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.