Factor and Subsequence Kernels and Signatures of Rational Languages

  • Ahmed Amarni
  • Sylvain Lombardy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7381)


The kernels are popular methods to measure the similarity between words for classification and learning. We generalize the definition of rational kernels in order to apply kernels to the comparison of languages. We study this generalization for factor and subsequence kernels and prove that these kernels are defined for parameters chosen in an appropriate interval. We give different methods to build weighted transducers which compute these kernels.


Formal Power Series Machine Learn Research Subsequence Signature Rational Kernel String 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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  1. 1.
    Burges, C.: A tutorial on support vector machines for pattern recognition. Data Mining Knowledge Discovery 2, 121–167 (1998)CrossRefGoogle Scholar
  2. 2.
    Lodhi, H., Saunders, C., Shawe-Taylor, J., Cristianini, N., Watkins, C.: Text classification using string kernels. Journal of Machine Learning Research 2, 419–444 (2002)zbMATHGoogle Scholar
  3. 3.
    Kontorovich, L., Cortes, C., Mohri, M.: Kernel methods for learning languages. Theoretical Computer Science 405, 223–236 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cortes, C., Haffner, P., Mohri, M.: Rational kernels. In: Becker, S., Thrun, S., Obermayer, K. (eds.) NIPS, pp. 601–608. MIT Press (2002)Google Scholar
  5. 5.
    Cortes, C., Haffner, P., Mohri, M.: Rational kernels: Theory and algorithms. Journal of Machine Learning Research 5, 1035–1062 (2004)MathSciNetzbMATHGoogle Scholar
  6. 6.
    Kuich, W., Salomaa, A.: Semirings, Automata, Languages. Monographs in Theoretical Computer Science. An EATCS Series, vol. 5. Springer (1986)Google Scholar
  7. 7.
    Sakarovitch, J.: Elements of Automata Theory. Cambridge University Press (2009)Google Scholar
  8. 8.
    Cortes, C., Haffner, P., Mohri, M.: Positive Definite Rational Kernels. In: Schölkopf, B., Warmuth, M.K. (eds.) COLT/Kernel 2003. LNCS (LNAI), vol. 2777, pp. 41–56. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Sakarovitch, J., Simon, I.: Subwords. In: Combinatorics on Words. Encyclopedia of Mathematics and its Applications, vol. 17, pp. 104–144. Addison-Wesley, Reading (1983)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Ahmed Amarni
    • 1
  • Sylvain Lombardy
    • 1
  1. 1.Laboratoire d’informatique Gaspard-MongeUniversity Paris-Est Marne-la-ValléeFrance

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