| 支持向量机的最大间隔和对偶性 |
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| 引用本文： | 鲁淑霞,王熙照.支持向量机的最大间隔和对偶性[J].河北大学学报(自然科学版),2007,27(5):449-452. |
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| 作者姓名： | 鲁淑霞 王熙照 |
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| 作者单位： | 河北大学,数学与计算机学院,河北,保定,071002 |
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| 基金项目： | 国家自然科学基金资助项目(6047304570571021)，河北省自然科学基金资助项目(A2005000087) |
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| 摘 要： | 最初出现的支持向量机理论是基于2类线性可分问题的.针对线性可分情况,研究表明线性硬间隔分类机的对偶问题与凸壳问题(平分最近点法)是等价的,线性硬间隔分类机的最大间隔与凸壳问题的2个最近点的距离相等:针对非线性可分情况,研究表明线性软间隔分类机的对偶问题与缩小的凸壳问题(推广的平分最近点法)是等价的,线性软间隔分类机的最大间隔与缩小的凸壳问题的2个最近点的距离相等.对支持向量机分类问题给出了直观解释.
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| 关 键 词： | 支持向量机 间隔 凸壳 对偶性 |
| 文章编号： | 1000-1565(2007)05-0449-04 |
| 修稿时间： | 2006年10月30 |
Margin and Duality in Support Vector Machines |
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| LU Shu-xia,WANG Xi-zhao.Margin and Duality in Support Vector Machines[J].Journal of Hebei University (Natural Science Edition),2007,27(5):449-452. |
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| Authors: | LU Shu-xia WANG Xi-zhao |
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| Abstract: | Support vector machine(SVM) theory was originally developed on the basis of a linearly separable binary classification problem.It is demonstrated that the dual problem of Hard-Margin is equivalent to the distance between the two closest points in the convex hulls in the linearly separable case.For the non-linearly separable case,the dual problem of Soft-Margin is exactly Reduced Convex-Hull.The maximum margin between the two sets in Soft-Margin is equivalent to the distance between the two closest points in the reduced convex hulls.An intuitive geometric interpretation of support vector machines for classification is developed. |
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| Keywords: | support vector machines margin convex hulls duality |
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