Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods
Abstract
Graph-based semi-supervised learning is the problem of propagating labels from a small number of labelled data points to a larger set of unlabelled data. This paper is concerned with the consistency of optimization-based techniques for such problems, in the limit where the labels have small noise and the underlying unlabelled data is well clustered. We study graph-based probit for binary classification, and a natural generalization of this method to multi-class classification using one-hot encoding. The resulting objective function to be optimized comprises the sum of a quadratic form defined through a rational function of the graph Laplacian, involving only the unlabelled data, and a fidelity term involving only the labelled data. The consistency analysis sheds light on the choice of the rational function defining the optimization.
Cite
@article{arxiv.1906.07658,
title = {Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods},
author = {Franca Hoffmann and Bamdad Hosseini and Zhi Ren and Andrew M. Stuart},
journal= {arXiv preprint arXiv:1906.07658},
year = {2020}
}