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Conference Paper

A Subspace Kernel for Nonlinear Feature Extraction

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http://pubman.mpdl.mpg.de/cone/persons/resource/persons84321

Wu,  M
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83909

Farquhar,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Wu, M., & Farquhar, J. (2007). A Subspace Kernel for Nonlinear Feature Extraction. Proceedings of the 20th International Joint Conference on Artificial Intelligence (IJCAI-07), 1125-1130.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-CEF7-9
Abstract
Kernel based nonlinear Feature Extraction (KFE) or dimensionality reduction is a widely used pre-processing step in pattern classification and data mining tasks. Given a positive definite kernel function, it is well known that the input data are implicitly mapped to a feature space with usually very high dimensionality. The goal of KFE is to find a low dimensional subspace of this feature space, which retains most of the information needed for classification or data analysis. In this paper, we propose a subspace kernel based on which the feature extraction problem is transformed to a kernel parameter learning problem. The key observation is that when projecting data into a low dimensional subspace of the feature space, the parameters that are used for describing this subspace can be regarded as the parameters of the kernel function between the projected data. Therefore current kernel parameter learning methods can be adapted to optimize this parameterized kernel function. Experimental results are provided to validate the effectiveness of the proposed approach.