A novel dimension reduction procedure for searching non-gaussian subspaces.
Motoaki Kawanabe, Gilles Blanchard, Masashi Sugiyama, Vladimir Spokoiny and Klaus-Robert Müller
In: ICA 2006, 5-8 march 2006, Charleston, USA.
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 semiparametric 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.