Multivariate data approximation with preprocessing of data

  • Witold Kosiński Polish-Japanese Institute of Information Technology
  • Dorota Kowalczyk Kazimierz Wielki University in Bydgoszcz
  • Martyna Weigl Polska Telefonia Cyfrowa, ERA GSM

Abstract

An adaptive information system is constructed in order to approximate a set of multidimensional data. To get better approximation properties a pre-processing stage of data is proposed in which the set of points, forming the multidimensional data base and called a training set TRE, undergoes a clustering analysis. In the analysis two independent clustering algorithms are used; on each cluster a feed-forward neural network is trained and a membership function of a fuzzy set is constructed. The constructed system contains a module of two-conditional fuzzy rules consequent parts of which are of the functional type. Each rule is designed on a pair of clusters.

Keywords

References

REFERENCES
[1] M.R. Anderberg. Cluster Analysis for Applications. Probability and Mathematical Statistics, Academic Press, New York, 1973.
[2] J.J. Buckley, Y. Hayashi. Numerical relationships between neural networks, continuous functions, and fuzzy systems. Fuzzy Sets and Systems, 60: 1-8, 1993.
[3] G. Cybenko. Approximation by superpositions of sigmoidal function. Mathematics of Control, Signals, and Systems, 2: 303-314, 1989.
[4] K. Funahashi. On the approximate realization of continuous mapping by neural networks. Neural Networks, 2: 183-192, 1989.
[5] D.J . Hand. Discrimination and Classification. Wiley, Chichester, 1981.
Published
Aug 17, 2022
How to Cite
KOSIŃSKI, Witold; KOWALCZYK, Dorota; WEIGL, Martyna. Multivariate data approximation with preprocessing of data. Computer Assisted Methods in Engineering and Science, [S.l.], v. 14, n. 4, p. 651-658, aug. 2022. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/798>. Date accessed: 23 dec. 2024.
Section
Articles