An Efficient Algorithm for Computing Kernel Function Defined with Anti-unification

  • Authors:
  • Koichiro Doi;Tetsuya Yamashita;Akihiro Yamamoto

  • Affiliations:
  • Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan;Graduate School of Information Science, Nara Institute Science and Technology, 8916-5 Takayama-cho, Ikoma-shi, Nara 630-0101, Japan;Graduate School of Informatics, Kyoto University, Yoshida-honmachi, Sakyo-ku, Kyoto 606-8501, Japan

  • Venue:
  • Inductive Logic Programming
  • Year:
  • 2007

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Abstract

In this paper, we give an algorithm for computing the value of the kernel function KTERM, which takes a pair of terms in first-order logic as its inputs, and facilitates Support Vector Machines classifying terms in a higher dimension space. The value of KTERM(s,t) is given as the total number of terms which subsume both sand t. The algorithm presented in the paper computes KTERM(s,t) without enumerating all such terms. We also implement the algorithm and present some experimental examples of classification of first-order terms with KTERM. Furthermore, we also propose the concept of intentional kernels as a generalization of KTERM.