Non-Gaussian Component Analysis: Testing the Dimension of the Signal Subspace

Abstract

Dimension reduction is a common strategy in multivariate data analysis which seeks a subspace which contains all interesting features needed for the subsequent analysis. Non-Gaussian component analysis attempts for this purpose to divide the data into a non-Gaussian part, the signal, and a Gaussian part, the noise. We will show that the simultaneous use of two scatter functionals can be used for this purpose and suggest a bootstrap test to test the dimension of the non-Gaussian subspace. Sequential application of the test can then for example be used to estimate the signal dimension.

ICS for multivariate functional anomaly detection with applications to predictive maintenance and quality control

“…ICS can be considered in this case to be non-Gaussian component analysis (NGCA) ( Nordhausen et al, 2017 ), where we assume that all of the outliers lie in a subspace that obviously is non-Gaussian and that this subspace is independent from the uncontaminated Gaussian subspace. Tyler et al (2009) ; Nordhausen et al (2017) ; Radojicic and Nordhausen (2020) then show that the eigenvalues d 1 , . .…”