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Biclustering meets triadic concept analysis

Mehdi Kaytoue 1 Sergei Kuznetsov 2 Juraj Macko 3 Amedeo Napoli 4
1 DM2L - Data Mining and Machine Learning
LIRIS - Laboratoire d'InfoRmatique en Image et Systèmes d'information
4 ORPAILLEUR - Knowledge representation, reasonning
Inria Nancy - Grand Est, LORIA - NLPKD - Department of Natural Language Processing & Knowledge Discovery
Abstract : Biclustering numerical data became a popular data-mining task at the be-ginning of 2000's, especially for gene expression data analysis and recommender sys-tems. 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 impor-tant 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 theo-retical and computational aspects on biclustering numerical data with triadic concept analysis. These results also scale to n-dimensional numerical datasets.
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Submitted on : Friday, January 9, 2015 - 5:07:57 PM
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Mehdi Kaytoue, Sergei Kuznetsov, Juraj Macko, Amedeo Napoli. Biclustering meets triadic concept analysis. Annals of Mathematics and Artificial Intelligence, Springer Verlag, 2014, 70, pp.55 - 79. ⟨10.1007/s10472-013-9379-1⟩. ⟨hal-01101143⟩



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