Hidden Markov independent components for biosignal analysis

Much research in unsupervised learning builds on the idea of using generative models for modelling the probability distribution over a set of observations. These approaches suggest that powerful new data analysis tools may be derived by combining existing models using a probabilistic generative framework. We follow this approach and combine hidden Markov models (HMMs), independent component analysis (ICA) and generalised autoregressive models (GAR) into a single generative model for the analysis of nonstationary multivariate time series. Our motivation for this work derives from our desire to analyse biomedical signals which are known to be highly non-stationary. Moreover, in signals such as the electroencephalogram (EEG), for example, we have a number of sensors (electrodes) which detect signals emanating from a number of cortical sources via an unknown mixing process. This naturally fits an ICA approach which is further enhanced by noting that the sources themselves are characterised by their dynamic content. This leads us to the use of generalised autoregressive (GAR) processes to model the sources.