Skip to main content
SpringerLink
Log in

Kernel Functions Based on Derivation

  • Conference paper
New Frontiers in Applied Data Mining (PAKDD 2008)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5433))

Included in the following conference series:

Abstract

In this paper we explain the fundamental idea of designing a class of kernel functions, called the intentional kernel, for structured data. The intentional kernel is designed with the property that every structured data is defined by derivation. Derivation means transforming a data or an expression into another. Typical derivation can be found in the field of formal language theory: A grammar defines a language in the sense that a sequence belongs to a language if it is transformed from a starting symbol by repeated application of the production rules in the grammar. Another example is in mathematical logic: A formula is proved if it is obtained from axioms by repeated application of inference rules. Combining derivation with the kernel-based learning mechanism derives the class of the intentional kernel.

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 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. Cristianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines and Other Kernel-Based Learning Methods. Cambridge University Press, Cambridge (2000)

    Book  Google Scholar 

  2. Doi, K., Yamashita, T., Yamamoto, A.: An Efficient Algorithm for Computing Kernel Function Defined with Anti-unification. In: Muggleton, S., Otero, R., Tamaddoni-Nezhad, A. (eds.) ILP 2006. LNCS (LNAI), vol. 4455, pp. 139–153. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  3. Gärtner, T.: A Survey of Kernel for Structured Data. SIGKDD Explorations 5(1), 268–275 (2003)

    Article  Google Scholar 

  4. Haussler, D.: Convolution Kernels on Discrete Structures, Technical Report UCS-CRL-99-10, University of California - Santa Cruz (1999)

    Google Scholar 

  5. Khardon, R., Roth, D., Servedio, R.: Efficiency versus Convergence of Boolean Kernels for On-Line Learning Algorithms. Journal of Artificial Intelligence Research 24, 341–356 (2005)

    Google Scholar 

  6. Laird, P.D.: Learning from Good and Bad Data. Kluwer Academic Publishers, Dordrecht (1988)

    Book  Google Scholar 

  7. Lassez, J.-L., Maher, M.J., Marriott, K.: Unification Revisited. In: Minker, J. (ed.) Foundations of Deductive Databases and Logic Programming, pp. 587–626. Morgan-Kaufman, San Francisco (1988)

    Chapter  Google Scholar 

  8. Muggleton, S., Lodhi, H., Amini, A., Sternberg, M.J.E.: Support Vector Inductive Logic Programming. In: Hoffmann, A., Motoda, H., Scheffer, T. (eds.) DS 2005. LNCS (LNAI), vol. 3735, pp. 163–175. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  9. Nienhuys-Cheng, S.-H., de Wolf, R.: Foundations of Inductive Logic Programming. Springer, Heidelberg (1997)

    Book  Google Scholar 

  10. Plotkin, G.D.: A Note on Inductive Generalization. Machine Intelligence 5, 153–163 (1970)

    Google Scholar 

  11. Sadohara, K.: Learning of Boolean Functions Using Support Vector Machine. In: Abe, N., Khardon, R., Zeugmann, T. (eds.) ALT 2001. LNCS (LNAI), vol. 2225, pp. 106–118. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. Sadohara, K.: On a Capacity Control Using Boolean Kernels for the Learning of Boolean Functions. In: Proceedings of the IEEE International Conference on Data Mining, pp. 410–417 (2002)

    Google Scholar 

  13. Sankoh, H., Doi, K., Yamamoto, A.: An Intentional Kernel Function for RNA Classification. In: Corruble, V., Takeda, M., Suzuki, E. (eds.) DS 2007. LNCS (LNAI), vol. 4755, pp. 281–285. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  14. Scholkopf, B., Smola, A.J.: Learning With Kernels: Support Vector Machines, Regularization, Optimization and Beyond. MIT Press, Cambridge (2001)

    Google Scholar 

  15. Shapiro, E.Y.: Inductive Inference of Theories From Facts, Technical Report 192, Department of Computer Science, Yale University (1981); also in: Lassez, J.-L., Plotkin, G. (eds.) Computational Logic, pp. 199–254.The MIT Press, Cambridge (1991)

    Google Scholar 

  16. Yamamoto, A.: Inductive Logic Programming: Yet Another Application of Logic. In: Umeda, M., Wolf, A., Bartenstein, O., Geske, U., Seipel, D., Takata, O. (eds.) INAP 2005. LNCS (LNAI), vol. 4369, pp. 102–116. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto, 606-8501, Japan

    Koichiro Doi & Akihiro Yamamoto

Authors
  1. Koichiro Doi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Akihiro Yamamoto
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Information Technologies, University of Sydney, NSW, Australia

    Sanjay Chawla

  2. The Institute of Scientific and Industrial Research, Osaka University, 8-1, Mihogaoka, Ibaraki, 567, Osaka, Japan

    Takashi Washio

  3. Division of Computing Science, Hokkaido University, 060-0814, Sapporo, Japan

    Shin-ichi Minato

  4. School of Medicine, Department of Medical Informatics, Shimane University, 89-1 Enya-cho, Izumo, 693-8501, Shimane, Japan

    Shusaku Tsumoto

  5. Central Research Institute of Electric Power Industry, 2-11-1 Iwado-kita, Komae-shi, 201-8511, Tokyo, Japan

    Takashi Onoda

  6. National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, 101-8430, Tokyo, Japan

    Seiji Yamada

  7. The Institute of Scientific and Industrial Research, Osaka University, 8-1 Mihogaoka, Ibaraki, 567, Osaka, Japan

    Akihiro Inokuchi

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Doi, K., Yamamoto, A. (2009). Kernel Functions Based on Derivation. In: Chawla, S., et al. New Frontiers in Applied Data Mining. PAKDD 2008. Lecture Notes in Computer Science(), vol 5433. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00399-8_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00399-8_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00398-1

  • Online ISBN: 978-3-642-00399-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation