Robust Geometric Metric Learning
| Autor: | Antoine Collas, Arnaud Breloy, Guillaume Ginolhac, Chengfang Ren, Jean-Philippe Ovarlez |
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| Přispěvatelé: | Sondra, CentraleSupélec, Université Paris-Saclay (SONDRA), ONERA-CentraleSupélec-Université Paris-Saclay, Laboratoire Energétique Mécanique Electromagnétisme (LEME), Université Paris Nanterre (UPN), Laboratoire d'Informatique, Systèmes, Traitement de l'Information et de la Connaissance (LISTIC), Université Savoie Mont Blanc (USMB [Université de Savoie] [Université de Chambéry]), DEMR, ONERA, Université Paris Saclay [Palaiseau], ONERA-Université Paris-Saclay |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | 30th European Signal Processing Conference, EUSIPCO 2022 30th European Signal Processing Conference, EUSIPCO 2022, Aug 2022, Belgrade, Serbia |
| Popis: | This paper proposes new algorithms for the metric learning problem. We start by noticing that several classical metric learning formulations from the literature can be viewed as modified covariance matrix estimation problems. Leveraging this point of view, a general approach, called Robust Geometric Metric Learning (RGML), is then studied. This method aims at simultaneously estimating the covariance matrix of each class while shrinking them towards their (unknown) barycenter. We focus on two specific costs functions: one associated with the Gaussian likelihood (RGML Gaussian), and one with Tyler's M -estimator (RGML Tyler). In both, the barycenter is defined with the Riemannian distance, which enjoys nice properties of geodesic convexity and affine invariance. The optimization is performed using the Riemannian geometry of symmetric positive definite matrices and its submanifold of unit determinant. Finally, the performance of RGML is asserted on real datasets. Strong performance is exhibited while being robust to mislabeled data. Published in EUSIPCO 2022. Best student paper award |
| Databáze: | OpenAIRE |
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