Refining Invariant Coordinate Selection via Local Projection Pursuit

Invariant coordinate selection (ICS), introduced by Tyler et al. (J. Roy. Stat. Soc. B 71(3):549–592, 2009), 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 (Ann. Stat. 13(2):435–525, 1985). Precisely, our local search is based on gradient descent applied to estimated differential entropy as a function of the projection matrix.