The DTM-signature for a geometric comparison of metric-measure spaces from samples

Claire Brécheteau 1, 2
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : In this paper, we introduce the notion of DTM-signature, a measure on R + that can be associated to any metric-measure space. This signature is based on the distance to a measure (DTM) introduced by Chazal, Cohen-Steiner and Mérigot. It leads to a pseudo-metric between metric-measure spaces, upper-bounded by the Gromov-Wasserstein distance. Under some geometric assumptions, we derive lower bounds for this pseudo-metric. Given two N-samples, we also build an asymptotic statistical test based on the DTM-signature, to reject the hypothesis of equality of the two underlying metric-measure spaces, up to a measure-preserving isometry. We give strong theoretical justifications for this test and propose an algorithm for its implementation.
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https://hal.inria.fr/hal-01426331
Contributeur : Claire Brécheteau <>
Soumis le : jeudi 9 février 2017 - 14:00:21
Dernière modification le : jeudi 20 juillet 2017 - 09:26:44
Document(s) archivé(s) le : mercredi 10 mai 2017 - 13:51:27

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  • HAL Id : hal-01426331, version 2

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Claire Brécheteau. The DTM-signature for a geometric comparison of metric-measure spaces from samples. 2017. <hal-01426331v2>

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