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Earth Mover's Distance (EMD) is an important similarity measure between twodistributions, used in computer vision and many other application domains.However, its exact calculation is computationally and memory intensive, whichhinders its scalability and applicability for large-scale problems. Variousapproximate EMD algorithms have been proposed to reduce computational costs,but they suffer lower accuracy and may require additional memory usage ormanual parameter tuning. In this paper, we present a novel approach, NNS-EMD,to approximate EMD using Nearest Neighbor Search (NNS), in order to achievehigh accuracy, low time complexity, and high memory efficiency. The NNSoperation reduces the number of data points compared in each NNS iteration andoffers opportunities for parallel processing. We further accelerate NNS-EMD viavectorization on GPU, which is especially beneficial for large datasets. Wecompare NNS-EMD with both the exact EMD and state-of-the-art approximate EMDalgorithms on image classification and retrieval tasks. We also apply NNS-EMDto calculate transport mapping and realize color transfer between images.NNS-EMD can be 44x to 135x faster than the exact EMD implementation, andachieves superior accuracy, speedup, and memory efficiency over existingapproximate EMD methods.

Efficient approximation of Earth Mover's Distance Based on Nearest Neighbor Search