Linear-Complexity Data-Parallel Earth Mover's Distance Approximations

The Earth Mover's Distance (EMD) is a state-of-the art metric for comparing discrete probability distributions, but its high distinguishability comes at a high cost in computational complexity. Even though linear-complexity approximation algorithms have been proposed to improve its scalability, these algorithms are either limited to vector spaces with only a few dimensions or they become ineffective when the degree of overlap between the probability distributions is high. We propose novel approximation algorithms that overcome both of these limitations, yet still achieve linear time complexity. All our algorithms are data parallel, and thus, we take advantage of massively parallel computing engines, such as Graphics Processing Units (GPUs). On the popular text-based 20 Newsgroups dataset, the new algorithms are four orders of magnitude faster than a multi-threaded CPU implementation of Word Mover's Distance and match its nearest-neighbors-search accuracy. On MNIST images, the new algorithms are four orders of magnitude faster than a GPU implementation of the Sinkhorn's algorithm while offering a slightly higher nearest-neighbors-search accuracy.