Comparison of Classical Dimensionality Reduction Methods with Novel Approach Based on Formal Concept Analysis
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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.
Keywordsdimensionality reduction discrete data factor analysis formal concept analysis fuzzy logic matrix decomposition principal component analysis
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- 1.Belohlavek, R.: Algorithms for fuzzy concept lattices. In: Proc. Fourth Int. Conf. on Recent Advances in Soft Computing, pp. 67–68 (2002)Google Scholar
- 4.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)Google Scholar
- 5.Moulisova, M.: Investigation of policeman perception. Kriminalistika 42(1), 56–71 (2009) (in Czech)Google Scholar
- 6.Ganter, B., Wille, R.: Formal concept analysis. Mathematical Foundations. Springer, Berlin (1999)Google Scholar
- 9.Wille, R.: Restructuring lattice theory: an approach based on hierarchies of concepts. In: Rival, I. (ed.) Ordered Sets, pp. 445–470 (1982)Google Scholar