Approximate Joint Diagonalization According to the Natural Riemannian Distance
| Autor: | Jérôme Malick, Marco Congedo, Florent Bouchard |
|---|---|
| Přispěvatelé: | GIPSA - Vision and Brain Signal Processing (GIPSA-VIBS), Département Images et Signal (GIPSA-DIS), Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Grenoble Images Parole Signal Automatique (GIPSA-lab ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut Polytechnique de Grenoble - Grenoble Institute of Technology-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Données, Apprentissage et Optimisation (DAO), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), European Project: 320684,EC:FP7:ERC,ERC-2012-ADG_20120216,CHESS(2013) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Optimization problem
Diagonal form Hermitian positive definite matrices Matrix norm 020206 networking & telecommunications 010103 numerical & computational mathematics 02 engineering and technology Positive-definite matrix Riemannian geometry Riemannian optimization 01 natural sciences Hermitian matrix Orthogonal diagonalization Combinatorics symbols.namesake approximate joint diagonalization 0202 electrical engineering electronic engineering information engineering symbols Applied mathematics 0101 mathematics Divergence (statistics) [SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing Mathematics |
| Zdroj: | Lecture Notes in Computer Science LVA/ICA 2017-13th International Conference on Latent Variable Analysis and Signal Separation LVA/ICA 2017-13th International Conference on Latent Variable Analysis and Signal Separation, Feb 2017, Grenoble, France. pp.290-299, ⟨10.1007/978-3-319-53547-0_28⟩ Latent Variable Analysis and Signal Separation ISBN: 9783319535463 LVA/ICA |
| DOI: | 10.1007/978-3-319-53547-0_28⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|