New hypothesis test: a repropagation method to test the applicability of linear ICA to a given problem (highlighted by an EEG case study applied to epilepsy)

A new method, in the form of a hypothesis test, is presented that compares the eigenvalues of a multichannel data set to eigenvalues of a synthetic mixture. The synthetic mixture is created from a set of independent components (IC) that have been demixed from the original data. The IC are then repropagated from a fictitious source space to a set of fictitious sensors under independent component analysis (ICA) rules. The hypothesis is: if the real data has been formed in compliance with the ICA rules then its eigenvalues should be the same as the synthetic mixture formed from the repropagated IC. The hypothesis test is a general method and can be applied to any ICA problem. The first part of the publication demonstrates how the method works on known synthetically generated data. It also highlights how the technique can be extended for space-time processing. The second part of the publication shows how the method was used to validate whether or not ICA can be applied to biomedical data obtained from electroencephalograms (EEG) of four common cases of epilepsy.