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.
Additional Information
© 2020 Franca Hoffmann, Bamdad Hosseini, Zhi Ren and Andrew M. Stuart. License: CC-BY 4.0, see https://creativecommons.org/licenses/by/4.0/. Attribution requirements are provided at http://jmlr.org/papers/v21/19-500.html. Submitted 6/19; Revised 3/20; Published 7/20. The authors are grateful to Nicolás García-Trillos, Mark Girolami and Omiros Papaspiliopoulos for helpful discussions about the probit methodology and spectral clustering. FH is partially supported by Caltech's von Kármán postdoctoral instructorship. BH is supported in part by an NSERC PDF fellowship. AMS is grateful to AFOSR (grant FA9550-17-1-0185) and NSF (grant DMS 18189770) for financial support.Attached Files
Published - 15-900.pdf
Submitted - 1906.07658.pdf
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Additional details
- Eprint ID
- 97303
- Resolver ID
- CaltechAUTHORS:20190722-075729960
- Caltech
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- FA9550-17-1-0185
- Air Force Office of Scientific Research (AFOSR)
- DMS-18189770
- NSF
- Created
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2019-07-22Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field