Semi-supervised learning on singular data sets
Journal:
arXiv
Published Date:
Oct 18, 2026
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 $7\times7$.
