PreprintarXiv licencearXiv
Semi-supervised learning on singular data sets
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 7×7.
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BibTeX
@misc{valette2026semisupervised,
title = {{Semi-supervised learning on singular data sets}},
author = {Guillaume Valette},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25450},
eprint = {2610.25450},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25450},
}
RIS
TY - UNPB
TI - Semi-supervised learning on singular data sets
AU - Guillaume Valette
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.25450
UR - https://arxiv.org/abs/2610.25450
AB - 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 7×7.
ER -