Log-PCA versus Geodesic PCA of histograms in the Wasserstein space
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CAZELLES, Elsa | |
| hal.structure.identifier | Graduate School of Informatics [Kyoto] | |
| dc.contributor.author | SEGUY, Vivien | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BIGOT, Jérémie | |
| hal.structure.identifier | Centre de Recherche en Économie et Statistique [CREST] | |
| dc.contributor.author | CUTURI, Marco | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PAPADAKIS, Nicolas | |
| dc.date.accessioned | 2024-04-04T02:41:29Z | |
| dc.date.available | 2024-04-04T02:41:29Z | |
| dc.date.created | 2017-09 | |
| dc.date.issued | 2018 | |
| dc.identifier.issn | 1064-8275 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191155 | |
| dc.description.abstractEn | This paper is concerned by the statistical analysis of data sets whose elements are random histograms. For the purpose of learning principal modes of variation from such data, we consider the issue of computing the PCA of histograms with respect to the 2-Wasserstein distance between probability measures. To this end, we propose to compare the methods of log-PCA and geodesic PCA in the Wasserstein space as introduced by Bigot et al. (2015) and Seguy and Cuturi (2015). Geodesic PCA involves solving a non-convex optimization problem. To solve it approximately, we propose a novel forward-backward algorithm. This allows a detailed comparison between log-PCA and geodesic PCA of one-dimensional histograms, which we carry out using various data sets, and stress the benefits and drawbacks of each method. We extend these results for two-dimensional data and compare both methods in that setting. | |
| dc.description.sponsorship | Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010 | |
| dc.language.iso | en | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.subject.en | Non-convex optimization | |
| dc.subject.en | Wasserstein Space | |
| dc.subject.en | Geodesic Principal Componant Analysis | |
| dc.title.en | Log-PCA versus Geodesic PCA of histograms in the Wasserstein space | |
| dc.type | Article de revue | |
| dc.subject.hal | Statistiques [stat]/Calcul [stat.CO] | |
| dc.identifier.arxiv | 1708.08143 | |
| bordeaux.journal | SIAM Journal on Scientific Computing | |
| bordeaux.page | B429–B456 | |
| bordeaux.volume | 40 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01581699 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01581699v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=SIAM%20Journal%20on%20Scientific%20Computing&rft.date=2018&rft.volume=40&rft.issue=2&rft.spage=B429%E2%80%93B456&rft.epage=B429%E2%80%93B456&rft.eissn=1064-8275&rft.issn=1064-8275&rft.au=CAZELLES,%20Elsa&SEGUY,%20Vivien&BIGOT,%20J%C3%A9r%C3%A9mie&CUTURI,%20Marco&PAPADAKIS,%20Nicolas&rft.genre=article |
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