Shared and specific independent components analysis for between-group comparison

Independent component analysis (ICA) has been extensively used in individual and within-group data sets in real-world applications, but how can it be employed in a between-groups or conditions design? Here, we propose a new method to embed group membership information into the FastICA algorithm so as to extract components that are either shared between groups or specific to one or a subset of groups. The proposed algorithm is designed to automatically extract the pattern of differences between different experimental groups or conditions. A new constraint is added to the FastICA algorithm to simultaneously deal with the data of multiple groups in a single ICA run. This cost function restricts the specific components of one group to be orthogonal to the subspace spanned by the data of the other groups. As a result of performing a single ICA on the aggregate data of several experimental groups, the entire variability of data sets is used to extract the shared components. The results of simulations show that the proposed algorithm performs better than the regular method in both the reconstruction of the source signals and classification of shared and specific components. Also, the sensitivity to detect variations in the amplitude of shared components across groups is enhanced. A rigorous proof of convergence is provided for the proposed iterative algorithm. Thus, this algorithm is guaranteed to extract and classify shared and specific independent components across different experimental groups and conditions in a systematic way.