Hierarchical and Parallel Models for Non-stationary IndependentComponent AnalysisC
We review the limited progress which has been made to date on the problem of identiication of independent sourcess from a linear mixture of such sources when the sources are non-stationary. In particular, we investigate the model of Matsuoka et al and show that their claim to have a linear model is in fact not correct. We demonstrate a hierarchical feedforward model which is more linear than that of Matsuoka et al. An extension which allows for parallel identiication of independent sources is also demonstrated. 1 Introduction Separation of a single signal from a mixture of source signals is an area of some current research interest. Most intensive work is being carried out on the problem of the blind separation of source signals-so called because we assume no prior knowledge of either the signals or the mixture model which created the observed mixture. This problem is closely related to that known as Independent Component Analysis, the analysis of independent components which together make up a set of observations. The problem of demixing linear mixtures has been largely solved using a number of often related, perhaps sometimes equivalent, techniques. The linear problem may be stated as: consider a set of independent zero mean signals, s = fs 1 ; s 2 at most one of which may be Gaussian. Let there be a non-singular mixing matrix A which is used to create observations, x = fx 1 ; x 2 ; :::; x m g = As. It is often assumed that A is square or at least that m n. Then the problem is to nd that matrix W such that y = Wx = s, up to a permutation and scaling. Attention is now shifting to more diicult problems such as those associated with non-linear mixing or those associated with non-stationarity. We will concentrate on the latter and consider the problem of linear mixtures of non-stationary signals. There has been relatively little research published in this area compared with the rather large volume of research published over the last two years on linear ICA. We will look at the model of Matsuoka et al 2] in some detail below. Other work includes that of Parga and Nadal 4] who extend the algebraic method of diagonalising both the covariance matrix C 0 = E(s i (t)s j (t)) and its time delayed second order equivalent, C = E(s i (t)s …