Afficher la notice abrégée

dc.contributor.authorPeyré, Gabriel
dc.contributor.authorCuturi, Marco
dc.contributor.authorSolomon, Justin
dc.date.accessioned2018-02-16T13:02:32Z
dc.date.available2018-02-16T13:02:32Z
dc.date.issued2016
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17407
dc.language.isoenen
dc.subjectGromov-Wassersteinen
dc.subjectOptimal Transporten
dc.subjectWassersteinen
dc.subjectmetric spacesen
dc.subjectshapesen
dc.subject.ddc621.3en
dc.titleGromov-Wasserstein Averaging of Kernel and Distance Matricesen
dc.typeCommunication / Conférence
dc.description.abstractenThis paper presents a new technique for computing the barycenter of a set of distance or kernel matrices. These matrices, which define the interrelationships between points sampled from individual domains, are not required to have the same size or to be in row-by-row correspondence. We compare these matrices using the softassign criterion , which measures the minimum distortion induced by a probabilistic map from the rows of one similarity matrix to the rows of another; this criterion amounts to a regularized version of the Gromov-Wasserstein (GW) distance between metric-measure spaces. The barycenter is then defined as a Fréchet mean of the input matrices with respect to this criterion, minimizing a weighted sum of softassign values. We provide a fast iterative algorithm for the resulting noncon-vex optimization problem, built upon state-of-the-art tools for regularized optimal transportation. We demonstrate its application to the computation of shape barycenters and to the prediction of energy levels from molecular configurations in quantum chemistry.en
dc.relation.ispartoftitleProceedings of the 33rd International Conference on International Conference on Machine Learningen
dc.relation.ispartofpublnameACM - Association for Computing Machineryen
dc.relation.ispartofpublcityNew York, NYen
dc.relation.ispartofdate2016
dc.subject.ddclabelTraitement du signalen
dc.relation.conftitle33rd International Conference on International Conference on Machine Learningen
dc.relation.confdate2016-06
dc.relation.confcityNew Yorken
dc.relation.confcountryUnited Statesen
dc.relation.forthcomingnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2018-02-16T12:05:28Z
hal.person.labIds60
hal.person.labIds469093
hal.person.labIds


Fichiers attachés à cette notice

Thumbnail

Ce document fait partie de la (des) collection(s) suivante(s)

Afficher la notice abrégée