Whitening-Free Least-Squares Non-Gaussian Component Analysis

Hiroaki Shiino; Hiroaki Sasaki; Gang Niu; Masashi Sugiyama

Whitening-Free Least-Squares Non-Gaussian Component Analysis

Hiroaki Shiino, Hiroaki Sasaki, Gang Niu, Masashi Sugiyama ;

Proceedings of the Ninth Asian Conference on Machine Learning, PMLR 77:375-390, 2017.

Abstract

\emphNon-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian “signals” from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of \emphprojection pursuit (PP) and \emphindependent component analysis (ICA) to multi-dimensional and dependent non-Gaussian components. Indeed, seminal approaches to NGCA are based on PP and ICA. Recently, a novel NGCA approach called \emphleast-squares NGCA (LSNGCA) has been developed, which gives a solution analytically through least-squares estimation of \emphlog-density gradients and eigendecomposition. However, since \emphpre-whitening of data is involved in LSNGCA, it performs unreliably when the data covariance matrix is ill-conditioned, which is often the case in high-dimensional data analysis. In this paper, we propose a \emphwhitening-free variant of LSNGCA and experimentally demonstrate its superiority.

Related Material

@InProceedings{pmlr-v77-shiino17a, title = {Whitening-Free Least-Squares Non-Gaussian Component Analysis}, author = {Hiroaki Shiino and Hiroaki Sasaki and Gang Niu and Masashi Sugiyama}, booktitle = {Proceedings of the Ninth Asian Conference on Machine Learning}, pages = {375--390}, year = {2017}, editor = {Min-Ling Zhang and Yung-Kyun Noh}, volume = {77}, series = {Proceedings of Machine Learning Research}, address = {}, month = {15--17 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v77/shiino17a/shiino17a.pdf}, url = {http://proceedings.mlr.press/v77/shiino17a.html}, abstract = {\emphNon-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian “signals” from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of \emphprojection pursuit (PP) and \emphindependent component analysis (ICA) to multi-dimensional and dependent non-Gaussian components. Indeed, seminal approaches to NGCA are based on PP and ICA. Recently, a novel NGCA approach called \emphleast-squares NGCA (LSNGCA) has been developed, which gives a solution analytically through least-squares estimation of \emphlog-density gradients and eigendecomposition. However, since \emphpre-whitening of data is involved in LSNGCA, it performs unreliably when the data covariance matrix is ill-conditioned, which is often the case in high-dimensional data analysis. In this paper, we propose a \emphwhitening-free variant of LSNGCA and experimentally demonstrate its superiority.} }

%0 Conference Paper %T Whitening-Free Least-Squares Non-Gaussian Component Analysis %A Hiroaki Shiino %A Hiroaki Sasaki %A Gang Niu %A Masashi Sugiyama %B Proceedings of the Ninth Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Min-Ling Zhang %E Yung-Kyun Noh %F pmlr-v77-shiino17a %I PMLR %J Proceedings of Machine Learning Research %P 375--390 %U http://proceedings.mlr.press %V 77 %W PMLR %X \emphNon-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian “signals” from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of \emphprojection pursuit (PP) and \emphindependent component analysis (ICA) to multi-dimensional and dependent non-Gaussian components. Indeed, seminal approaches to NGCA are based on PP and ICA. Recently, a novel NGCA approach called \emphleast-squares NGCA (LSNGCA) has been developed, which gives a solution analytically through least-squares estimation of \emphlog-density gradients and eigendecomposition. However, since \emphpre-whitening of data is involved in LSNGCA, it performs unreliably when the data covariance matrix is ill-conditioned, which is often the case in high-dimensional data analysis. In this paper, we propose a \emphwhitening-free variant of LSNGCA and experimentally demonstrate its superiority.

Shiino, H., Sasaki, H., Niu, G. & Sugiyama, M.. (2017). Whitening-Free Least-Squares Non-Gaussian Component Analysis. Proceedings of the Ninth Asian Conference on Machine Learning, in PMLR 77:375-390