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Factorizing Three-Way Binary Data with Triadic Formal Concepts

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Knowledge-Based and Intelligent Information and Engineering Systems (KES 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6276))

Abstract

We present a problem of factor analysis of three-way binary data. Such data is described by a 3-dimensional binary matrix I, describing a relationship between objects, attributes, and conditions. The aim is to decompose I into three binary matrices, an object-factor matrix A, an attribute-factor matrix B, and a condition-factor matrix C, with a small number of factors. The difference from the various decomposition-based methods of analysis of three-way data consists in the composition operator and the constraint on A, B, and C to be binary. We present a theoretical analysis of the decompositions and show that optimal factors for such decompositions are provided by triadic concepts developed in formal concept analysis. Moreover, we present an illustrative example, propose a greedy algorithm for computing the decompositions.

Supported by grant no. P202/10/0262 of the Czech Science Foundation and by grant no. MSM 6198959214.

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Author information

Authors and Affiliations

  1. Dept. Computer Science, Palacky University, Olomouc 17. listopadu 12, CZ-771 46, Olomouc, Czech Republic

    Radim Belohlavek & Vilem Vychodil

Authors
  1. Radim Belohlavek
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  2. Vilem Vychodil
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Editor information

Editors and Affiliations

  1. School of Engineering, The Parade, Cardiff University, CF24 3AA, Cardiff, UK

    Rossitza Setchi

  2. Dept. of Computer Science and Software Engineering, BUckingham Building, Lion Terrace, University of Portsmouth, PO1 3HE, Portsmouth, UK

    Ivan Jordanov

  3. KES International, 145-157, St. John Street, EC1V 4PY, London, UK

    Robert J. Howlett

  4. School of Electrical and Information Engineering, University of South Australia, ,, Adelaide, Mawson Lakes Campus, 5095, SA, Australia

    Lakhmi C. Jain

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Belohlavek, R., Vychodil, V. (2010). Factorizing Three-Way Binary Data with Triadic Formal Concepts. In: Setchi, R., Jordanov, I., Howlett, R.J., Jain, L.C. (eds) Knowledge-Based and Intelligent Information and Engineering Systems. KES 2010. Lecture Notes in Computer Science(), vol 6276. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15387-7_51

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  • DOI: https://doi.org/10.1007/978-3-642-15387-7_51

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15386-0

  • Online ISBN: 978-3-642-15387-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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