Homeopathic ICA: A simple approach to expand the use of independent component analysis (ICA)

Abstract

Independent component analysis (ICA) is an increasingly popular method to resolve complex data sets, such as chemical image data, into images and their associated spectra. Unfortunately, the pre-requisite of statistical independence severely limits the application of ICA. In this paper we will show that, for a certain class of data, increasing the sparsity of a data set increases the independence of components, which enables the successful application of ICA. The sparsity can be increased by simply adding zeros to the data set or by applying a Haar-wavelet transform. ICA will be explained using simple numerical examples and actual data sets obtained by energy dispersive X-ray spectrometry (EDS) of a Cu–Ni diffusion couple and a braze interface.