Abstract
In the paper we deal with dimensionality reduction techniques for a dataset with discrete attributes. Dimensionality reduction is considered as one of the most important problems in data analysis. The main aim of our paper is to show advantages of a novel approach introduced and developed by Belohlavek and Vychodil in comparison of two classical dimensionality reduction methods which can be used for ordinal attributes (CATPCA and factor analysis). The novel technique is fundamentally different from existing ones since it is based on another kind of mathematical apparatus (namely, Galois connections, lattice theory, fuzzy logic). Therefore, this method is able to bring a new insight to examined data. The comparison is accompanied by analysis of two data sets which were obtained by questionnaire survey.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Belohlavek, R.: Algorithms for fuzzy concept lattices. In: Proc. Fourth Int. Conf. on Recent Advances in Soft Computing, pp. 67–68 (2002)
Belohlavek, R.: Fuzzy Relational Systems: Foundations and Principles. Kluwer Academic/Plenum Publishers, New York (2002)
Belohlavek, R., Vychodil, V.: Factor analysis of incidence data via novel decomposition of matrices. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS, vol. 5548, pp. 83–97. Springer, Heidelberg (2009)
Belohlavek, R., Vychodil, V.: On Boolean factor analysis with formal concepts as factors. In: Int. Conf. Soft Computing and Intelligent Systems & Int. Symposium on Intelligent Systems, pp. 1054–1059 (2006)
Moulisova, M.: Investigation of policeman perception. Kriminalistika 42(1), 56–71 (2009) (in Czech)
Ganter, B., Wille, R.: Formal concept analysis. Mathematical Foundations. Springer, Berlin (1999)
Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic, Dordrecht (1998)
Klir, G.J., Yuan, B.: Fuzzy Sets and Fuzzy Logic. Theory and Applications. Prentice-Hall, Englewood Cliffs (1995)
Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470 (1982)
Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bartl, E., Rezankova, H., Sobisek, L. (2011). Comparison of Classical Dimensionality Reduction Methods with Novel Approach Based on Formal Concept Analysis. In: Yao, J., Ramanna, S., Wang, G., Suraj, Z. (eds) Rough Sets and Knowledge Technology. RSKT 2011. Lecture Notes in Computer Science(), vol 6954. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24425-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-24425-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24424-7
Online ISBN: 978-3-642-24425-4
eBook Packages: Computer ScienceComputer Science (R0)