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arXiv · 0904.0292

Sublinear Time Algorithms for Earth Mover's Distance

Khanh Do Ba·Huy L Nguyen·Huy N Nguyen·Ronitt Rubinfeld
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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 $[0, Δ]^d$, 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 L1 metric, and give optimal algorithms.

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Khanh Do Ba, Huy L Nguyen, Huy N Nguyen, Ronitt Rubinfeld. 2009-04-02. Sublinear Time Algorithms for Earth Mover's Distance. https://arxiv.org/abs/0904.0292

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