Year: 2026
Type: preprint
Abstract: We propose to model singular data clouds by subanalytic sets, and develop an approach to semi-supervised learning in this setting. It relies on a Morrey-type embedding for Sobolev spaces relative to globally subanalytic measures with possibly singular support. As an illustration, we present a greedy method based on a Monte Carlo approximation of the Sobolev norm of the candidate solutions. We report numerical experiments on point clouds sampled from real algebraic varieties, as well as a test on a classification problem based on MNIST images downsampled into $7\times7$.
Source: arXiv (Cornell University)
Author: Valette, Guillaume
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223019974