Properly-weighted graph Laplacian for semi-supervised learning
Abstract
The performance of traditional graph Laplacian methods for semi-supervised learning degrades substantially as the ratio of labeled to unlabeled data decreases, due to a degeneracy in the graph Laplacian. Several approaches have been proposed recently to address this, however we show that some of them remain ill-posed in the large-data limit. In this paper, we show a way to correctly set the weights in Laplacian regularization so that the estimator remains well posed and stable in the large-sample limit. We prove that our semi-supervised learning algorithm converges, in the infinite sample size limit, to the smooth solution of a continuum variational problem that attains the labeled values continuously. Our method is fast and easy to implement.
Cite
@article{arxiv.1810.04351,
title = {Properly-weighted graph Laplacian for semi-supervised learning},
author = {Jeff Calder and Dejan Slepcev},
journal= {arXiv preprint arXiv:1810.04351},
year = {2019}
}