Independent component analysis (ICA) is a statistical method for
transforming an observed multidimensional random vector into
components that are statistically as independent from each other as
possible. In this paper, we use a combination of two
different approaches for linear ICA:
Comon's information-theoretic approach
and the projection pursuit approach.
Using maximum entropy approximations of differential entropy, we
introduce a family of new contrast
(objective) functions for ICA.
These contrast functions enable both the estimation of the whole
decomposition by minimizing mutual information, and estimation of
individual independent components as projection pursuit directions.
The statistical properties
of the estimators based on such contrast functions are
analyzed under the assumption of the linear mixture model,
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 optimize the contrast functions very fast
and reliably.
