L1-PCA signal subspace identification for non-sphered data under the ICA model

Principal component analysis (PCA) is an ubiquitous data compression and feature extraction technique in signal processing and machine learning. As compared with the classical L2-norm PCA, its L1-norm version offers increased robustness to outliers that are usually present in faulty data. Recently, L1-PCA was shown to perform source recovery when the observed data follow an independent component analysis (ICA) model. However, proof of this result requires the data to be sphered, i.e., to be preprocessed to constrain their covariance matrix to be the identity. The present contribution extends this result by relaxing the sphering assumption and allowing the data to have arbitrary covariance matrix. We prove that L1-PCA is indeed able to identify the mixing matrix columns associated with the strongest independent sources, thus performing signal subspace identification with improved robustness to outliers. Numerical experiments illustrate and confirm the theoretical findings.