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 Frobenius 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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Acknowledgment
This work has been partially supported by the LabEx PERSYVAL-Lab (ANR-11-LABX-0025-01) funded by the French program “Investissement d’avenir” and the European Research Council, project CHESS 2012-ERC-AdG-320684.
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Bouchard, F., Malick, J., Congedo, M. (2017). Approximate Joint Diagonalization According to the Natural Riemannian Distance. In: Tichavský, P., Babaie-Zadeh, M., Michel, O., Thirion-Moreau, N. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2017. Lecture Notes in Computer Science(), vol 10169. Springer, Cham. https://doi.org/10.1007/978-3-319-53547-0_28
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DOI: https://doi.org/10.1007/978-3-319-53547-0_28
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