Fixed-point algorithms for constrained ICA and their applications in fMRI data analysis

Constrained independent component analysis (CICA) eliminates the order ambiguity of standard ICA by incorporating prior information into the learning process to sort the components intrinsically. However, the original CICA (OCICA) and its variants depend on a learning rate, which is not easy to be tuned for various applications. To solve this problem, two learning-rate-free CICA algorithms were derived in this paper using the fixed-point learning concept. A complete stability analysis was provided for the proposed methods, which also made a correction to the stability analysis given to OCICA. Variations for adding constraints either to the components or to the associated time courses were derived too. Using synthetic data, the proposed methods yielded a better stability and a better source separation quality in terms of higher signal-to-noise-ratio and smaller performance index than OCICA. For the artificially generated brain activations, the new CICAs demonstrated a better sensitivity/specificity performance than standard univariate general linear model (GLM) and standard ICA. Original CICA showed a similar sensitivity/specificity gain but failed to converge for several times. Using functional magnetic resonance imaging (fMRI) data acquired with a well-characterized sensorimotor task, the proposed CICAs yielded better sensitivity than OCICA, standard ICA and GLM in all the target functional regions in terms of either higher t values or larger suprathreshold cluster extensions using the same significance threshold. In addition, they were more stable than OCICA and standard ICA for analyzing the sensorimotor fMRI data.