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| 线性支持向量分类机的平凡解 | |
| 引用本文： | 刘小茂,全廷伟,张钧.线性支持向量分类机的平凡解[J].华中科技大学学报(自然科学版),2007,35(10):57-59,66. |
| 作者姓名： | 刘小茂 全廷伟 张钧 |
| 作者单位： | 1. 华中科技大学,数学系,湖北,武汉,430074 2. 华中科技大学,数学系,湖北,武汉,430074;湖北教育学院,数学系,湖北,武汉,430205 3. 华中科技大学,图像识别与人工智能研究所,湖北,武汉,430074 |
| 摘 要： | 对二类分类问题,在线性可分或近似线性可分情况下,对线性支持向量分类机的平凡解进行了讨论,得出了解为平凡解的充要条件,说明了其几何意义,指出了避免出现这一现象的解决办法.该充要条件表明:对给定的训练集T,最优解是否为平凡解取决于训练集T的样本点在空间的分布位置,与惩罚参数C值的选取无关.一旦出现平凡解,线性支持向量分类机将会失效.为解决这一问题,可通过增加或减少训练集T中的样本点来实现. |
| 关 键 词： | 线性支持向量分类机 KKT条件 平凡解 线性可分 线性可分 支持向量分类机 平凡解 support vector machine linear solution 分类问题 失效 选取 罚参数 分布位置 空间 样本点 最优解 训练集 现象 几何意义 条件 情况 近似 |
| 文章编号： | 1671-4512（2007）10-0057-03 |
| 修稿时间： | 2006-07-26 |
Degenerate solution to linear support vector machine |
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| Liu Xiaomao,Quan Tingwei,Zhang Jun.Degenerate solution to linear support vector machine[J].JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE,2007,35(10):57-59,66. | |
| Authors: | Liu Xiaomao Quan Tingwei Zhang Jun |
| Institution: | 1 Department of Mathematics, Institute for Pattern Recognition and Artificial Intelligence, Huazhong University of Science and Technology, Wuhan 430074, China; 2 Department of Mathematics, Hubei Institute of Education, Wuhan 430205, China |
| Abstract: | For binary classifying problem,we discuss the degeneracy of linear support vector machine(LSVM) which is applied for linearly separable or approximately linearly separable cases: derive necessary and sufficient conditions for the occurrence of degenerate solution and give their geometric explanations.The method to avoid its occurrence is also proposed.The necessary and sufficient conditions for the occurrence of degenerate solution indicate that for given training set,the optimal solution is whether degenerate one or not depends on the position of the training set T distributed in the space and is independent of the penalty parameter C.Whenever the optimal solution is degenerate,the linear support vector machine will be unavailable.To solve this problem,we may add or reduce some elements of the training set. |
| Keywords: | inear support vector machine KKT(Karush Kuhm Tuchker) conditions degenerate solution linearly separable |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ | |