On the Estimation of Entropy in the FastICA Algorithm

TL;DR

This paper critically examines the fastICA algorithm, revealing that its approximations can hinder pattern recognition in data, and emphasizes the need for caution when applying it.

Contribution

The paper provides both theoretical analysis and practical examples showing limitations of fastICA due to its approximations, highlighting potential pitfalls.

Findings

fastICA can fail to recognize clear data structures

The approximations in fastICA impact its effectiveness

Care is needed when applying fastICA to data

Abstract

The fastICA method is a popular dimension reduction technique used to reveal patterns in data. Here we show both theoretically and in practice that the approximations used in fastICA can result in patterns not being successfully recognised. We demonstrate this problem using a two-dimensional example where a clear structure is immediately visible to the naked eye, but where the projection chosen by fastICA fails to reveal this structure. This implies that care is needed when applying fastICA. We discuss how the problem arises and how it is intrinsically connected to the approximations that form the basis of the computational efficiency of fastICA.