Factorizing Three-Way Binary Data with Triadic Formal Concepts

  • Radim Belohlavek
  • Vilem Vychodil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6276)


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.


Formal Concept Binary Matrix Nonnegative Matrix Factorization Formal Context Formal Concept Analysis 
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© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Radim Belohlavek
    • 1
  • Vilem Vychodil
    • 1
  1. 1.Dept. Computer SciencePalacky UniversityOlomoucCzech Republic

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