Approximate Joint Diagonalization within the Riemannian Geometry Framework

Florent Bouchard (1) , Louis Korczowski (1) , Jérôme Malick (2) , Marco Congedo (1)

1 GIPSA-VIBS - GIPSA - Vision and Brain Signal Processing
2 DAO - Données, Apprentissage et Optimisation

We consider the approximate joint diagonalization problem (AJD) related to the well known blind source separation (BSS) problem within the Riemannian geometry framework. We define a new manifold named special polar manifold equivalent to the set of full rank matrices with a unit determinant of their Gram matrix. The Riemannian trust-region optimization algorithm allows us to define a new method to solve the AJD problem. This method is compared to previously published NoJOB and UWEDGE algorithms by means of simulations and shows comparable performances. This Riemannian optimization approach thus shows promising results. Since it is also very flexible, it can be easily extended to block AJD or joint BSS.

Mots clés: Riemannian geometry; Riemannian optimization; approximate joint diagonalization; blind source separation; special polar manifold

Domaines: Traitement du signal et de l'image [eess.SP]

Florent Bouchard, Louis Korczowski, Jérôme Malick, Marco Congedo. Approximate Joint Diagonalization within the Riemannian Geometry Framework. EUSIPCO 2016 - 24th European Signal Processing Conference, Aug 2016, Budapest, Hungary. pp.210-214, ⟨10.1109/EUSIPCO.2016.7760240⟩. ⟨hal-01370052⟩