Better embeddings for Planar Earth-Mover Distance over sparse sets
Name
892737687-MIT.pdf
Description
Full printable version
Size
1.3 MB
Format
Adobe PDF
Checksum (MD5)
06e2a4a5ac8f5836ea620e4982634dc1
Author(s)
Backurs, Arturs
Advisor(s)
Piotr Indyk.
Alternative Title
Better embeddings for Planar EMD over sparse sets
Date Issued
2014
Publisher
Massachusetts Institute of Technology
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.
Description
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).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
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.
Persistent DSpace Link
