Granular representation of temporal signals using differential quadratures

  • Authors:

  • Michał Momot;Alina Momot;Krzysztof Horoba;Janusz Jeżewski

  • Affiliations:

  • Institute of Medical Technology and Equipment ITAM, Zabrze, Poland;Silesian University of Technology, Institute of Computer Science, Gliwice, Poland;Institute of Medical Technology and Equipment ITAM, Zabrze, Poland;Institute of Medical Technology and Equipment ITAM, Zabrze, Poland

  • Venue:
  • ACIIDS'11 Proceedings of the Third international conference on Intelligent information and database systems - Volume Part II
  • Year:
  • 2011

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Abstract

This article presents the general idea of granular representation of temporal data, particularly signal sampled with constant frequency. The core of presented method is based on using fuzzy numbers as information granules. Three types of fuzzy numbers are considered, as interval numbers, triangular numbers and Gaussian numbers. The input space contains values of first few derivatives of underlying signal, which are computed using certain numerical differentiation algorithms, including polynomial interpolation as well as polynomial approximation. Data granules are constructed using the optimization method according to objective function based on two criteria: high description ability and compactness of fuzzy numbers. The data granules are subject to the clustering process, namely fuzzy c-means. The centroids of created clusters form a granular vocabulary. Quality of description is quantitatively assessed by reconstruction criterion. Results of numerical experiments are presented, which incorporate exemplary biomedical signal, namely electrocardiographic signal.