Ground Metric Learning on Graphs
| Autor: | David Coeurjolly, Gabriel Peyré, Matthieu Heitz, Nicolas Bonneel, Marco Cuturi |
|---|---|
| Přispěvatelé: | Geometry Processing and Constrained Optimization (M2DisCo), Laboratoire d'InfoRmatique en Image et Systèmes d'information (LIRIS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-École Centrale de Lyon (ECL), Université de Lyon-Université Lumière - Lyon 2 (UL2)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Université Lumière - Lyon 2 (UL2), Origami (Origami), Modélisation Géométrique, Géométrie Algorithmique, Fractales (GeoMod), Google Brain, Paris, Département de Mathématiques et Applications - ENS Paris (DMA), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), European Project: H2020 724175, NORIA, Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Lumière - Lyon 2 (UL2)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS-PSL), ANR-16-CE23-0009, Agence Nationale de la Recherche |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Statistics and Probability Computer Science - Machine Learning Geodesic Computer science Parameterized complexity Machine Learning (stat.ML) 02 engineering and technology Machine Learning (cs.LG) Computer Science - Graphics [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] Statistics - Machine Learning FOS: Mathematics 0202 electrical engineering electronic engineering information engineering Mathematics - Optimization and Control Applied Mathematics Inverse problem Condensed Matter Physics Graphics (cs.GR) Graph Optimization and Control (math.OC) Modeling and Simulation Probability distribution 020201 artificial intelligence & image processing Geometry and Topology Computer Vision and Pattern Recognition Algorithm |
| Zdroj: | Journal of Mathematical Imaging and Vision Journal of Mathematical Imaging and Vision, Springer Verlag, 2021, 63, pp.89-107 Journal of Mathematical Imaging and Vision, Springer Verlag, 2021, 63, pp.89-107. ⟨10.1007/s10851-020-00996-z⟩ Journal of Mathematical Imaging and Vision, 2021, 63 (1), pp.89-107. ⟨10.1007/s10851-020-00996-z⟩ J Math Imaging Vis |
| ISSN: | 0924-9907 1573-7683 |
| Popis: | Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is suitably chosen. Selecting it adaptively and algorithmically from prior knowledge, the so-called ground metric learning GML) problem, has therefore appeared in various settings. We consider it in this paper when the learned metric is constrained to be a geodesic distance on a graph that supports the measures of interest. This imposes a rich structure for candidate metrics, but also enables far more efficient learning procedures when compared to a direct optimization over the space of all metric matrices. We use this setting to tackle an inverse problem stemming from the observation of a density evolving with time: we seek a graph ground metric such that the OT interpolation between the starting and ending densities that result from that ground metric agrees with the observed evolution. This OT dynamic framework is relevant to model natural phenomena exhibiting displacements of mass, such as for instance the evolution of the color palette induced by the modification of lighting and materials. Fixed sign of gradient |
| Databáze: | OpenAIRE |
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