Skip to main content
SpringerLink
Log in

Kernelization of Softassign and Motzkin-Strauss Algorithms

  • Conference paper
Bio-Inspired Systems: Computational and Ambient Intelligence (IWANN 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5517))

Included in the following conference series:

  • 1637 Accesses

Abstract

This paper reviews two continuous methods for graph matching: Softassign and Replicator Dynamics. These methods can be applied to non-attributed graphs, but considering only structural information results in a higher ambiguity in the possible matching solutions. In order to reduce this ambiguity, we propose to extract attributes from non-attributed graphs and embed them in the graph-matching cost function, to be used as a similarity measure between the nodes in the graphs. Then, we evaluate their performance within the reviewed graph-matching algorithms.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
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. Barrow, H., Popplestone, R.: Relational descriptions in picture processing. Machine Intelligence VI, 377–396 (1971)

    Google Scholar 

  2. Baum, L.E., Eagon, J.A.: An inequality with applications to statistical estimation for probabilistic functions of Markov processes and to a model for ecology. Bull. Amer. Math. Soc. 73, 360–363 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chung, F.R.K.: Spectral Graph Theory. Conference Board of the Mathematical Sciences (CBMS). American Mathematical Society 92 (1997)

    Google Scholar 

  4. Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000)

    MATH  Google Scholar 

  5. Finch, A.M., Wilson, R.C., Hancock, E.R.: Symbolic Graph Matching with the EM algorithm. Pattern Recognition 31(11), 1777–1790 (1998)

    Article  Google Scholar 

  6. Finch, A.M., Wilson, R.C., Hancock, E.R.: An Energy Function and Continuous Edit Process for Graph Matching. Neural Computation 10(7) (1998)

    Google Scholar 

  7. Fischler, M., Elschlager, R.: The representation and matching of pictorical structures. IEEE Transactions on Computers 22(1), 67–92 (1972)

    Google Scholar 

  8. Kondor, R.I., Lafferty, J.: Diffusion Kernels on Graphs and other Discrete Input Spaces. In: Machine Learning, Proceedings of the Nineteenth International Conference (ICML 2002), pp. 315–322 (2002)

    Google Scholar 

  9. Gold, S., Rangarajan, A.: A Graduated Assignement Algorithm for Graph Matching. IEEE Transactions on Pattern Analysis and Machine Intelligence 18(4), 377–388 (1996)

    Article  Google Scholar 

  10. Lozano, M.A.: Kernelized Graph Matching and Clustering. Ph.D. Thesis, University of Alicante, Spain (2008)

    Google Scholar 

  11. Lyubich, Y., Maistrowskii, G.D., Ol’khovskii, Y.G.: Selection-induced convergence to equilibrium in a single-locus autosomal population. Problems of Information Transmission 16, 66–75 (1980)

    MathSciNet  Google Scholar 

  12. Motzkin, T.S., Straus, E.G.: Maxima for graphs and a new proof of a theorem of Turn. Canad. J. Math. 17, 533–540 (1965)

    Article  MATH  Google Scholar 

  13. Mller, K.-R., Mika, S., Rshc, G., Tsuda, K., Schlkopf, B.: An Introduction to Kernel-based Learning Algorithms. IEEE Transactions on Neural Networks 12(2), 181–201 (2001)

    Article  Google Scholar 

  14. Pelillo, M.: Replicator Equations, Maximal Cliques, and Graph Isomorphism. Neural Computation 11(8), 1933–1955 (1999)

    Article  Google Scholar 

  15. Schlkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002)

    Google Scholar 

  16. Sinkhorn, R.: A Relationship Between Arbitrary Positive Matrices and Doubly Stochastic Matrices. Annals of Mathematical Statistics 35, 876–879 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  17. Smola, A., Kondor, R.I.: Kernels and Regularization on Graphs. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS, vol. 2777, pp. 144–158. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  18. Taylor, P., Jonker, L.: Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145–156 (1978)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Robot Vision Group, Departamento de Ciencia de la Computacin e IA, Universidad de Alicante, Spain

    M. A. Lozano & F. Escolano

Authors
  1. M. A. Lozano
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Escolano
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Departamento de Ingeniería Electrónica, Universitat Politècnica de Catalunya (UPC). E.T.S.I. de Telecomunicación., , , ,, Campus Norte, Edificio C4, C/ Jordi Girona, 1-3, E08034, Barcelona, Spain

    Joan Cabestany

  2. Grupo ISIS, Dpto. Tecnología Electrónica ETSI Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Francisco Sandoval

  3. Department of Computer Architecture and Computer Technology, University of Granada, Spain

    Alberto Prieto

  4. Department of Informatics, University of Salamanca, Salamanca, Spain

    Juan M. Corchado

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lozano, M.A., Escolano, F. (2009). Kernelization of Softassign and Motzkin-Strauss Algorithms. In: Cabestany, J., Sandoval, F., Prieto, A., Corchado, J.M. (eds) Bio-Inspired Systems: Computational and Ambient Intelligence. IWANN 2009. Lecture Notes in Computer Science, vol 5517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02478-8_51

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-02478-8_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02477-1

  • Online ISBN: 978-3-642-02478-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation