Whitening-Free Least-Squares Non-Gaussian Component Analysis
This is an incremental improvement for researchers in unsupervised dimension reduction, addressing a specific bottleneck in high-dimensional data analysis.
The paper tackles the unreliability of least-squares non-Gaussian component analysis (LSNGCA) when data covariance is ill-conditioned by proposing a whitening-free method, and experimentally shows its superiority.
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.