2026-09-19T10:29:48Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/910982022-01-13T07:54:01Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Piotr Indyk.
Backurs, Arturs
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2014-10-21T17:25:56Z
2014-10-21T17:25:56Z
2014
2014
http://hdl.handle.net/1721.1/91098
892737687
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014.
11
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 43-44).
We consider the problem of constructing low-distortion embeddings of the Planar Earth-Mover Distance (EMD) into lp spaces. EMD is a popular measure of dissimilarity between sets of points, e.g., bags of geometric features. We present a collection of embeddings with the property that their distortion and/or host-space dimension are parametrized by the size (or the sparsity) of the embedded sets s. Our specific results include: -- An O(log s)-distortion embedding of EMD over s-subsets into l1-e. This is the first embedding of EMD into a "tractable" lp, space whose distortion is a function of the sparsity, not the size of the ambient space; -- An O(log n)-distortion embedding of EMD into lp, with dimension O(s2 log2 n), where the embedded sets are subsets of an n x n grid. For low values of s this significantly improves over the best previous dimension bound of 0(n 2 ) obtained for general sets.
by Arturs Backurs.
S.M.
44 pages
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Better embeddings for Planar Earth-Mover Distance over sparse sets
Better embeddings for Planar EMD over sparse sets
Thesis
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Publication
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<Abstract>We consider the problem of constructing low-distortion embeddings of the Planar Earth-Mover Distance (EMD) into lp spaces. EMD is a popular measure of dissimilarity between sets of points, e.g., bags of geometric features. We present a collection of embeddings with the property that their distortion and/or host-space dimension are parametrized by the size (or the sparsity) of the embedded sets s. Our specific results include: -- An O(log s)-distortion embedding of EMD over s-subsets into l1-e. This is the first embedding of EMD into a "tractable" lp, space whose distortion is a function of the sparsity, not the size of the ambient space; -- An O(log n)-distortion embedding of EMD into lp, with dimension O(s2 log2 n), where the embedded sets are subsets of an n x n grid. For low values of s this significantly improves over the best previous dimension bound of 0(n 2 ) obtained for general sets.</Abstract>
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