Intersection and Signed-Intersection Kernels for Intervals

  • Authors:
  • Francisco J. Ruiz;Cecilio Angulo;Núria Agell

  • Affiliations:
  • Knowledge Engineering Research Group. Universitat Politècnica de Catalunya;Knowledge Engineering Research Group. Universitat Politècnica de Catalunya;Department of Quantitative Methods Management. ESADE-Universitat Ramon Llull

  • Venue:
  • Proceedings of the 2008 conference on Artificial Intelligence Research and Development: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence
  • Year:
  • 2008

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Abstract

In this paper two kernels for interval data based on the intersection operation are introduced. On the one hand, it is demonstrated that the intersection length of two intervals is a positive definite (PD) kernel. On the other hand, a signed variant of this kernel, which also permits discriminating between disjoint intervals, is demonstrated to be a conditionally positive definite (CPD) kernel. The potentiality and performance of the two kernels presented when applying them to learning machine techniques based on kernel methods are shown by considering three different examples involving interval data.