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Semi-Supervised Learning$
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Olivier Chapelle, Bernhard Scholkopf, and Alexander Zien

Print publication date: 2006

Print ISBN-13: 9780262033589

Published to MIT Press Scholarship Online: August 2013

DOI: 10.7551/mitpress/9780262033589.001.0001

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The Geometric Basis of Semi-Supervised Learning

The Geometric Basis of Semi-Supervised Learning

(p.217) 12 The Geometric Basis of Semi-Supervised Learning
Semi-Supervised Learning

Sindhwani Vikas

Belkin Misha

Niyogi Partha

The MIT Press

This chapter presents an algorithmic framework for semi-supervised inference based on geometric properties of probability distributions. This approach brings together Laplacian-based spectral techniques, regularization with kernel methods, and algorithms for manifold learning. This framework provides a natural semi-supervised extension for kernel methods and resolves the problem of out-of-sample inference in graph-based transduction. An interpretation is discussed here in terms of a family of globally defined data-dependent kernels and unsupervised learning within the same framework is also addressed. The algorithms in this chapter effectively exploit both manifold and cluster assumptions to demonstrate state-of-the-art performance on various classification tasks. This chapter also reviews other recent work on out-of-sample extension for transductive graph-based methods.

Keywords:   algorithmic framework, semi-supervised inference, geometric properties, probability distributions, Laplacian-based spectral techniques, regularization with kernel methods, algorithms for manifold learning

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