Faster ICA under orthogonal constraint

TL;DR

This paper introduces Picard-O, a fast and robust optimization method for ICA that outperforms FastICA in speed and robustness by using a preconditioned L-BFGS approach on orthogonal matrices.

Contribution

The paper presents Picard-O, a novel optimization algorithm for ICA that improves speed and robustness over existing methods like FastICA.

Findings

Picard-O is faster than FastICA in numerical experiments.

Picard-O is more robust to data variations.

Both algorithms recover the same sources from data.

Abstract

Independent Component Analysis (ICA) is a technique for unsupervised exploration of multi-channel data widely used in observational sciences. In its classical form, ICA relies on modeling the data as a linear mixture of non-Gaussian independent sources. The problem can be seen as a likelihood maximization problem. We introduce Picard-O, a preconditioned L-BFGS strategy over the set of orthogonal matrices, which can quickly separate both super- and sub-Gaussian signals. It returns the same set of sources as the widely used FastICA algorithm. Through numerical experiments, we show that our method is faster and more robust than FastICA on real data.