec's (SK) algorithm and Mitchell-Dem'yanov-Malozemov's (MDM) algorithm, to be softened to achieve the corresponding learning L-1-SVM classifiers. Intrinsically, the resulting soft algorithms are to find E-optimal nearest points between two soft convex hulls. Theoretical analysis has indicated that our proposed soft algorithms are essentially generalizations of the corresponding existing hard algorithms, and consequently, they have the same properties of convergence and almost the identical cost of computation. As a specific example, the problem of solving nu-SVMs by the proposed soft MDM algorithm is investigated and the corresponding solution procedure is specified and analyzed. To validate the general soft technique, several real classification experiments are conducted with the proposed L-1-norm based MDM algorithms and numerical results have demonstrated that their performance is competitive to that of the corresponding L-2-norm based algorithms, such as SK and MDM algorithms. (C) 2007 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.