Non-Gaussian Component Analysis: A Semi-Parametric Framework for Linear Dimension Reduction
Abstract
We propose a new linear method for dimension reduction to identify nonGaussian components in high dimensional data. Our method, NGCA (non-Gaussian component analysis), uses a very general semi-parametric framework. In contrast to existing projection methods we define what is uninteresting (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, like data visualization, clustering, denoising or classification. A numerical study demonstrates the usefulness of our method.
Cite
Text
Blanchard et al. "Non-Gaussian Component Analysis: A Semi-Parametric Framework for Linear Dimension Reduction." Neural Information Processing Systems, 2005.Markdown
[Blanchard et al. "Non-Gaussian Component Analysis: A Semi-Parametric Framework for Linear Dimension Reduction." Neural Information Processing Systems, 2005.](https://mlanthology.org/neurips/2005/blanchard2005neurips-nongaussian/)BibTeX
@inproceedings{blanchard2005neurips-nongaussian,
title = {{Non-Gaussian Component Analysis: A Semi-Parametric Framework for Linear Dimension Reduction}},
author = {Blanchard, Gilles and Sugiyama, Masashi and Kawanabe, Motoaki and Spokoiny, Vladimir and Müller, Klaus-Robert},
booktitle = {Neural Information Processing Systems},
year = {2005},
pages = {131-138},
url = {https://mlanthology.org/neurips/2005/blanchard2005neurips-nongaussian/}
}