Comparison of Classical Dimensionality Reduction Methods with Novel Approach Based on Formal Concept Analysis

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.