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 152 articles , 1 standard article )

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  1. Chizat, Lénaïc; Peyré, Gabriel; Schmitzer, Bernhard; Vialard, François-Xavier: Unbalanced optimal transport: dynamic and Kantorovich formulations (2018)
  2. Dsilva, Carmeline J.; Talmon, Ronen; Coifman, Ronald R.; Kevrekidis, Ioannis G.: Parsimonious representation of nonlinear dynamical systems through manifold learning: a chemotaxis case study (2018)
  3. Leeb, William: The mixed Lipschitz space and its dual for tree metrics (2018)
  4. Li, Wuchen; Ryu, Ernest K.; Osher, Stanley; Yin, Wotao; Gangbo, Wilfrid: A parallel method for Earth mover’s distance (2018)
  5. Sommerfeld, Max; Munk, Axel: Inference for empirical Wasserstein distances on finite spaces (2018)
  6. Yu, Xiaokang; Lei, Na; Zheng, Xiaopeng; Gu, Xianfeng: Surface parameterization based on polar factorization (2018)
  7. Gerber, Samuel; Maggioni, Mauro: Multiscale strategies for computing optimal transport (2017)
  8. Kuang, Max; Tabak, Esteban G.: Preconditioning of optimal transport (2017)
  9. Mendivil, Franklin: Computing the Monge-Kantorovich distance (2017)
  10. Puccetti, Giovanni: An algorithm to approximate the optimal expected inner product of two vectors with given marginals (2017)
  11. Whidden, Chris; Matsen, Frederick A.IV: Ricci-Ollivier curvature of the rooted phylogenetic subtree-prune-regraft graph (2017)
  12. Wolansky, Gershon: On optimal partitions, individual values and cooperative games: does a wiser agent always produce a higher value? (2017)
  13. Abramov, Rafail V.; Kjerland, Marc: The response of reduced models of multiscale dynamics to small external perturbations (2016)
  14. Berrendero, José R.; Cuevas, Antonio; Pateiro-López, Beatriz: Shape classification based on interpoint distance distributions (2016)
  15. Christlieb, Andrew; Lawlor, David; Wang, Yang: A multiscale sub-linear time Fourier algorithm for noisy data (2016)
  16. Cuturi, Marco; Peyré, Gabriel: A smoothed dual approach for variational Wasserstein problems (2016)
  17. Dsilva, Carmeline J.; Talmon, Ronen; Gear, C.William; Coifman, Ronald R.; Kevrekidis, Ioannis G.: Data-driven reduction for a class of multiscale fast-slow stochastic dynamical systems (2016)
  18. Huang, Juntao; Yong, Wen-An; Hong, Liu: Generalization of the Kullback-Leibler divergence in the Tsallis statistics (2016)
  19. Koulouri, Alexandra; Rimpiläinen, Ville; Brookes, Mike; Kaipio, Jari P.: Compensation of domain modelling errors in the inverse source problem of the Poisson equation: application in electroencephalographic imaging (2016)
  20. Leeb, William; Coifman, Ronald: Hölder-Lipschitz norms and their duals on spaces with semigroups, with applications to earth mover’s distance (2016)

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