Modelling with independent components

Independent Component Analysis (ICA) is a computational technique for identifying hidden statistically independent sources from multivariate data. In its basic form, ICA decomposes a 2D data matrix (e.g. time × voxels) into separate components that have distinct characteristics. In FMRI it is used to identify hidden FMRI signals (such as activations). Since the first application of ICA to Functional Magnetic Resonance Imaging (FMRI) in 1998, this technique has developed into a powerful tool for data exploration in cognitive and clinical neurosciences. In this contribution to the commemorative issue 20 years of FMRI I will briefly describe the basic principles behind ICA, discuss the probabilistic extension to ICA and touch on what I think are some of the most notorious loose ends. Further, I will describe some of the most powerful 'killer' applications and finally share some thoughts on where I believe the most promising future developments will lie.