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Factor analysis of ordinal data via decomposition of matrices with grades

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Abstract

We present new results on a recently developed method of factor analysis of data with ordinal attributes. The method is based on the apparatus of logic, the theory of relations and ordered sets, and provides an alternative to traditional methods of factor analysis. It utilizes formal concepts as factors and we demonstrate on several examples using sports data that the factors produced by the method are reasonable and easy-to-interpret. In addition, we propose ways to address various natural questions regarding the method and its use and put forward new research issues.

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Authors and Affiliations

  1. Department of Computer Science, Palacky University, Olomouc, Czech Republic

    Radim Belohlavek & Marketa Krmelova

Authors
  1. Radim Belohlavek
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  2. Marketa Krmelova
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Corresponding author

Correspondence to Marketa Krmelova.

Additional information

We acknowledge support by Grant No. P202/10/0262 of the Czech Science Foundation. A preliminary version of this paper was presented at CLA 2012.

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Belohlavek, R., Krmelova, M. Factor analysis of ordinal data via decomposition of matrices with grades. Ann Math Artif Intell 72, 23–44 (2014). https://doi.org/10.1007/s10472-014-9398-6

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  • DOI: https://doi.org/10.1007/s10472-014-9398-6

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