CAZELLES, Elsa; SEGUY, Vivien; BIGOT, Jérémie; CUTURI, Marco; PAPADAKIS, Nicolas

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CAZELLES, Elsa
Institut de Mathématiques de Bordeaux [IMB]

SEGUY, Vivien
Graduate School of Informatics [Kyoto]

BIGOT, Jérémie
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

SIAM Journal on Scientific Computing. 2018, vol. 40, n° 2, p. B429–B456

Society for Industrial and Applied Mathematics

Résumé en anglais

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.< Réduire

Mots clés en anglais

Non-convex optimization

Wasserstein Space

Geodesic Principal Componant Analysis

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191155

Project ANR

Generalized Optimal Transport Models for Image processing - ANR-16-CE33-0010

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251