Public thesis defense Remi Delogne - ICTEAM
sst |
Random embeddings and efficient representations for signal processing and subspace methods
Tuesday September 8th, 2026 - 5pm - Auditorium BARB92- Place Sainte-Barbe 1, 1348 Louvain-la-Neuve
This thesis studies how high-dimensional signals and subspace-valued data can be represented more efficiently while preserving the information needed for processing. The main focus is on random quadratic embeddings which provide compact representations that can be processed without reconstructing the original data.
The first contribution shows that debiased quadratic random embeddings satisfy a sign product embedding property. This makes it possible to estimate squared scalar products, and therefore perform tasks such as localised signal estimation or classification, directly from quadratic sketches.
The thesis then studies data represented by low-dimensional subspaces on the Grassmannian manifold. Classical Grassmannian kernels become costly on large datasets because they require full Gram matrices. To address this, random features based on rank-one projections of subspace projectors are introduced. Binary and periodic bounded transformations are used to control heavy-tailed measurements, producing compact features whose inner products approximate well-defined rotation-invariant Grassmannian kernels depending only on principal angles.
Finally, the thesis studies efficient implementations of these embeddings. Structured Hadamard-based transforms reduce computational cost, while optical processing units provide a hardware implementation of large-scale quadratic random projections. A quantisation and binary encoding method is also developed to extend these optical embeddings to multi-bits input data.
Overall, the thesis shows how random quadratic representations can be used to process signals and subspaces more efficiently, while keeping the information needed for tasks such as estimation, classification and kernel approximation, and while reducing computation, memory and storage requirements.
Jury members
Prof. Laurent Jacques (UCLouvain), Supervisor
Prof. Pierre-Antoine Absil (UCLouvain), Chairperson
Prof. Christophe De Vleeschouwer (UCLouvain), Secretary
Prof. Laurent Daudet (Université Paris-Cité, France)
Dr. Titouan Vayer (INRIA, France)