Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods

Franca Hoffmann; Bamdad Hosseini; Zhi Ren; Andrew M. Stuart

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arXiv · 1906.07658

Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods

Franca Hoffmann·Bamdad Hosseini·Zhi Ren·Andrew M. Stuart

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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.

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BibTeX RIS

Franca Hoffmann, Bamdad Hosseini, Zhi Ren, Andrew M. Stuart. 2019-06-18. Consistency of semi-supervised learning algorithms on graphs: Probit and one-hot methods. https://arxiv.org/abs/1906.07658

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