  Independent component selection (ICS), introduced by Tyler et al. (2009, JRSS
B), is a powerful tool to find potentially interesting projections of
multivariate data. In some cases, some of the projections proposed by ICS come
close to really interesting ones, but little deviations can result in a blurred
view which does not reveal the feature (e.g. a clustering) which would
otherwise be clearly visible. To remedy this problem, we propose an automated
and localized version of projection pursuit (PP), cf. Huber (1985, Ann.
Statist.}. Precisely, our local search is based on gradient descent applied to
estimated differential entropy as a function of the projection matrix.
