de Surrel, M Thibault (2023) *Riding and squeezing the manifold* PFE - Project Graduation, ENSTA.

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## Abstract

The goal of Brain Computer Interfaces is to translate a user’s brain activity into a command. For this, Electroencephalography (EEG) is typically used to record a multivariate time series that captures the electrical activity of the brain. The most common representation of an EEG in a machine learning pipeline is its covariance matrix. Such matrices are symmetric positive definite and therefore we use Riemannian geometry to manipulate them. The problem with this representation is that it fails at capturing the temporal dynamics of the signal. In the first part of my internship, I implemented a new algorithm for classifying EEGs. This algorithm relies on a trajectory of covariance matrices, indexed by time for example, instead of just one covariance matrix. The goal is to compute a mean trajectory using a smart matching relying on the Dynamic Time Warping algorithm and then to compute a weighted Riemannian mean. This way, we hope to leverage more information out of a single EEG and therefore, better tackle the variability and the non-stationarities of the signal. In the second part of my internship, I studied two dimension reduction algorithms : MDS and t-SNE and tried to adapt them to a Riemannian setting. The goal was to visualize in a low dimensional space covariances matrices that live in a high dimensional space. For both projects, we conducted experiments on synthetic data to show the contribution of our methods, and then tested them on real EEG data.

Item Type: | Thesis (PFE - Project Graduation) |
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Uncontrolled Keywords: | Brain Computer Interfaces, Electroencephalography, Riemannian Geometry, Covariance matrix, Time series, Dimension Reduction |

Subjects: | Mathematics and Applications |

ID Code: | 9850 |

Deposited By: | Thibault De Surrel de Saint Julien |

Deposited On: | 30 oct. 2023 15:10 |

Dernière modification: | 30 oct. 2023 15:10 |

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