On the Link Between L1-PCA and ICA - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue IEEE Transactions on Pattern Analysis and Machine Intelligence Année : 2017

On the Link Between L1-PCA and ICA

Résumé

Principal component analysis (PCA) based on L1- norm maximization is an emerging technique that has drawn growing interest in the signal processing and machine learning research communities, especially due to its robustness to outliers. The present work proves that L1-norm PCA can perform independent component analysis (ICA) under the whitening assumption. However, when the source probability distributions fulfil certain conditions, the L1-norm criterion needs to be minimized rather than maximized, which can be accomplished by simple modifications on existing optimal algorithms for L1- PCA. If the sources have symmetric distributions, we show in addition that L1-PCA is linked to kurtosis optimization. A number of numerical experiments illustrate the theoretical results and analyze the comparative performance of different algorithms for ICA via L1-PCA. Although our analysis is asymptotic in the sample size, this equivalence opens interesting new perspectives for performing ICA using optimal algorithms for L1-PCA with guaranteed global convergence while inheriting the increased robustness to outliers of the L1-norm criterion.
Fichier non déposé

Dates et versions

hal-01302690 , version 1 (14-04-2016)

Identifiants

Citer

Rubén Martín-Clemente, Vicente Zarzoso. On the Link Between L1-PCA and ICA. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, ⟨10.1109/TPAMI.2016.2557797⟩. ⟨hal-01302690⟩
217 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More