3 papers
math.NA2026
Data-Driven Diffusion Processes on Differential Forms via the Projected Ambient Connection Laplacian
Alvaro Almeida Gomez, Jorge Duque Franco
We develop a data-driven approximation of the projected ambient connection Laplacian acting on differential forms over smooth Riemannian manifolds sampled by point clouds. The prop…
cs.LG2025
A Data-Driven Interpolation Method on Smooth Manifolds via Diffusion Processes and Voronoi Tessellations
Alvaro Almeida Gomez
We propose a data-driven interpolation framework for reconstructing real-valued functions on smooth manifolds from scattered pointwise observations. The method combines a Gaussian…
cs.LG2025
Hodge Laplacians and Hodge Diffusion Maps
Alvaro Almeida Gomez, Jorge Duque Franco
We introduce Hodge Diffusion Maps, a novel manifold learning algorithm designed to analyze and extract topological information from high-dimensional data-sets. This method approxim…