Estelle Massart

PhD student in Applied mathematics, Université catholique de Louvain

I am a teaching assistant in the mathematical engineering department (which is part of the ICTEAM institute ) at UCL .

My research is about data fitting problems on manifolds. More specifically, I am mainly working on averaging and interpolation problems on the manifold of positive (semi-)definite matrices.

My PhD advisors are Julien Hendrickx and Pierre-Antoine Absil.

Research projects

  • Fitting on the set of positive semi-definite matrices

    Many applications involve covariance matrices. Often (when the underlying process is high-dimensional), those matrices are low-rank. A common approach consists then in estimating the rank of the matrices, representing them as points on the manifold of fixed-rank positive semi-definite matrices. An example of such a high-dimensional process is the wind field in a given area.
    In collaboration with Pierre-Yves Gousenbourger , we have proposed some algorithms for curve fitting on manifolds (see this paper), and we applied them to the wind field estimation problem here.

  • Averaging positive definite matrices

    We have proposed an incremental gradient descent algorithm for computing the Riemannian barycenter on the manifold of positive definite matrices (endowed with its classical affine-invariant metric). The algorithm is equipped with a deterministic shuffling process, resulting on average in a faster convergence that the well-known stochastic gradient algorithm. The detail is contained in this paper. We proposed here to use an incremental algorithm for mean computation, to build an adaptative classifier for EEG signals. Finally, this work presents a decentralized algorithm for mean computation on the set of positive definite matrices, based on ideas from consensus theory.