(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2006) Blanchard, Gilles; Kawanabe, Motoaki; Sugiyama, Masashi; Spokoiny, Vladimir; Müller, Klaus-Robert
Finding non-Gaussian components of high-dimensional data is an
important preprocessing step for efficient information processing. This
article proposes a new em 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 essentially based
on the fact that we can construct a linear operator which, to any arbitrary
nonlinear (smooth) function, associates a vector which belongs 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
