HIDDEN MARKOV INDEPENDENT COMPONENTS FOR BIOSIGNAL ANALYSIS William D. Penny , Stephen J. Roberts and Richard M. Everson 1. Department of Engineering Science, University of Oxford, UK. 2. Department of Computer Science, University of Exeter, UK. INTRODUCTION Much recent research in unsupervised learn- ing builds on the idea of using generative models for modelling the probability distri- bution over a set of observations. These ap- proaches suggest that powerful new data anal- ysis tools may be derived by combining exist- ing models using a probabilistic ‘generative’ framework. In this paper, we follow this ap- proach 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 se- ries. Our motivation for this work derives from our desire to analyse biomedical signals which are known to be highly non-stationary. More- over, in signals such as the electroencephalo- gram (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 nat- urally fits an ICA approach which is further enhanced by noting that the sources them- selves are characterised by their dynamic con- tent. This leads us to the use of Generalised Autoregressive (GAR) processes to model the sources. The overall generative model is shown in Figure 1. Email: wpenny@robots.ox.ac.uk, Fax: +44 (0)1865 273908. K=1 V1, c1 K=2 V2, c2 Figure 1: Generative model. At time the state of the HMM is . Associated with each state is a mixing matrix and a set of GAR coefficients, , one for each source . The ob- servations are generated as and the th source is generated as where is a vector of previous source values and is non-Gaussian noise. THEORY Hidden Markov Models The HMM model has discrete hidden states, an initial state probability vector , a state transition matrix with entries and an observation density, , for data point and hidden state . The pa- rameters of the observation model (which in this paper, we consider to be an ICA model) are concatenated into the parameter set . The parameters of the HMM, as a whole, 1