Journal
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
Volume 43, Issue 1, Pages 162-172Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.acha.2016.09.001
Keywords
Least squares support vector machine; Indefinite kernel; Classification; Kernel principal component analysis
Categories
Funding
- Alexander von Humboldt Foundation
- National Natural Science Foundation of China [61603248]
- ERC [290923]
- KUL [GOA/10/09 MaNet]
- OPTEC [CoE PFV/10/002]
- BIL12/11T
- FWO [G.0377.12, G.088114N]
- SBO POM [100031]
- IUAP [P7/19 DYSCO]
- [BIL12/11T]
- European Research Council (ERC) [290923] Funding Source: European Research Council (ERC)
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Because of several successful applications, indefinite kernels have attracted many research interests in recent years. This paper addresses indefinite learning in the framework of least squares support vector machines (LS-SVM). Unlike existing indefinite kernel learning methods, which usually involve non-convex problems, the indefinite LS-SVM is still easy to solve, but the kernel trick and primal-dual relationship for LS-SVM with a Mercer kernel is no longer valid. In this paper, we give a feature space interpretation for indefinite LS-SVM. In the same framework, kernel principal component analysis with an infinite kernel is discussed as well. In numerical experiments, LS-SVM with indefinite kernels for classification and kernel principal component analysis is evaluated. Its good performance together with the feature space interpretation given in this paper imply the potential use of indefinite LS-SVM in real applications. (C) 2016 Elsevier Inc. All rights reserved.
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