Averaging trajectories on the manifold of covariance matrices

This repository contains the code of the methods proposed in Averaging trajectories on the manifold of symmetric positive definite matrices.

In this repository, we have two notebooks :

• Trajectory_MDM_BCI_data : In this notebook, you can find an example of our two proposed algorithms PT-MDM and DTW_MDM tested on a BCI dataset from MOABB [1].
• Trajectory_MDM_Synthetic_data: In this notebook, you can find an example of our two proposed algorithms PT-MDM and DTW_MDM tested on the sythetic datasets descibed in the paper.

In this repository is also provided the core code that we developped for our two methods : PT-MDM and DTW-MDM. The codes can be found in the folder sources. The come in two versions :

• trajectory_mdm : This code is the basic PT-MDM and DTW-MDM that we developped. It is used for the synthetic experiments. One can use this code when the SPD trajectories have already be computed and one juste need to train a classifier from them.
• trajectory_fgmdm_for_BCI : This code is a slight variant of the previous code : here, we take as input the multivariate time series, then we cut the times series into smaller windows of size size_window (a hyperparameter) and compute a covariance matrix for each window. The default covariance estimator used is the sample covariance matrix, but it is a parameter so it can be chosen by the user. Once the covariance matrix trajectories have been computed, we apply the we apply a Fisher Geodesic Discriminant Analysis (FGDA) filter [2] to all of the covariance matrices. (See the paper for more details). This code is used in the experiments on real BCI data.

Requirements

Theses are the packages needed in order to run the code.

numpy==1.24.2
matplotlib==3.7.1
moabb==0.4.6
pymanopt==2.1.1
scipy==1.10.1
pyriemann==0.4
scikit-learn
tqdm==4.65.0
joblib==1.2.0

One can install them using the command :

pip install -r requirements.txt

References

[1]: V. Jayaram and A. Barachant, “Moabb: trustworthy algorithm benchmarking for bcis,” J Neural Eng, vol. 15, no. 6, pp. 066011, 2018.

[2]: A. Barachant, S. Bonnet, M. Congedo, and C. Jutten, “Riemannian geometry applied to BCI classification,” in LVA/ICA 2010. Sept. 2010, vol. 6365, p. 629, Springer.