Sublinear time algorithms for earth mover's distance
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Author(s)
Do Ba, Khanh
Nguyen, Huy L.
Nguyen, Huy N.
Rubinfeld, Ronitt
Date Issued
April 2010
Journal
Theory of Computing Systems
Publisher
Springer New York
Citation
Ba, Khanh Do et al. “Sublinear Time Algorithms for Earth Mover’s Distance.” Theory of Computing Systems 48.2 (2010): 428-442.
Version
Author's final manuscript
Abstract
We study the problem of estimating the Earth Mover’s Distance (EMD) between probability distributions
when given access only to samples of the distributions. We give closeness testers and additive-error
estimators over domains in [0, 1][superscript 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 the dependencies on these parameters to be essentially optimal. 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 l 1 metric, and give tight
upper and lower bounds.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00224-010-9265-8
