Semi-supervised learning on singular data sets
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 $7\times7$.
| Authors | Guillaume Valette |
|---|---|
| Primary category | cs.LG |
| Published | 18 October 2026 |
| Last updated at source | 18 October 2026 |
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