On support vector regression machines with linguistic interpretation of the kernel matrix

  • Authors:
  • Jacek M. Łski

  • Affiliations:
  • Institute of Electronics, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2006

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Abstract

Initially, the idea of approximate reasoning using generalized modus ponens and a fuzzy implication is recalled. Next, a fuzzy system based on logical interpretation of if-then rules and with parametric conclusions is presented. Then, it is shown that global and local @e-insensitive learning of the above fuzzy system may be presented as the learning of a support vector regression machine with a special type of a kernel matrix obtained from clustering. The kernel matrix may be interpreted in terms of linguistic values based on the premises of if-then rules. A new method of obtaining a fuzzy system by means of a support vector machine (SVM) with a data-dependent kernel matrix is introduced. This paper contains examples of a SVM used to design fuzzy models of real-life data. Simulation results show an improvement in the generalization ability of a fuzzy system learned by the new method compared with traditional learning methods.