Towards Bridging the Gap between Statistical and Structural Pattern Recognition: Two New Concepts in Graph Matching

  • H. Bunke
  • S. Günter
  • X. Jiang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2013)


Two novel concepts in structural pattern recognition are discussed in this paper. The first, median of a set of graphs, can be used to characterize a set of graphs by just a single prototype. Such a characterization is needed in various tasks, for example, in clustering. The second novel concept is weighted mean of a pair of graphs. It can be used to synthesize a graph that has a specified degree of similarity, or distance, to each of a pair of given graphs. Such an operation is needed in many machine learning tasks. It is argued that with these new concepts various well-established techniques from statistical pattern recognition become applicable in the structural domain, particularly to graph representations. Concrete examples include k-means clustering, vector quantization, and Kohonen maps.


Graph matching error-tolerant matching edit distance median graph weighted mean 


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  1. [1]
    A. Admin, D. Dori, P. Pudil, and H. Freemann, editors. Advances in Pattern Recognition. Number 1451 in LNCS. Springer, 1998.Google Scholar
  2. [2]
    H. Bunke, editor. Advances in Structural and Syntactical Pattern Recognition. World Scientific Publ. Co., 1992.Google Scholar
  3. [3]
    H. Bunke. Error-tolerant graph matching: a formal framework and algorithms. In [1], pages 1–14. 1998.Google Scholar
  4. [4]
    H. Bunke and A. Kandel. Mean and maximum common subgraph of two graphs. Pattern Recognition Letters, 21:163–168, 2000.CrossRefGoogle Scholar
  5. [5]
    H. Bunke, A. Münger, and X. Jiang. Combinatorial search versus genetic algorithms: a case study based on the generalized mean graph problem. Pattern Recognition Letters, 20:1271–1277, 1999.CrossRefGoogle Scholar
  6. [6]
    H. Bunke and A. Sanfeliu, editors. Syntactic and Structural Pattern Recognition-Theory and Applications. World Scientific Publ. Co., 1990.Google Scholar
  7. [7]
    F. Casacuberta and M. Antonia. A greedy algorithm for computing approximate median strings. In Proc. Nat. Symp. of Pattern Recognition and Image Analysis, pages 193–198, Barcelona, Spain, 1996.Google Scholar
  8. [8]
    D. Dori and A. Bruckstein, editors. Shape, Structure and Pattern Recognition. World Scientific Publ. Co., 1995.Google Scholar
  9. [9]
    R. Englert and R. Glanz. Towards the clustering of graphs. In Proc. 2nd IAPR-TC-15 Workshop on Graph Based Representations, pages 125–133, 2000.Google Scholar
  10. [10]
    K. Fu. Syntactic Pattern Recognition and Applications. Prentice Hall, 1982.Google Scholar
  11. [11]
    S. Günter. Kohonen map for the domain of graphs. Master’s thesis, University of Bern. In progress (in German).Google Scholar
  12. [12]
    A. Jain, R. Duin, and J. Mao. Statistical Pattern Recognition: A Review. IEEE Trans PAMI, 22:4–37, 2000.Google Scholar
  13. [13]
    X. Jiang, A. Münger, and H. Bunke. Synthesis of representative symbols by computing generalized median graphs. In Proc. Int. Workshop on Graphics Recognition GREC’ 99, pages 187–194, Jaipur, 1999.Google Scholar
  14. [14]
    X. Jiang, A. Münger, and H. Bunke. Computing the generalized median of a set of graphs. In Proc. 2nd IAPR-TC-15 Workshop on Graph Based Representations, pages 115–124, 2000.Google Scholar
  15. [15]
    X. Jiang, A. Münger, and H. Bunke. On median graphs: Properties, algorithms, and applications. Submitted, 2000.Google Scholar
  16. [16]
    X. Jiang, L. Schiffmann, and H. Bunke. Computation of median shapes. In 4th Asian Conf. on Computer Vision, pages 300–305, Taipei, Taiwan, 2000.Google Scholar
  17. [17]
    T. Kohonen. Self-Organizing Maps. Springer Verlag, 1995.Google Scholar
  18. [18]
    F. Kruzslicz. Improved greedy algorithm for computing approximate median strings. Acta Cybernetica, 14:331–339, 1999.MATHMathSciNetGoogle Scholar
  19. [19]
    D. Lopresti and J. Zhou. Using consensus voting to correct OCR errors. Computer Vision and Image Understanding, 67(1):39–47, 1997.CrossRefGoogle Scholar
  20. [20]
    S.-Y. Lu. A tree-to-tree distance and its application to cluster analysis. IEEE Trans. PAMI, 1:219–224, 1979.MATHGoogle Scholar
  21. [21]
    P. Perner, P. Wang, and A. Rosenfeld, editors. Advances in Structural and Syntactical Pattern Recognition. Number 1121 in LNCS. Springer, 1996.Google Scholar
  22. [22]
    S. Rice, J. Kanai, and T. Nartker. A difference algorithm for OCR-generated text. In [2], pages 333–341, 1992.Google Scholar
  23. [23]
    D. Seong, H. Kim, and K. Park. Incremental clustering of attributed graphs. IEEE Trans. SMC, 23:1399–1411, 1993.Google Scholar
  24. [24]
    R. Wagner and M. Fischer. The string-to-string correction problem. Journal of the Association for Computing Machinery, 21(1):168–173, 1974.MATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • H. Bunke
    • 1
  • S. Günter
    • 1
  • X. Jiang
    • 1
  1. 1.Dept. of Computer ScienceUniv. of BernSwitzerland

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