Evolutionary Weighted Mean Based Framework for Generalized Median Computation with Application to Strings

  • Lucas Franek
  • Xiaoyi Jiang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7626)


A new general framework for generalized median approximation is proposed based on the concept of weighted mean of a pair of objects. It can be easily adopted for different application domains like strings, graphs or clusterings, among others. The framework is validated for strings showing its superiority over the state-of-the-art.


Generalize Median Edit Distance Input String Edit Operation Median Graph 
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.
    Bunke, H., Günter, S.: Weighted mean of a pair of graphs. Computing 67(3), 209–224 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bunke, H., Jiang, X., Abegglen, K., Kandel, A.: On the weighted mean of a pair of strings. Pattern Anal. Appl. 5(1), 23–30 (2002)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ferrer, M., Valveny, E., Serratosa, F., Riesen, K., Bunke, H.: Generalized median graph computation by means of graph embedding in vector spaces. Pattern Recognition 43(4), 1642–1655 (2010)zbMATHCrossRefGoogle Scholar
  4. 4.
    Franek, L.: Ensemble Algorithms with Applications to Clustering and Image Segmentation. Ph.D. thesis, University of Münster (2012)Google Scholar
  5. 5.
    Franek, L., Jiang, X.: Weighted mean of a pair of clusterings. Pattern Anal. Appl. (under revision)Google Scholar
  6. 6.
    Jiang, X., Münger, A., Bunke, H.: On median graphs: Properties, algorithms, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 23(10), 1144–1151 (2001)CrossRefGoogle Scholar
  7. 7.
    Jiang, X., Wentker, J., Ferrer, M.: Generalized median string computation by means of string embedding in vector spaces. Pattern Recognition Letters 33(7), 842–852 (2012)CrossRefGoogle Scholar
  8. 8.
    Munkres, J.: Algorithms for the assignment and transportation problems. Journal of the Society of Industrial and Applied Mathematics 5(1), 32–38 (1957)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Rokach, L.: Pattern classification using ensemble methods. World Scientific Pub. Co. Inc. (2010)Google Scholar
  10. 10.
    Sim, J.S., Park, K.: The consensus string problem for a metric is NP-complete. J. Discrete Algorithms 1(1), 111–117 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Singh, V., Mukherjee, L., Peng, J., Xu, J.: Ensemble clustering using semidefinite programming with applications. Mach. Learn. 79(1-2), 177–200 (2010)CrossRefGoogle Scholar
  12. 12.
    Vega-Pons, S., Ruiz-Shulcloper, J.: A survey of clustering ensemble algorithms. Int. J. Pattern Recognition and Artificial Intelligence 25(3), 337–372 (2011)CrossRefGoogle Scholar
  13. 13.
    Wagner, R.A., Fischer, M.J.: The string-to-string correction problem. J. ACM 21(1), 168–173 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Weiszfeld, E., Plastria, F.: On the point for which the sum of the distances to n given points is minimum. Annals of Operations Research 167, 7–41 (2009)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Lucas Franek
    • 1
  • Xiaoyi Jiang
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of MünsterGermany

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