ICA, kernel methods and nonnegativity: New paradigms for dynamical component analysis of fMRI data

Exploratory data–driven techniques or Blind Source Separation (BSS) methods in fMRI data analysis are neither based on explicit signal models nor on the a priori knowledge of the underlying physiological process. One such method is Independent Component Analysis (ICA) which searches for stochastically independent signals within the multivariate observations. Recently, a new paradigm in ICA emerged, that of implementing kernel–based measures of dependence between the components. The Kernel nonlinear ICA overcomes the restrictions of linearity of the mixing process encountered with PCA and ICA and implements thus a nonlinear blind source separation technique. For the fMRI data, a comparative quantitative evaluation between Kernel nonlinear ICA with different kernels, NMF and some other BSS algorithms was performed. The comparative results were evaluated by (1) task– related activation maps, (2) associated time–courses and (3) ROC study. The most important findings in this paper are: (1) Kernel nonlinear ICA and Sparse NMF able to identify signal components with high correlation to the fMRI stimulus, and (2) Kernel nonlinear ICA with a Gaussian kernel is comparable to standard ICA algorithms and even yield more separated results.