Approximate Joint Diagonalization According to the Natural Riemannian Distance

Florent Bouchard 1 Jérôme Malick 2 Marco Congedo 1
1 GIPSA-VIBS - VIBS
GIPSA-DIS - Département Images et Signal
2 DAO - Données, Apprentissage et Optimisation
LJK - Laboratoire Jean Kuntzmann
Abstract : In this paper, we propose for the first time an approximate joint diagonalization (AJD) method based on the natural Riemannian distance of Hermitian positive definite matrices. We turn the AJD problem into an optimization problem with a Riemannian criterion and we developp a framework to optimize it. The originality of this criterion arises from the diagonal form it targets. We compare the performance of our Riemannian criterion to the classical ones based on the Frobe-nius norm and the log-det divergence, on both simulated data and real electroencephalographic (EEG) signals. Simulated data show that the Riemannian criterion is more accurate and allows faster convergence in terms of iterations. It also performs well on real data, suggesting that this new approach may be useful in other practical applications.
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13th International Conference on Latent Variable Analysis and Signal Separation (LVA-ICA 2017), Feb 2017, Grenoble, France. Lecture Notes in Computer Science, 10169, pp.290-299, 2017, Latent Variable Analysis and Signal Separation 13th International Conference, LVA/ICA 2017, Grenoble, France, February 21-23, 2017, Proceedings. 〈http://www.lva-ica-2017.com/〉. 〈10.1007/978-3-319-53547-0_28〉
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Florent Bouchard, Jérôme Malick, Marco Congedo. Approximate Joint Diagonalization According to the Natural Riemannian Distance. 13th International Conference on Latent Variable Analysis and Signal Separation (LVA-ICA 2017), Feb 2017, Grenoble, France. Lecture Notes in Computer Science, 10169, pp.290-299, 2017, Latent Variable Analysis and Signal Separation 13th International Conference, LVA/ICA 2017, Grenoble, France, February 21-23, 2017, Proceedings. 〈http://www.lva-ica-2017.com/〉. 〈10.1007/978-3-319-53547-0_28〉. 〈hal-01551813〉

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