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Biclustering meets triadic concept analysis

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Abstract

Biclustering numerical data became a popular data-mining task at the beginning of 2000’s, especially for gene expression data analysis and recommender systems. A bicluster reflects a strong association between a subset of objects and a subset of attributes in a numerical object/attribute data-table. So-called biclusters of similar values can be thought as maximal sub-tables with close values. Only few methods address a complete, correct and non-redundant enumeration of such patterns, a well-known intractable problem, while no formal framework exists. We introduce important links between biclustering and Formal Concept Analysis (FCA). Indeed, FCA is known to be, among others, a methodology for biclustering binary data. Handling numerical data is not direct, and we argue that Triadic Concept Analysis (TCA), the extension of FCA to ternary relations, provides a powerful mathematical and algorithmic framework for biclustering numerical data. We discuss hence both theoretical and computational aspects on biclustering numerical data with triadic concept analysis. These results also scale to n-dimensional numerical datasets.

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Authors and Affiliations

  1. Université de Lyon, CNRS, INSA-Lyon, LIRIS, 20, Avenue Albert Einstein, 69621, Villeurbanne Cedex, France

    Mehdi Kaytoue

  2. Higher School of Economis (HSE), Pokrovskiy Bd. 11, 109028, Moscow, Russia

    Sergei O. Kuznetsov

  3. Palacky University, 17. listopadu, 77146, Olomouc, Czech Republic

    Juraj Macko

  4. Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), B.P. 239, 54500, Vandœuvre-lès-Nancy, France

    Amedeo Napoli

Authors
  1. Mehdi Kaytoue
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  2. Sergei O. Kuznetsov
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  3. Juraj Macko
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  4. Amedeo Napoli
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Correspondence to Mehdi Kaytoue.

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Kaytoue, M., Kuznetsov, S.O., Macko, J. et al. Biclustering meets triadic concept analysis. Ann Math Artif Intell 70, 55–79 (2014). https://doi.org/10.1007/s10472-013-9379-1

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