Geodesically-convex optimization for averaging partially observed covariance matrices
Yger, Florian; Chevallier, S.; Barthélemy, Q.; Suvrit, S. (2020), Geodesically-convex optimization for averaging partially observed covariance matrices, Proceedings of the 12th Asian Conference on Machine Learning, PMLR 129
TypeCommunication / Conférence
Conference titleProceedings of the Asian Conference on Machine Learning (ACML)
Book titleProceedings of the 12th Asian Conference on Machine Learning, PMLR 129
MetadataShow full item record
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
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.
Subjects / KeywordsSPD matrices; average; missing data; data imputation
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