Sublinear time algorithms for earth mover's distance
Author(s)Do Ba, Khanh; Nguyen, Huy L.; Nguyen, Huy N.; Rubinfeld, Ronitt
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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.
DepartmentMassachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory; Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Theory of Computing Systems
Springer New York
Ba, Khanh Do et al. “Sublinear Time Algorithms for Earth Mover’s Distance.” Theory of Computing Systems 48.2 (2010): 428-442.
Author's final manuscript