Independent Component Analysis: A exible non-linearity and decorrelating manifold approach

Independent Components Analysis nds a linear transformation to variables which are maximally statistically independent. We examine ICA and algorithms for nding the best transformation from the point of view of maximising the likelihood of the data. In particular, examine the way in which scaling of the unmixing matrix permits a \static" nonlinearity to adapt to various margninal densities. We demonstrate a new algorithm that uses generalised exponential functions to model the marginal densities and is able to separate densities with light tails. Numerical experiments show that the manifold of decorrelating matrices lies along the ridges of high-likelihood unmixing matrices in the space of all unmixing matrices. We show how to nd the optimum ICA matrix on the manifold of decorrelating matrices as an example use the algorithm to nd independent component basis vectors for an ensemble of portraits.