Better embeddings for Planar Earth-Mover Distance over sparse sets

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2014

Author dc:creator

• Backurs, Arturs

Advisor dc:contributor.advisor

• Piotr Indyk.

• Electrical Engineering and Computer Science.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/91098

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/91098