Whitening-Free Least-Squares Non-Gaussian Component Analysis

TL;DR

This paper introduces a whitening-free version of least-squares NGCA, improving robustness in high-dimensional data analysis where data covariance matrices are ill-conditioned.

Contribution

We propose a novel whitening-free LSNGCA method that overcomes the limitations of the original approach involving pre-whitening, enhancing reliability in high-dimensional settings.

Findings

The proposed method outperforms traditional LSNGCA in experiments.

Whitening-free LSNGCA is more stable with ill-conditioned covariance matrices.

Experimental results demonstrate the superiority of the new approach.

Abstract

Non-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 projection pursuit (PP) and independent 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 least-squares NGCA (LSNGCA) has been developed, which gives a solution analytically through least-squares estimation of log-density gradients and eigendecomposition. However, since pre-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 whitening-free LSNGCA method and experimentally demonstrate its superiority.