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Metric-Preserving Reduction Of Earth Mover'S Distance

Author

Listed:
  • YUICHI TAKANO

    (Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan)

  • YOSHITSUGU YAMAMOTO

    (Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan)

Abstract

Earth mover's distance (EMD for short) is a perceptually meaningful dissimilarity measure between histograms. The computation of EMD reduces to a network flow optimization problem; however, it lays a heavy computational burden when the number of locations of histograms is large. In this paper, we address an efficient formulation for computing the exact EMD value. We prove that the EMD problem reduces to a problem with half the number of constraints regardless of the ground distance. We then propose a further reduced formula in which the number of variables is reduced fromO(m2)toO(m)for histograms withmlocations when the ground distance is derived from a graph with a homogeneous neighborhood structure. Specifically, EMD problems withL1,L∞andD-norm ground distances can be reduced in this manner. Some experiments show that the reduction helps compute the EMD efficiently.

Suggested Citation

  • Yuichi Takano & Yoshitsugu Yamamoto, 2010. "Metric-Preserving Reduction Of Earth Mover'S Distance," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(01), pages 39-54.
    • Handle: RePEc:wsi:apjorx:v:27:y:2010:i:01:n:s0217595910002545
    DOI: 10.1142/S0217595910002545
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