Kernel Functions Based on Derivation

  • Authors:
  • Koichiro Doi;Akihiro Yamamoto

  • Affiliations:
  • Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501;Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501

  • Venue:
  • New Frontiers in Applied Data Mining
  • Year:
  • 2009

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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.