Eliminating indeterminacy in ICA

This paper presents a method to eliminate inherent indeterminacy of permutation and dilation existing in the classical independent component analysis (ICA). The method incorporates additional requirements or a priori information as constraints in the ICA contrast function. We illustrate how this approach sorts independent components (ICs) according to some statistic and normalizes the demixing matrix or the energies of separated ICs. With some prior knowledge, the algorithm is able to identify and extract the original sources perfectly from their mixtures. The experiments with simulated random signals and real audio signals demonstrate the versatility of eliminating indeterminacy in the ICA. An application separating functional magnetic resonance imaging (fMRI) data into activation maps ordered according to their sparseness is also presented. c © 2002 Elsevier Science B.V. All rights reserved.