Faster ICA under orthogonal constraint
This work addresses a computational bottleneck for researchers and practitioners using ICA in observational sciences, offering an incremental improvement in speed and robustness over existing methods.
The paper tackles the problem of slow convergence in Independent Component Analysis (ICA) by introducing Picard-O, a preconditioned L-BFGS method over orthogonal matrices, which achieves faster and more robust separation of super- and sub-Gaussian signals compared to FastICA, as demonstrated through numerical experiments on real data.
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.