Whitening-Free Least-Squares Non-Gaussian Component Analysis

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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.

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