Adaptive Non-linearities, the Decorrelating Manifold and Non-stationary Mixing for Ica

Independent Components Analysis nds a linear transformation to variables which are maximally statistically independent. We examine ICA from the point of view of maximising the likelihood of the data. We elucidate how scaling of the unmixing matrix permits a \static" nonlinearity to adapt to various marginal densities and we demonstrate a new algorithm that uses generalised exponentials functions to model the marginal densities and is able to separate densities with light tails. We characterise decorrelating matrices and numerically show that the manifold of decorrelating matrices lies along the ridges of high-likelihood separating matrices in the space of all unmixing matrices. An algorithm to nd the optimum ICA matrix on the manifold of decorrelating matrices is presented. We show how a state-space formulation of ICA permits simultaneous learning of non-stationary mixing matrices and stationary sources.