Sublinear algorithms for Earth Mover's Distance
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426032273-MIT.pdf
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Full printable version
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825.35 KB
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1f81d0232fd9ddb73f3b03ce18c4c31d
Author(s)
Do Ba, Khanh
Advisor(s)
Piotr Indyk.
Date Issued
2009
Publisher
Massachusetts Institute of Technology
Abstract
We study the problem of estimating the Earth Mover's Distance (EMD) between probability distributions when given access only to samples. We give closeness testers and additive-error estimators over domains in [0, [delta]]d, with sample complexities independent of domain size - permitting the testability even of continuous distributions over infinite domains. Instead, our algorithms depend on other parameters, such as the diameter of the domain space, which may be significantly smaller. We also prove lower bounds showing our testers to be optimal in their dependence on these parameters. Additionally, we consider whether natural classes of distributions exist for which there are algorithms with better dependence on the dimension, and show that for highly clusterable data, this is indeed the case. Lastly, we consider a variant of the EMD, defined over tree metrics instead of the usual L₁ metric, and give optimal algorithms.
Description
Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.
Includes bibliographical references (p. 14-15).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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