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Geodesically-convex optimization for averaging partially observed covariance matrices

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yger20a.pdf (664.6Kb)
Date
2020
Dewey
Informatique générale
Sujet
SPD matrices; average; missing data; data imputation
Conference name
Proceedings of the Asian Conference on Machine Learning (ACML)
Conference date
11-2020
Conference city
Bangkok
Conference country
Thailand
Book title
Proceedings of the 12th Asian Conference on Machine Learning, PMLR 129
URI
https://basepub.dauphine.fr/handle/123456789/21519
Collections
  • LAMSADE : Publications
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Author
Yger, Florian
989 Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Chevallier, S.
Barthélemy, Q.
Suvrit, S.
Type
Communication / Conférence
Abstract (EN)
Symmetric 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.

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