Skip to main content

A Recursive Embedding Approach to Median Graph Computation

  • Conference paper
Graph-Based Representations in Pattern Recognition (GbRPR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5534))

Abstract

The median graph has been shown to be a good choice to infer a representative of a set of graphs. It has been successfully applied to graph-based classification and clustering. Nevertheless, its computation is extremely complex. Several approaches have been presented up to now based on different strategies. In this paper we present a new approximate recursive algorithm for median graph computation based on graph embedding into vector spaces. Preliminary experiments on three databases show that this new approach is able to obtain better medians than the previous existing approaches.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Schenker, A., Bunke, H., Last, M., Kandel, A.: Graph-Theoretic Techniques for Web Content Mining. World Scientific Publishing, USA (2005)

    Book  MATH  Google Scholar 

  2. Jiang, X., Münger, A., Bunke, H.: On median graphs: Properties, algorithms, and applications. IEEE Trans. Pattern Anal. Mach. Intell. 23(10), 1144–1151 (2001)

    Article  Google Scholar 

  3. Münger, A.: Synthesis of prototype graphs from sample graphs. Diploma Thesis, University of Bern (1998) (in German)

    Google Scholar 

  4. Hlaoui, A., Wang, S.: Median graph computation for graph clustering. Soft Comput. 10(1), 47–53 (2006)

    Article  Google Scholar 

  5. Ferrer, M., Serratosa, F., Sanfeliu, A.: Synthesis of median spectral graph. In: Marques, J.S., Pérez de la Blanca, N., Pina, P. (eds.) IbPRIA 2005. LNCS, vol. 3523, pp. 139–146. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Riesen, K., Neuhaus, M., Bunke, H.: Graph embedding in vector spaces by means of prototype selection. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 383–393. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Bunke, H., Allerman, G.: Inexact graph matching for structural pattern recognition. Pattern Recognition Letters 1(4), 245–253 (1983)

    Article  MATH  Google Scholar 

  8. Bunke, H., Günter, S.: Weighted mean of a pair of graphs. Computing 67(3), 209–224 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Ferrer, M., Valveny, E., Serratosa, F., Riesen, K., Bunke, H.: An approximate algorithm for median graph computation using graph embedding. In: Proceedings of 19th ICPR, pp. 287–297 (2008)

    Google Scholar 

  10. Sanfeliu, A., Fu, K.: A distance measure between attributed relational graphs for pattern recognition. IEEE Transactions on Systems, Man and Cybernetics 13(3), 353–362 (1983)

    Article  MATH  Google Scholar 

  11. Neuhaus, M., Riesen, K., Bunke, H.: Fast suboptimal algorithms for the computation of graph edit distance. In: Yeung, D.-Y., Kwok, J.T., Fred, A., Roli, F., de Ridder, D. (eds.) SSPR 2006 and SPR 2006. LNCS, vol. 4109, pp. 163–172. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  12. Riesen, K., Neuhaus, M., Bunke, H.: Bipartite graph matching for computing the edit distance of graphs. In: Escolano, F., Vento, M. (eds.) GbRPR 2007. LNCS, vol. 4538, pp. 1–12. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. White, D., Wilson, R.C.: Mixing spectral representations of graphs. In: 18th International Conference on Pattern Recognition (ICPR 2006), Hong Kong, China, August 20-24, pp. 140–144. IEEE Computer Society, Los Alamitos (2006)

    Chapter  Google Scholar 

  14. Weiszfeld, E.: Sur le point pour lequel la somme des distances de n points donnés est minimum. Tohoku Math. Journal (43), 355–386 (1937)

    Google Scholar 

  15. Riesen, K., Bunke, H.: IAM graph database repository for graph based pattern recognition and machine learning. In: SSPR/SPR, pp. 287–297 (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ferrer, M., Karatzas, D., Valveny, E., Bunke, H. (2009). A Recursive Embedding Approach to Median Graph Computation. In: Torsello, A., Escolano, F., Brun, L. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2009. Lecture Notes in Computer Science, vol 5534. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02124-4_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02124-4_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02123-7

  • Online ISBN: 978-3-642-02124-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics