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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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Modifying Distances

Modifying Distances

Chapter:
(p.309) 17 Modifying Distances
Source:
Semi-Supervised Learning
Author(s):

Orlitsky Alon

Publisher:
The MIT Press
DOI:10.7551/mitpress/9780262033589.003.0017

This chapter discusses density-based metrics induced by Riemannian manifold structures. It presents asymptotically consistent methods to estimate and compute these metrics and present upper and lower bounds on their estimation and computation errors. Finally, it is discussed how these metrics can be used for semi-supervised learning and present experimental results. Learning algorithms use a notion of similarity between data points to make inferences. Semi-supervised algorithms assume that two points are similar to each other if they are connected by a high-density region of the unlabeled data. Apart from semi-supervised learning, such density-based distance metrics also have applications in clustering and nonlinear interpolation.

Keywords:   density-based metrics, Riemannian manifold structures, asymptotically consistent methods, computation errors, semi-supervised learning, clustering, nonlinear interpolation

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