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Kernels over Relational Algebra Structures

  • Adam Woźnica
  • Alexandros Kalousis
  • Melanie Hilario
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3518)

Abstract

In this paper we present a novel and general framework based on concepts of relational algebra for kernel-based learning over relational schema. We exploit the notion of foreign keys to define a new attribute that we call instance-set and we use this type of attribute to define a tree like structured representation of the learning instances. We define kernel functions over relational schemata which are instances of \(\Re\)-Convolution kernels and use them as a basis for a relational instance-based learning algorithm. These kernels can be considered as being defined over typed and unordered trees where elementary kernels are used to compute the graded similarity between nodes. We investigate their formal properties and evaluate the performance of the relational instance-based algorithm on a number of relational data sets.

Keywords

Feature Space Relational Schema Relational Algebra Polynomial Kernel Convolution Kernel 
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.

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References

  1. 1.
    Dzeroski, S., Lavrac, N.: Relational Data Mining. Springer, New York (2001)zbMATHGoogle Scholar
  2. 2.
    Haussler, D.: Convolution kernels on discrete structures. Technical report, UC Santa Cruz (1999)Google Scholar
  3. 3.
    Gärtner, T., Lloyd, J., Flach, P.: Kernels and distances for structured data. Machine Learning (2004)Google Scholar
  4. 4.
    Collins, M., Duffy, N.: Convolution kernels for natural language. In: Dietterich, T.G., Becker, S., Ghahramani, Z. (eds.) Advances in Neural Information Processing Systems, vol. 14. MIT Press, Cambridge (2002)Google Scholar
  5. 5.
    Schölkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2002)Google Scholar
  6. 6.
    Gärtner, T., Flach, P., Kowalczyk, A., Smola, A.: Multi-instance kernels. In: Sammut, C. (ed.) ICML 2002. Morgan Kaufmann, San Francisco (2002)Google Scholar
  7. 7.
    Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)Google Scholar
  8. 8.
    Dzeroski, S., Schulze-Kremer, S., Heidtke, K.R., Siems, K., Wettschereck, D.: Applying ILP to diterpene structure elucidation from 13c NMR spectra. In: Inductive Logic Programming Workshop, pp. 41–54 (1996)Google Scholar
  9. 9.
    Dietterich, T.G., Lathrop, R.H., Lozano-Perez, T.: Solving the multiple instance problem with axis-parallel rectangles. Artificial Intelligence 89, 31–71 (1997)zbMATHCrossRefGoogle Scholar
  10. 10.
    Srinivasan, A., Muggleton, S., King, R., Sternberg, M.: Mutagenesis: ILP experiments in a non-determinate biological domain. In: Wrobel, S. (ed.) Proceedings of the 4th International Workshop on Inductive Logic Programming, vol. 237, pp. 217–232 (1994)Google Scholar
  11. 11.
    Mahé, P., Ueda, N., Akutsu, T., Perret, J.L., Vert, J.P.: Extensions of marginalized graph kernels. In: ICML 2004 (2004)Google Scholar
  12. 12.
    Wrobel, S.: An algorithm for multi-relational discovery of subgroups. In: Komorowski, J., Żytkow, J.M. (eds.) PKDD 1997. LNCS, vol. 1263, pp. 78–87. Springer, Heidelberg (1997)Google Scholar
  13. 13.
    Kashima, H., Koyanagi, T.: Kernels for semi-structured data. In: ICML 2002 (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Adam Woźnica
    • 1
  • Alexandros Kalousis
    • 1
  • Melanie Hilario
    • 1
  1. 1.Computer Science DepartmentUniversity of GenevaGeneva 4Switzerland

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