A new algorithm of non-Gaussian component analysis with radial kernel functions |
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Authors: | Motoaki Kawanabe Masashi Sugiyama Gilles Blanchard Klaus-Robert Müller |
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Affiliation: | (1) Fraunhofer FIRST.IDA, Kekuléstr. 7, 12489 Berlin, Germany;(2) Department of Computer Science, Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8552, Japan;(3) CNRS, Laboratoire de mathématiques, Université Paris-Sud, 91405 Orsay, France;(4) Department of Computer Science, Technical University of Berlin, Franklinstr. 28/29, 10587 Berlin, Germany |
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Abstract: | We consider high-dimensional data which contains a linear low-dimensional non-Gaussian structure contaminated with Gaussian noise, and discuss a method to identify this non-Gaussian subspace. For this problem, we provided in our previous work a very general semi-parametric framework called non-Gaussian component analysis (NGCA). NGCA has a uniform probabilistic bound on the error of finding the non-Gaussian components and within this framework, we presented an efficient NGCA algorithm called Multi-index Projection Pursuit. The algorithm is justified as an extension of the ordinary projection pursuit (PP) methods and is shown to outperform PP particularly when the data has complicated non-Gaussian structure. However, it turns out that multi-index PP is not optimal in the context of NGCA. In this article, we therefore develop an alternative algorithm called iterative metric adaptation for radial kernel functions (IMAK), which is theoretically better justifiable within the NGCA framework. We demonstrate that the new algorithm tends to outperform existing methods through numerical examples. |
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Keywords: | Linear dimension reduction Non-Gaussian subspace Projection pursuit Semiparametric model Stein’ s identity |
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