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

Kubilay Atasu, Thomas Mittelholzer
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:364-373, 2019.

Abstract

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 therefore, we can 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 search accuracy. On MNIST images, the new algorithms are four orders of magnitude faster than Cuturi’s GPU implementation of the Sinkhorn’s algorithm while offering a slightly higher search accuracy.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-atasu19a, title = {Linear-Complexity Data-Parallel Earth Mover’s Distance Approximations}, author = {Atasu, Kubilay and Mittelholzer, Thomas}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {364--373}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/atasu19a/atasu19a.pdf}, url = {https://proceedings.mlr.press/v97/atasu19a.html}, abstract = {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 therefore, we can 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 search accuracy. On MNIST images, the new algorithms are four orders of magnitude faster than Cuturi’s GPU implementation of the Sinkhorn’s algorithm while offering a slightly higher search accuracy.} }
Endnote
%0 Conference Paper %T Linear-Complexity Data-Parallel Earth Mover’s Distance Approximations %A Kubilay Atasu %A Thomas Mittelholzer %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-atasu19a %I PMLR %P 364--373 %U https://proceedings.mlr.press/v97/atasu19a.html %V 97 %X 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 therefore, we can 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 search accuracy. On MNIST images, the new algorithms are four orders of magnitude faster than Cuturi’s GPU implementation of the Sinkhorn’s algorithm while offering a slightly higher search accuracy.
APA
Atasu, K. & Mittelholzer, T.. (2019). Linear-Complexity Data-Parallel Earth Mover’s Distance Approximations. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:364-373 Available from https://proceedings.mlr.press/v97/atasu19a.html.

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