Refining Invariant Coordinate Selection via Local Projection Pursuit

TL;DR

This paper introduces a localized projection pursuit method that refines invariant coordinate selection by using gradient descent on estimated differential entropy, improving the detection of interesting data features.

Contribution

It develops an automated, localized approach to invariant coordinate selection by integrating gradient descent on differential entropy, enhancing feature detection in multivariate data.

Findings

Improved detection of clustering structures in data projections.

Enhanced visualization of interesting features with localized search.

Demonstrated effectiveness on simulated and real datasets.

Abstract

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.