Information Maximization and Independent Component Analysis: Is There a Difference?

This article provides a detailed and rigorous analysis of the two commonly used methods for redundancy reduction: linear independent component analysis (ICA) posed as a direct minimization of a suitably chosen redundancy measure and information maximization (InfoMax) of a continuous stochastic signal transmitted through an appropriate nonlinear network. The article shows analytically that ICA based on the Kullback-Leibler information as a redundancy measure and InfoMax lead to the same solution if the parameterization of the output nonlinear functions in the latter method is sufficiently rich. Furthermore, this work discusses the alternative redundancy measures not based on the Kullback-Leibler information distance. The practical issues of applying ICA and InfoMax are also discussed and illustrated on the problem of extracting statistically independent factors from a linear, pixel-by-pixel mixture of images.