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In search of non-Gaussian components of a high-dimensional distribution

  • Finding non-Gaussian components of high-dimensional data is an important preprocessing step for efficient information processing. This article proposes a new linear method to identify the '' non-Gaussian subspace '' within a very general semi-parametric framework. Our proposed method, called NGCA (non-Gaussian component analysis), is based on a linear operator which, to any arbitrary nonlinear (smooth) function, associates a vector belonging to the low dimensional non-Gaussian target subspace, up to an estimation error. By applying this operator to a family of different nonlinear functions, one obtains a family of different vectors lying in a vicinity of the target space. As a final step, the target space itself is estimated by applying PCA to this family of vectors. We show that this procedure is consistent in the sense that the estimaton error tends to zero at a parametric rate, uniformly over the family, Numerical examples demonstrate the usefulness of our method

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Metadaten
Author:Gilles BlanchardGND, Motoaki Kawanabe, Masashi Sugiyama, Vladimir G. Spokoiny, Klaus-Robert Müller
URL:http://portal.acm.org/affiliated/jmlr/
ISSN:1532-4435
Document Type:Article
Language:English
Year of first Publication:2006
Year of Completion:2006
Release Date:2017/03/24
Source:Journal of machine learning research. - ISSN 1532-4435. - 7 (2006), S. 247 - 282
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Peer Review:Referiert
Publication Way:Open Access