TY  - JOUR
A1  - Blanchard, Gilles
A1  - Kawanabe, Motoaki
A1  - Sugiyama, Masashi
A1  - Spokoiny, Vladimir G.
A1  - Müller, Klaus-Robert
T1  - In search of non-Gaussian components of a high-dimensional distribution
N2  - 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
Y1  - 2006
UR  - http://portal.acm.org/affiliated/jmlr/
SN  - 1532-4435
ER  - 
TY  - JOUR
A1  - Kawanabe, Motoaki
A1  - Blanchard, Gilles
A1  - Sugiyama, Masashi
A1  - Spokoiny, Vladimir G.
A1  - Müller, Klaus-Robert
T1  - A novel dimension reduction procedure for searching non-Gaussian subspaces
N2  - In this article, we consider high-dimensional data which contains a low-dimensional non-Gaussian structure contaminated with Gaussian noise and propose a new linear method to identify the non-Gaussian subspace. Our method NGCA (Non-Gaussian Component Analysis) is based on a very general semi-parametric framework and has a theoretical guarantee that the estimation error of finding the non-Gaussian components tends to zero at a parametric rate. NGCA can be used not only as preprocessing for ICA, but also for extracting and visualizing more general structures like clusters. A numerical study demonstrates the usefulness of our method
Y1  - 2006
UR  - http://www.springerlink.com/content/105633/
U6  - https://doi.org/10.1007/11679363_19
SN  - 0302-9743
ER  -