Advertisement

Decision Rules with Collinearity Models

  • Leon BobrowskiEmail author
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 56)

Abstract

Data mining algorithms are used for discovering general regularities based on the observed patterns in data sets. Flat (multicollinear) patterns can be observed in data sets when many feature vectors are located on a planes in the multidimensional feature space. Collinear patterns can be useful in modeling linear interactions between multiple variables (features) and can be used also in a decision support process. Flat patterns can be efficiently discovered in large, multivariate data sets through minimization of the convex and piecewise linear (CPL) criterion functions.

Keywords

Data mining Decision rules Collinear models CPL criterion functions 

Notes

Acknowledgments

This work was supported by the project S/WI/2/2016 from the Białystok University of Technology, Poland.

References

  1. 1.
    Hand, D., Smyth, P., Mannila, H.: Principles of Data Mining. MIT Press, Cambridge (2001)Google Scholar
  2. 2.
    Duda, O.R., Hart, P.E., Stork, D.G.: Pattern Classification. J. Wiley, New York (2001)zbMATHGoogle Scholar
  3. 3.
    Bobrowski, L.: K-lines clustering with convex and piecewise linear. CPL) functions, MATHMOD, Vienna (2012)Google Scholar
  4. 4.
    Bobrowski, L.: Discovering main vertexical planes in a multivariate data space by using CPL functions. In: Perner, P. (ed.) ICDM 2014. Springer, Berlin (2014)Google Scholar
  5. 5.
    Duda, O.R., Hart, P.E.: Use of the hough transformation to detect lines and curves in pictures. Commun. Assoc. Comput. Mach. 15(1), 11–15 (1972)zbMATHGoogle Scholar
  6. 6.
    Ballard, D.H.: Generalizing the hough transform to detect arbitrary shapes. Pattern Recogn. 13(2), 111–122 (1981)CrossRefzbMATHGoogle Scholar
  7. 7.
    Bobrowski, L.: Data Mining Based on Convex and Piecewise Linear Criterion Functions (in Polish). Technical University Białystok (2005)Google Scholar
  8. 8.
    Bobrowski, L.: Design of piecewise linear classifiers from formal neurons by some basis exchange technique. Pattern Recogn. 24(9), 863–870 (1991)CrossRefGoogle Scholar
  9. 9.
    Simonnard, M.: Linear Programming. Prentice-Hall (1966)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Computer ScienceBiałystok University of TechnologyBiałystokPoland
  2. 2.Institute of Biocybernetics and Biomedical Engineering, PASWarsawPoland

Personalised recommendations