Training of Support Vector Machines with Mahalanobis Kernels
Training of Support Vector Machines with Mahalanobis Kernels
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DOI：
10.1007/11550907_90
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发表时间：
2005-09
影响因子：
2.7
通讯作者：
S. Abe
中科院分区：
文献类型：
--
作者：
S. Abe
径向基函数（RBF）核函数被广泛用于支持向量机。但是对于模型选择，我们需要通过耗时的交叉验证来优化核参数和边缘参数。为了解决这个问题，在本文中，我们提出使用Mahalanobis核，这是广义RBF核。我们使用对应于相关类的训练数据来确定Mahalanobis内核的协方差矩阵。模型选择是通过线性搜索完成的。即，首先优化边缘参数，然后优化Mahalanobis核参数。通过对两类问题的计算机实验，发现协方差矩阵为对角矩阵的马氏核比协方差矩阵为全矩阵的马氏核具有更好的泛化能力，而线搜索优化的马氏核与网格搜索优化的RBF核具有相当的泛化能力.
Radial basis function (RBF) kernels are widely used for support vector machines. But for model selection, we need to optimize the kernel parameter and the margin parameter by time-consuming cross validation. To solve this problem, in this paper we propose using Mahalanobis kernels, which are generalized RBF kernels. We determine the covariance matrix for the Mahalanobis kernel using the training data corresponding to the associated classes. Model selection is done by line search. Namely, first the margin parameter is optimized and then the Mahalanobis kernel parameter is optimized. According to the computer experiments for two-class problems, a Mahalanobis kernel with a diagonal covariance matrix shows better generalization ability than a Mahalanobis kernel with a full covariance matrix, and a Mahalanobis kernel optimized by line search shows comparable performance with that with an RBF kernel optimized by grid search.