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Probabilistic Formal Concepts with Negation

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Perspectives of System Informatics (PSI 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8974))

Abstract

The probabilistic generalization of formal concept analysis, as well as it’s comparison to standard formal analysis is presented. Construction is resistant to noise in the data and give one an opportunity to consider contexts with negation (object-attribute relation which allows both attribute presence and it’s absence). This generalization is obtained from the notion of formal concepts with its definition as fixed points of implications, when implications, possibly with negations, are replaced by probabilistic laws. We prove such fixed points (based on the probabilistic implications) to be consistent and wherefore determine correct probabilistic formal concepts. In the end, the demonstration for the probabilistic formal concepts formation is given together with noise resistance example.

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Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    E. E. Vityaev

  2. Novosibirsk State University, Novosibirsk, Russia

    E. E. Vityaev & V. V. Martinovich

Authors
  1. E. E. Vityaev
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  2. V. V. Martinovich
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Corresponding author

Correspondence to E. E. Vityaev .

Editor information

Editors and Affiliations

  1. School of Computer Science, University of Manchester, Manchester, United Kingdom

    Andrei Voronkov

  2. A.P. Ershov Institute of Informatics Systems, Novosibirsk, Russia

    Irina Virbitskaite

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Vityaev, E.E., Martinovich, V.V. (2015). Probabilistic Formal Concepts with Negation. In: Voronkov, A., Virbitskaite, I. (eds) Perspectives of System Informatics. PSI 2014. Lecture Notes in Computer Science(), vol 8974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46823-4_31

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  • DOI: https://doi.org/10.1007/978-3-662-46823-4_31

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-46822-7

  • Online ISBN: 978-3-662-46823-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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