Fast and robust fixed-point algorithms for independent component analysis

Independent component analysis (ICA) is a statistical method for transformi ng an observed multidimensional random vector into components that are stat istically as independent from each other as possible. In this paper, we use a combination of two different approaches for linear ICA: Comon's informat ion-theoretic approach and the projection pursuit approach. Using maximum e ntropy approximations of differential entropy, we introduce a family of new contrast (objective) functions for ICA. These contrast functions enable bo th the estimation of the whole decomposition by minimizing mutual informati on, and estimation of individual independent components as projection pursu it directions, The statistical properties of the estimators based on such c ontrast functions are analyzed under the assumption of the linear mixture m odel, and it is shown how to choose contrast functions that are robust and/ or of minimum variance, Finally, we introduce simple fixed-point algorithms for practical optimization of the contrast functions. These algorithms opt imize the contrast functions very fast and reliably.