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hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorYger, Florian
HAL ID: 17768
ORCID: 0000-0002-7182-8062
hal.structure.identifier
dc.contributor.authorChevallier, S.
HAL ID: 1937
ORCID: 0000-0003-3027-8241
hal.structure.identifier
dc.contributor.authorBarthélemy, Q.
hal.structure.identifier
dc.contributor.authorSuvrit, S.
dc.date.accessioned2021-01-15T09:53:16Z
dc.date.available2021-01-15T09:53:16Z
dc.date.issued2020
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/21519
dc.language.isoenen
dc.subjectSPD matricesen
dc.subjectaverageen
dc.subjectmissing dataen
dc.subjectdata imputationen
dc.subject.ddc004en
dc.titleGeodesically-convex optimization for averaging partially observed covariance matricesen
dc.typeCommunication / Conférence
dc.description.abstractenSymmetric positive definite (SPD) matrices permeates numerous scientific disciplines, including machine learning, optimization, and signal processing. Equipped with a Riemannian geometry, the space of SPD matrices benefits from compelling properties and its derived Riemannian mean is now the gold standard in some applications, e.g. brain-computer interfaces (BCI). This paper addresses the problem of averaging covariance matrices with missing variables. This situation often occurs with inexpensive or unreliable sensors, or when artifact-suppression techniques remove corrupted sensors leading to rank deficient matrices, hindering the use of the Riemannian geometry in covariance-based approaches. An alternate but questionable method consists in removing the matrices with missing variables, thus reducing the training set size. We address those limitations and propose a new formulation grounded in geodesic convexity. Our approach is evaluated on generated datasets with a controlled number of missing variables and a known baseline, demonstrating the robustness of the proposed estimator. The practical interest of this approach is assessed on real BCI datasets. Our results show that the proposed average is more robust and better suited for classification than classical data imputation methods.en
dc.relation.ispartoftitleProceedings of the 12th Asian Conference on Machine Learning, PMLR 129en
dc.subject.ddclabelInformatique généraleen
dc.relation.conftitleProceedings of the Asian Conference on Machine Learning (ACML)en
dc.relation.confdate2020-11
dc.relation.confcityBangkoken
dc.relation.confcountryThailanden
dc.relation.forthcomingnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2021-01-15T09:44:00Z
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