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.

References in corpus (3)

• Consistency of spectral clustering
• Robustness and Regularization of Support Vector Machines
• A modern maximum-likelihood theory for high-dimensional logistic regression

Cited by in corpus (2)

• Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs
• Efficient Graph-Based Active Learning with Probit Likelihood via Gaussian Approximations