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 243 articles , 1 standard article )

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  1. Bauer, Martin; Hartman, Emmanuel; Klassen, Eric: The square root normal field distance and unbalanced optimal transport (2022)
  2. Edoh, Ayaboe K.: A new kinetic-energy-preserving method based on the convective rotational form (2022)
  3. Heinemann, Florian; Munk, Axel; Zemel, Yoav: Randomized Wasserstein barycenter computation: resampling with statistical guarantees (2022)
  4. Komarichev, Artem; Hua, Jing; Zhong, Zichun: Learning geometry-aware joint latent space for simultaneous multimodal shape generation (2022)
  5. Lin, Fengming; Fang, Xiaolei; Gao, Zheming: Distributionally robust optimization. A review on theory and applications (2022)
  6. Tapley, Benjamin K.; Andersson, Helge I.; Celledoni, Elena; Owren, Brynjulf: Computational geometric methods for preferential clustering of particle suspensions (2022)
  7. Torregrosa, Sergio; Champaney, Victor; Ammar, Amine; Herbert, Vincent; Chinesta, Francisco: Surrogate parametric metamodel based on optimal transport (2022)
  8. Yu, Lu; Lu, Yuliang; Shen, Yi; Zhao, Jun; Zhao, Jiazhen: PBDiff: Neural network based program-wide diffing method for binaries (2022)
  9. Bronevich, Andrey G.; Rozenberg, Igor N.: The measurement of relations on belief functions based on the Kantorovich problem and the Wasserstein metric (2021)
  10. Chen, Yaqing; Müller, Hans-Georg: Wasserstein gradients for the temporal evolution of probability distributions (2021)
  11. Heimowitz, Ayelet; Sharon, Nir; Singer, Amit: Centering noisy images with application to cryo-EM (2021)
  12. Heitz, Matthieu; Bonneel, Nicolas; Coeurjolly, David; Cuturi, Marco; Peyré, Gabriel: Ground metric learning on graphs (2021)
  13. Hyde, David A. B.; Bao, Michael; Fedkiw, Ronald: On obtaining sparse semantic solutions for inverse problems, control, and neural network training (2021)
  14. Leclaire, Arthur; Rabin, Julien: A stochastic multi-layer algorithm for semi-discrete optimal transport with applications to texture synthesis and style transfer (2021)
  15. Liu, Jialin; Yin, Wotao; Li, Wuchen; Chow, Yat Tin: Multilevel optimal transport: a fast approximation of Wasserstein-1 distances (2021)
  16. López-Lobato, Adriana Laura; Avendaño-Garrido, Martha Lorena: Fitting a Gaussian mixture model through the Gini index (2021)
  17. Ma, Guixiang; Ahmed, Nesreen K.; Willke, Theodore L.; Yu, Philip S.: Deep graph similarity learning: a survey (2021)
  18. Nielsen, Frank; Marti, Gautier; Ray, Sumanta; Pyne, Saumyadipta: Clustering patterns connecting COVID-19 dynamics and human mobility using optimal transport (2021)
  19. Ping, Yuhan; Wei, Guodong; Yang, Lei; Cui, Zhiming; Wang, Wenping: Self-attention implicit function networks for 3D dental data completion (2021)
  20. Qian, Yitian; Pan, Shaohua: An inexact PAM method for computing Wasserstein barycenter with unknown supports (2021)

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