Extensions of Laplacian Eigenmaps for Manifold Learning

dc.contributor.advisor	Benedetto, John J	en_US
dc.contributor.advisor	Czaja, Wojciech	en_US
dc.contributor.author	Halevy, Avner	en_US
dc.contributor.department	Mathematics	en_US
dc.contributor.publisher	Digital Repository at the University of Maryland	en_US
dc.contributor.publisher	University of Maryland (College Park, Md.)	en_US
dc.date.accessioned	2011-07-07T05:33:18Z
dc.date.available	2011-07-07T05:33:18Z
dc.date.issued	2011	en_US
dc.description.abstract	This thesis deals with the theory and practice of manifold learning, especially as they relate to the problem of classification. We begin with a well known algorithm, Laplacian Eigenmaps, and then proceed to extend it in two independent directions. First, we generalize this algorithm to allow for the use of partially labeled data, and establish the theoretical foundation of the resulting semi-supervised learning method. Second, we consider two ways of accelerating the most computationally intensive step of Laplacian Eigenmaps, the construction of an adjacency graph. Both of them produce high quality approximations, and we conclude by showing that they work well together to achieve a dramatic reduction in computational time.	en_US
dc.identifier.uri	http://hdl.handle.net/1903/11634
dc.subject.pqcontrolled	Applied Mathematics	en_US
dc.title	Extensions of Laplacian Eigenmaps for Manifold Learning	en_US
dc.type	Dissertation	en_US

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