Algorithm for Automatic Definition of Validated and Non-Validated Region in Multi-Dimensional Space

  • Przemysław Klęsk


When having a set of measurement samples Θ at disposal, it is useful to create a definition of the region enclosing the samples — the domain of discourse. If the samples represent a system performing ℝn → ℝ mapping, then this is about defining such region within ℝn. In the case of clustering, the outcome region should be the sum of regions defined for single clusters. After having defined numerically this region, one can check if a certain testing sample (newly acquired), to be used as input to a ready model, is placed inside the validated region (VR) or outside it — in non-validated region (nVR). Such test allows to state whether the model output for this sample should be considered interpolation or extrapolation effect, and hence, how credible it is. This paper shows what approaches to VR definition could be chosen. Also, the paper presents the algorithm, the implementation of which would automatically define VR by producing a set of inequalities, forming the minimal convex region.

Key words

validated and non-validated region convex region input-output modeling extrapolation interpolation 


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  1. [1]
    Lászlo Kóczy and Kaoru Hirota. Interpolative reasoning with insufficient evidence. In Information Sciences, pages 169–201. Elsevier Science Publishing Co., 1993.Google Scholar
  2. [2]
    Martin Korzeń. Zastosowanie algorytmu ewolucyjnego w analizie skupien. In Materiaty Vllsesji naukowej informatyki, volume 2, Faculty of Computer Science and Information Systems, Technical University of Szczecin, Szczecin, Poland, 2002.Google Scholar
  3. [3]
    Andrzej Piegat. Fuzzy Modeling and Control. Physica Verlag Heidelberg, Germany, 2001.Google Scholar
  4. [4]
    Anthony Ralston. Wstep do analizy numerycznej. PWN, Warszawa, Poland, iii edition, 1983. Title of the original:A First Course in Numerical Analysis.Google Scholar
  5. [5]
    Izabela Rejer. Metoda modelowania wielkowymiarowego systemu z użyciem metod sztucznej inteligencji naprzyldadzie bezrobocia w Polsce. Szczecin, Poland, 2002. Ph.D. thesis.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Przemysław Klęsk
    • 1
  1. 1.Institute of Artificial Intelligence and Mathematical Methods, Faculty of Computer Science and Information SystemsTechnical University of SzczecinSzczecin

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