PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A new algorithm of non-Gaussian component analysis with radial kernel functions
Motoaki Kawanabe, Gilles Blanchard, Masahi Sugiyama and Klaus-Robert Müller
Annals of the Institute of Statistical Mathematics Volume 59, Number 1, pp. 57-75, 2007.

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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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2536
Deposited By:Gilles Blanchard
Deposited On:22 November 2006