Research overview

My research lies in applied mathematics, combining statistics, Riemannian geometry and machine learning to address challenges arising in signal processing and data analysis.

A central theme of my work is the development of robust learning methods for structured data, with a particular emphasis on covariance matrices, which naturally live on the manifold of symmetric positive definite (SPD) matrices.

PhD research

Robust Geometrical Learning for Electroencephalography
PhD, Université Paris-Saclay, 2025

My doctoral work addressed the limitations of Gaussian-based models for covariance matrices in noisy and non-Gaussian settings, such as EEG signals.

Main contributions include:

  • Statistical analysis of Elliptical Wishart and Inverse Elliptical Wishart distributions
  • Derivation of expectations, variances and Kronecker moments of arbitrary order
  • Development of an information-geometric framework for these distributions
  • Maximum likelihood estimation on the SPD manifold
  • Robust classification and clustering methods for covariance matrices

Applications

  • Electroencephalography (EEG) and brain–computer interfaces
  • Hyperspectral image analysis
  • Robust signal classification and clustering

Perspectives

My current interests include:

  • Robust learning on structured manifolds
  • Information geometry for statistical inference
  • Connections between Riemannian optimization and modern machine learning