Independent component analysis (ICA) finds a linear transformation to variables that are maximally statistically independent. We examine ICA and algorithms for finding the best transformation from the point of view of maximizing the likelihood of the data. In particular, we discuss the way in which scaling of the unmixing matrix permits a "static" nonlinearity to adapt to various marginal densities. We demonstrate a new algorithm that uses generalized exponential functions to model the marginal densities and is able to separate densities with light tails.
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