Hidden Markov Independent Component Analysis

Abstract

We propose a generative model for the analysis of non-stationary multivariate time series. The model uses a hidden Markov process to switch between independent component models where the components themselves are modelled as generalised autoregressive processes. The model is demonstrated on synthetic problems and EEG data. Much recent research in unsupervised learning [17,20] builds on the idea of using generative models [8] 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. In this paper, we follow this approach and combine hidden Markov models (HMM), Independent Component Analysis (ICA) and generalised autoregressive models (GAR) into a single generative model for the analysis of non-stationary multivariate time series.