11 papers
Universality of kernels on Riemannian symmetric spaces
Salem Said, Nathaël Da Costa, Franziskus Steinert +1
We investigate universality properties of continuous, positive-definite invariant kernels on Riemannian symmetric spaces, providing a unified harmonic-analytic characterization acr…
Escaping the Capacity Ceiling: Routing on the Stiefel Manifold for Bilinear SPD Layers
Isabella Costa Maia, Isabella C. Maia, Pedro L. C. Rodrigues +2
Deep networks on the symmetric positive-definite (SPD) manifold promise expressive representations by encoding data geometry as an inductive bias, but stacking BiMap layers with th…
Heat and Matérn Kernels on Matchings
Dmitry Eremeev, Salem Said, Viacheslav Borovitskiy
Applying kernel methods to matchings is challenging due to their discrete, non-Euclidean nature. In this paper, we develop a principled framework for constructing geometric kernels…
Curvature-based rejection sampling
Isabella Costa Maia, Marco Congedo, Pedro L. C. Rodrigues +1
The present work introduces curvature-based rejection sampling (CURS). This is a method for sampling from a general class of probability densities defined on Riemannian manifolds.…
Quasi-Synthetic Riemannian Data Generation for Writer-Independent Offline Signature Verification
Elias N. Zois, Moises Diaz, Salem Said +1
Offline handwritten signature verification remains a challenging task, particularly in writer-independent settings where models must generalize across unseen individuals. Recent de…
Universal kernels via harmonic analysis on Riemannian symmetric spaces
Franziskus Steinert, Salem Said, Cyrus Mostajeran
The universality properties of kernels characterize the class of functions that can be approximated in the associated reproducing kernel Hilbert space and are of fundamental import…
Gaussian integrals on symmetric spaces (the complex case and beyond)
Salem Said
The present work is concerned with Gaussian integrals on simply connected non-positively curved Riemannian symmetric spaces. It is motivated by the aim of explicitly finding the hi…
Beyond R-barycenters: an effective averaging method on Stiefel and Grassmann manifolds
Florent Bouchard, Nils Laurent, Salem Said +1
In this paper, the issue of averaging data on a manifold is addressed. While the Fréchet mean resulting from Riemannian geometry appears ideal, it is unfortunately not always avail…
Invariant kernels on the space of complex covariance matrices
Salem Said, Franziskus Steinert, Cyrus Mostajeran
The present work develops certain analytical tools required to construct and compute invariant kernels on the space of complex covariance matrices. The main result is the $\mathrm{…
Invariant kernels on Riemannian symmetric spaces: a harmonic-analytic approach
Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega +1
This work aims to prove that the classical Gaussian kernel, when defined on a non-Euclidean symmetric space, is never positive-definite for any choice of parameter. To achieve this…
Geometric Learning with Positively Decomposable Kernels
Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega +1
Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive-definite kernels, which map data spaces into reproducing kernel Hilbert spaces…