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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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Semi-Supervised Learning with Conditional Harmonic Mixing

Semi-Supervised Learning with Conditional Harmonic Mixing

(p.250) (p.251) 14 Semi-Supervised Learning with Conditional Harmonic Mixing
Semi-Supervised Learning

Burges Christopher J. C.

Platt John C.

The MIT Press

This chapter introduces a general probabilistic formulation called conditional harmonic mixing (CHM), in which the links are directed, a conditional probability matrix is associated with each link, and where the numbers of classes can vary from node to node. The posterior class probability at each node is updated by minimizing the Kullback-Leibler (KL) divergence between its distribution and that predicted by its neighbors. It is shown here that for arbitrary graphs, as long as each unlabeled point is reachable from at least one training point, a solution always exists, is unique, and can be found by solving a sparse linear system iteratively. This result holds even if the graph contains loops, or if the conditional probability matrices are not consistent. It is also shown how CHM can learn its transition probabilities. Using the Reuters database, it is shown here that CHM improves the accuracy of the best available classifier.

Keywords:   general probabilistic formulation, conditional harmonic mixing, CHM, Kullback-Leibler divergence, KL, Reuters database

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