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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hand, D., Smyth, P., Mannila, H.: Principles of Data Mining. MIT Press, Cambridge (2001)
Duda, O.R., Hart, P.E., Stork, D.G.: Pattern Classification. J. Wiley, New York (2001)
Bobrowski, L.: K-lines clustering with convex and piecewise linear. CPL) functions, MATHMOD, Vienna (2012)
Bobrowski, L.: Discovering main vertexical planes in a multivariate data space by using CPL functions. In: Perner, P. (ed.) ICDM 2014. Springer, Berlin (2014)
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)
Ballard, D.H.: Generalizing the hough transform to detect arbitrary shapes. Pattern Recogn. 13(2), 111–122 (1981)
Bobrowski, L.: Data Mining Based on Convex and Piecewise Linear Criterion Functions (in Polish). Technical University Białystok (2005)
Bobrowski, L.: Design of piecewise linear classifiers from formal neurons by some basis exchange technique. Pattern Recogn. 24(9), 863–870 (1991)
Simonnard, M.: Linear Programming. Prentice-Hall (1966)
Acknowledgments
This work was supported by the project S/WI/2/2016 from the Białystok University of Technology, Poland.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Bobrowski, L. (2016). Decision Rules with Collinearity Models. In: Czarnowski, I., Caballero, A., Howlett, R., Jain, L. (eds) Intelligent Decision Technologies 2016. IDT 2016. Smart Innovation, Systems and Technologies, vol 56. Springer, Cham. https://doi.org/10.1007/978-3-319-39630-9_24
Download citation
DOI: https://doi.org/10.1007/978-3-319-39630-9_24
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-39629-3
Online ISBN: 978-3-319-39630-9
eBook Packages: EngineeringEngineering (R0)