Code for the Earth Movers Distance (EMD). This is an implementation of the Earth Movers Distance, as described in [1]. The EMD computes the distance between two distributions, which are represented by signatures. The signatures are sets of weighted features that capture the distributions. The features can be of any type and in any number of dimensions, and are defined by the user. The EMD is defined as the minimum amount of work needed to change one signature into the other. The notion of ”work” is based on the user-defined ground distance which is the distance between two features. The size of the two signatures can be different. Also, the sum of weights of one signature can be different than the sum of weights of the other (partial match). Because of this, the EMD is normalized by the smaller sum. The code is implemented in C, and is based on the solution for the Transportation problem as described in [2] Please let me know of any bugs you find, or any questions, comments, suggestions, and criticisms you have. If you find this code useful for your work, I would like very much to hear from you. Once you do, I’ll inform you of any improvements, etc. Also, an acknowledgment in any publication describing work that uses this code would be greatly appreciated.

References in zbMATH (referenced in 224 articles , 1 standard article )

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  1. Chen, Yaqing; Müller, Hans-Georg: Wasserstein gradients for the temporal evolution of probability distributions (2021)
  2. Heitz, Matthieu; Bonneel, Nicolas; Coeurjolly, David; Cuturi, Marco; Peyré, Gabriel: Ground metric learning on graphs (2021)
  3. Leclaire, Arthur; Rabin, Julien: A stochastic multi-layer algorithm for semi-discrete optimal transport with applications to texture synthesis and style transfer (2021)
  4. Liu, Jialin; Yin, Wotao; Li, Wuchen; Chow, Yat Tin: Multilevel optimal transport: a fast approximation of Wasserstein-1 distances (2021)
  5. Ma, Guixiang; Ahmed, Nesreen K.; Willke, Theodore L.; Yu, Philip S.: Deep graph similarity learning: a survey (2021)
  6. Nielsen, Frank; Marti, Gautier; Ray, Sumanta; Pyne, Saumyadipta: Clustering patterns connecting COVID-19 dynamics and human mobility using optimal transport (2021)
  7. Qian, Yitian; Pan, Shaohua: An inexact PAM method for computing Wasserstein barycenter with unknown supports (2021)
  8. Balzanella, Antonio; Irpino, Antonio: Spatial prediction and spatial dependence monitoring on georeferenced data streams (2020)
  9. Bassetti, Federico; Gualandi, Stefano; Veneroni, Marco: On the computation of Kantorovich-Wasserstein distances between two-dimensional histograms by uncapacitated minimum cost flows (2020)
  10. Budinich, Renato; Plonka, Gerlind: A tree-based dictionary learning framework (2020)
  11. Cárcamo, Javier; Cuevas, Antonio; Rodríguez, Luis-Alberto: Directional differentiability for supremum-type functionals: statistical applications (2020)
  12. Katzfuss, Matthias; Stroud, Jonathan R.; Wikle, Christopher K.: Ensemble Kalman methods for high-dimensional hierarchical dynamic space-time models (2020)
  13. Luini, E.; Arbenz, P.: Density estimation of multivariate samples using Wasserstein distance (2020)
  14. Stuart, Andrew M.; Wolfram, Marie-Therese: Inverse optimal transport (2020)
  15. Surana, Amit: Koopman operator framework for time series modeling and analysis (2020)
  16. Xu, Ganggang; Zhu, Huirong; Lee, J. Jack: Borrowing strength and borrowing index for Bayesian hierarchical models (2020)
  17. Zhang, Shitao; Ma, Zhenzhen; Liu, Xiaodi; Wang, Zhiying; Jiang, Lihui: An integrated consensus improving strategy based on PL-Wasserstein distance and its application in the evaluation of network public opinion emergencies (2020)
  18. Carlsson, John Gunnar; Wang, Ye: Distributions with maximum spread subject to Wasserstein distance constraints (2019)
  19. Cloninger, Alexander; Roy, Brita; Riley, Carley; Krumholz, Harlan M.: People mover’s distance: class level geometry using fast pairwise data adaptive transportation costs (2019)
  20. de Gournay, Frédéric; Kahn, Jonas; Lebrat, Léo: Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure (2019)

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