Averaging trajectories on the manifold of symmetric positive definite matrices - Archive ouverte HAL
Communication Dans Un Congrès Année : 2024

Averaging trajectories on the manifold of symmetric positive definite matrices

Trajectoires moyennes sur la variété des matrices symétriques définies positives

Résumé

The goal of this paper is to leverage more information from a single measurement (e.g. an ElectroEncephalo-Graphic (EEG) trial) by representing it as a trajectory of covariance matrices (indexed by time for example) instead of a single aggregated one. Doing so, we aim at reducing the impact of non-stationarities and variabilities (e.g. due to fatigue or stress for EEG). Covariance matrices being symmetric positive definite (SPD) matrices, we present two algorithms to classify trajectories on the space of SPD matrices. These algorithms consist in computing, in two different ways, the mean trajectory of a set of training trajectories and use them as class prototypes. The first method computes a pointwise mean and the second one achieves a smart matching using the Dynamic Time Warping (DTW) algorithm. As we are considering SPD matrices, the geometry used along these processes is the Riemannian geometry of the SPD matrices. We tested our algorithms on synthetic data and on EEG data from six different datasets. We show that our algorithms yield better average results than the state-of-the-art classifier for EEG data.
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Dates et versions

hal-04708878 , version 1 (25-09-2024)

Identifiants

  • HAL Id : hal-04708878 , version 1

Citer

Thibault de Surrel, Sylvain Chevallier, Fabien Lotte, Florian Yger. Averaging trajectories on the manifold of symmetric positive definite matrices. EUSIPCO 2024 - 32nd European Signal Processing Conference, Aug 2024, Lyon, France. ⟨hal-04708878⟩
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