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| 基于闭凸包收缩的最大边缘线性分类器 |
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陶卿1,2, 孙德敏3, 范劲松4, 方廷健4
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1.中国科学院,自动化研究所,北京,100080;2.中国人民解放军炮兵学院,一系,安徽,合肥,230031;3.中国科学技术大学,自动化系,安徽,合肥,230027;4.中国科学院,合肥智能机械研究所,安徽,合肥,230031
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| 摘要: |
| SVM(support vector machines)是一种基于结构风险最小化原理的分类技术.给出实现结构风险最小化原理(最大边缘)的另一种方法.对线性可分情形,提出一种精确意义下的最大边缘算法,并通过闭凸包收缩的概念,将线性不可分的情形转化为线性可分情形.该算法与SVM算法及其Cortes软边缘算法异曲同工,但理论体系简单、严谨,其中的优化问题几何意义清楚、明确. |
| 关键词: 闭凸集 收缩 支持向量 最大边缘 分类器 |
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| 基金项目:国家自然科学基金资助项目(60175023);安徽省自然科学基金资助项目(01042304);安徽省优秀青年基金资助项目 |
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| Maximal Margin Linear Classifier Based on the Contraction of the Closed Convex Hull |
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TAO Qing,SUN De-min,FAN Jin-song,FANG Ting-jian4
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| Abstract: |
| The SVM (support vector machines) is a classification technique based on the structural risk minimization principle. In this paper, another method is given to implement the structural risk minimization principle. And an exact maximal margin algorithm is proposed when classification problem is linearly separable. The linearly non-separable problem can be changed to separable linearly by using the proposed concept of the contraction of a closed convex set. The method in this paper has the same function and quality as SVM and Cortes'soft margin algorithm,but its theoretical system is simple and strict,and geometric meaning of its optimization probem is very clear and obvious. |
| Key words: closed convex set contraction support vectors maximal margin classifier |
