Comparing two distributions is of fundamental importance to statistics and pattern recognition. The earth mover’s distance (EMD) has been considered an excellent distance measure between two distributions. It is defined to minimize the cost using a given cost matrix and formulated as the transportation problem which is a hard optimization problem. There are three special type cost matrices where efficient algorithms are known: nominal, ordinal, and modulo. Here the problem of identifying whether a given cost matrix has the shuffled ordinal property is considered and if so, the linear time complexity algorithm can be applied to compute the EMD efficiently.


Edit Distance Cost Matrix Cost Matrice Ordinal Property Hard Optimization Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Duda, R.O., Hart, P.E., Stork, D.G.: Pattern Classification, 2nd edn. Wiley, New York (2000)zbMATHGoogle Scholar
  2. 2.
    Rubner, Y., Tomasi, C., Guibas, L.J.: A metric for distributions with applications to image databases. In: Proc. of ICCV, pp. 59–66 (1998)Google Scholar
  3. 3.
    Levina, E., Bickel, P.: The Earth Mover’s distance is the Mallows distance: some insights from Statistics. In: Proc. of ICCV, pp. 251–256 (2001)Google Scholar
  4. 4.
    Hiller, F.S., Lieberman, G.J.: Introduction to mathematical programming, 2nd edn. McGraw-Hill, New York (1995)Google Scholar
  5. 5.
    Ahuha, R.K., Magnanti, T.L., Orlin, J.B.: Network Flows. Prentice Hall, Englewood Cliffs (1993)Google Scholar
  6. 6.
    Cha, S.-H.: Fast Image Template and Dictionary Matching Algorithms. In: Chin, R., Pong, T.-C. (eds.) ACCV 1998. LNCS, vol. 1351, pp. 370–377. Springer, Heidelberg (1997)Google Scholar
  7. 7.
    Cha, S.-H., Srihari, S.N.: Distance between Histograms of Angular Measurements and its Application to Handwritten Character Similarity. In: Proceedings of 15th ICPR 2000, September 3-8, 2000, pp. 21–24. IEEE Computer Society, Barcelona (2000)Google Scholar
  8. 8.
    Cha, S.-H., Srihari, S.N.: On Measuring the Distance between Histograms. Journal of Pattern Recognition 35(6), 1355–1370 (2002)CrossRefzbMATHGoogle Scholar
  9. 9.
    Henikoff, S.: Amino Acid Substitution Matrices from Protein Blocks. In: PNAS 1989, pp. 10915–10919 (1992)Google Scholar
  10. 10.
    Dayhoff, M.O., Schwartz, R.M., Orcutt, B.C.: A model of evolutionary change in proteins, matrices for detecting distant relationships. In: Atlas of Protein Sequence and Structure, vol. 5, pp. 345–358. National Biomedical Research Foundation, Washington DC (1978)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Sung-Hyuk Cha
    • 1
  1. 1.Department of Computer SciencePace UniversityPleasantvilleUSA

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