Orlitsky Alon
- Published in print:
- 2006
- Published Online:
- August 2013
- ISBN:
- 9780262033589
- eISBN:
- 9780262255899
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262033589.003.0017
- Subject:
- Computer Science, Machine Learning
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 ...
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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.Less
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.
