GENERALIZED MERCER THEOREM AND ITS APPLICATION TO FEATURE SPACE RELATED TO INDEFINITE KERNELS

摘要：

The support vector machine (SVM) is well understood when kernel functions are positive definite. However, in practice, indefinite kernels arise and demand application in SVM. These indefinite kernels often yield good empirical classification results. However, they are hard to understand for missing geometrical and theoretical understanding. In this paper we focus our topic on the structure of feature space related to indefinite kernels. We develop a new method by improving Mercer theorem to construct the mapping that maps input data set into the high-dimensional feature space for indefinite kernels. Via this mapping, structure of the feature space is easily observed. By this, we obtain a sound framework and motivation for SVM with indefinite kernels.

关键词： Indefinite kernel SVM Krein space Mercer theorem

作者: DE-GANG CHEN HENG-YOU WANG ERIC C.C.TSANG

作者单位: Department of Mathematics and Physics, North China Electric Power University, 102206, Beijing, P.R.C Department of computing, The Hong Kong Polytechnic University, Hung Horn, Kowloon, Hong Kong

会议类型: 国际会议

会议名称: 2008 International Conference on Machine Learning and Cybernetics(2008机器学习与控制论国际会议)

会议地点: 昆明

会议语种:英文

页码: 774-777

在线出版日期: 2008-07-12（万方平台首次上网日期，不代表论文的发表时间）