A Parcellation Based Nonparametric Algorithm for Independent Component Analysis with Application to fMRI Data

Independent Component analysis (ICA) is a widely used technique for separating signals that have been mixed together. In this manuscript, we propose a novel ICA algorithm using density estimation and maximum likelihood, where the densities of the signals are estimated via p-spline based histogram smoothing and the mixing matrix is simultaneously estimated using an optimization algorithm. The algorithm is exceedingly simple, easy to implement and blind to the underlying distributions of the source signals. To relax the identically distributed assumption in the density function, a modified algorithm is proposed to allow for different density functions on different regions. The performance of the proposed algorithm is evaluated in different simulation settings. For illustration, the algorithm is applied to a research investigation with a large collection of resting state fMRI datasets. The results show that the algorithm successfully recovers the established brain networks.