Comparison between principal component analysis and independent component analysis in electroencephalograms modelling

Principal Component Analysis (PCA) is a classical technique in statistical data analysis, feature extraction and data reduction, aiming at explaining observed signals as a linear combination of orthogonal principal components. Independent Component Analysis (ICA) is a technique of array processing and data analysis, aiming at recovering unobserved signals or 'sources' from observed mixtures, exploiting only the assumption of mutual independence between the signals. The separation of the sources by ICA has great potential in applications such as the separation of sound signals (like voices mixed in simultaneous multiple records, for example), in telecommunication or in the treatment of medical signals. However, ICA is not yet often used by statisticians. In this paper, we shall present ICA in a statistical framework and compare this method with PCA for electroencephalograms (EEG) analysis. We shall see that ICA provides a more useful data representation than PCA, for instance, for the representation of a particular characteristic of the EEG named event-related potential (ERP).