Encyclopedia of Machine Learning

2010 Edition
| Editors: Claude Sammut, Geoffrey I. Webb

Graph Kernels

  • Thomas Gärtner
  • Tamás Horváth
  • Stefan Wrobel
Reference work entry
DOI: https://doi.org/10.1007/978-0-387-30164-8_349

Definition

The term graph kernel is used in two related but distinct contexts: On the one hand, graph kernels can be defined between graphs, that is, as a kernel function\(k : \mathcal{G}\,\times \,\mathcal{G}\rightarrow \mathbb{R}\)

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

References

  1. Borgwardt, K. M., Petri, T., Vishwanathan, S. V. N., & Kriegel, H.-P. (2007). An efficient sampling scheme for comparison of large graphs. In Mining and learning with graphs (MLG 2007), Firenze.Google Scholar
  2. Collins, M., & Duffy, N. (2002). Convolution kernel for natural language. In Advances in neural information proccessing systems (NIPS), 16, 625–632.Google Scholar
  3. Deshpande, M., Kuramochi, M., & Karypis, G. (2002). Automated approaches for classifying structures. In Proceedings of the 2nd ACM SIGKDD workshop on data mining in bioinformatics (BIO KDD 2002).Google Scholar
  4. Gärtner, T. (2005). Predictive graph mining with kernel methods. In S. Bandyopadhyay, U. Maulik, L.B. Holder, and D.J. Cook (Eds.), Advanced methods for knowledge discovery from complex data. pp. 95–121, Springer, Heidelberg.Google Scholar
  5. Gärtner, T., Flach, P. A., & Wrobel, S. (2003). On graph kernels: Hardness results and efficient alternatives. In Proceedings of the 16th annual conference on computational learning theory and the 7th kernel workshop (COLT 2003), vol. 2777 of LNCS, pp. 129–143, Springer, Heidelberg.Google Scholar
  6. Gärtner, T., Le, Q. V., Burton, S., Smola, A. J., & Vishwanathan, S. V. N. (2006). Large-scale multiclass transduction. In Advances in neural information processing systems, vol. 18, pp. 411–418, MIT Press, Cambride, MA.Google Scholar
  7. Horvath, T., Gärtner, T., & Wrobel, S. (2004). Cyclic pattern kernels for predictive graph mining. In Proceedings of the international conference on knowledge discovery and data mining (KDD 2004), pp. 158–167, ACM Press, New York, NY.Google Scholar
  8. Kashima, H., Tsuda, K., & Inokuchi, A. (2003). Marginalized kernels between labeled graphs. In Proceedings of the 20th international conference on machine learning (ICML 2003), pp. 321–328, AAAI Press, Menlo Park, CA.Google Scholar
  9. Kondor, R. I., & Lafferty, J. (2002). Diffusion kernels on graphs and other discrete input spaces. In C. Sammut & A. Hoffmann (Eds.), Proceedings of the nineteenth international conference on machine learning (ICML 2002), pp. 315–322, Morgan Kaufmann, San Fransisco, CA.Google Scholar
  10. Mahé, P., Ueda, N., Akutsu, T., Perret, J.-L., & Vert, J.-P. (2004). Extensions of marginalized graph kernels. In Proceedings of the 21st international conference on machine learning (ICML 2004), pp. 70, ACM Press, New York, NY.Google Scholar
  11. Smola, A. J., & Kondor, R. (2003). Kernels and regularization on graphs. In Proceedings of the 16th annual conference on computational learning theory and the 7th kernel workshop (COLT 2003), vol. 2777 of LNCS, pp. 144–158, Springer, Heidelberg.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Thomas Gärtner
    • 1
  • Tamás Horváth
    • 1
  • Stefan Wrobel
    • 1
  1. 1.University of Bonn, Fraunhofer IAISSchloss BirlinghovenGermany