Independent component analysis, a new concept?
Signal Processing - Special issue on higher order statistics
New approximations of differential entropy for independent component analysis and projection pursuit
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
High-order contrasts for independent component analysis
Neural Computation
Blind source separation-semiparametric statistical approach
IEEE Transactions on Signal Processing
Neural Computation
Separation of statistically dependent sources using an L2-distance non-Gaussianity measure
Signal Processing - Special section: Distributed source coding
Finite sample effects of the fast ICA algorithm
Neurocomputing
Reduction of noise due to systematic uncertainties in 113mIn SPECT imaging using information theory
Computers in Biology and Medicine
A survey of watermarking security
IWDW'05 Proceedings of the 4th international conference on Digital Watermarking
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Independent component analysis (ICA) is the decomposition of a random vector in linear components which are "as independent as possible." Here, "independence" should be understood in its strong statistical sense: it goes beyond (second-order) decorrelation and thus involves the non-Gaussianity of the data. The ideal measure of independence is the "mutual information" and is known to be related to the entropy of the components when the search for components is restricted to uncorrelated components. This paper explores the connections between mutual information, entropy and non-Gaussianity in a larger framework, without resorting to a somewhat arbitrary decorrelation constraint. A key result is that the mutual information can be decomposed, under linear transforms, as the sum of two terms: one term expressing the decorrelation of the components and one expressing their non-Gaussianity.Our results extend the previous understanding of these connections and explain them in the light of information geometry. We also describe the "local geometry" of ICA by re-expressing all our results via a Gram-Charlier expansion by which all quantities of interest are obtained in terms of cumulants.