Non-Gaussian Component Analysis: a Semiparametric Framework for Linear Dimension Reduction
Gilles Blanchard, Motoaki Kawanabe, Masashi Sugiyama, Vladimir Spokoiny and Klaus-Robert Müller
In: NIPS 2005, 5-8 Dec 2005, Vancouver, Canada.

Abstract

We propose a new {\em linear} method for dimension reduction to identify non-Gaussian components in high dimensional data. Our method, NGCA (Non-Gaussian Component Analysis), uses a very general semiparametric framework. In contrast to existing projection methods we define what is {\em un}interesting (Gaussian): by projecting out uninterestingness we can estimate the relevant non-Gaussian subspace. We show that the estimation error of finding the non-Gaussian components tends to zero at a parametric rate. Once NGCA components are identified and extracted, various tasks can be applied in the data analysis process, say, data visualization, clustering, denoising or classification. A numerical study demonstrates the usefulness of our method.

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