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Quantitative Concept Analysis

  • Conference paper
Formal Concept Analysis (ICFCA 2012)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7278))

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Abstract

Formal Concept Analysis (FCA) begins from a context, given as a binary relation between some objects and some attributes, and derives a lattice of concepts, where each concept is given as a set of objects and a set of attributes, such that the first set consists of all objects that satisfy all attributes in the second, and vice versa. Many applications, though, provide contexts with quantitative information, telling not just whether an object satisfies an attribute, but also quantifying this satisfaction. Contexts in this form arise as rating matrices in recommender systems, as occurrence matrices in text analysis, as pixel intensity matrices in digital image processing, etc. Such applications have attracted a lot of attention, and several numeric extensions of FCA have been proposed. We propose the framework of proximity sets (proxets), which subsume partially ordered sets (posets) as well as metric spaces. One feature of this approach is that it extracts from quantified contexts quantified concepts, and thus allows full use of the available information. Another feature is that the categorical approach allows analyzing any universal properties that the classical FCA and the new versions may have, and thus provides structural guidance for aligning and combining the approaches.

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Author information

Authors and Affiliations

  1. Royal Holloway, University of London, UK

    Dusko Pavlovic

  2. University of Twente, The Netherlands

    Dusko Pavlovic

Authors
  1. Dusko Pavlovic
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Editors and Affiliations

  1. Computer Science Department, University of Nicosia, 46 Makedonitissas Ave., 1700, Nicosia, Cyprus

    Florent Domenach

  2. Higher School of Economics, National Research University, Pokrovsky Boulevard, 109028, Moscow, Russia

    Dmitry I. Ignatov

  3. Faculty of Business and Economics, Katholieke Universiteit Leuven, Naamsestraat 69, 3000, Leuven, Belgium

    Jonas Poelmans

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Pavlovic, D. (2012). Quantitative Concept Analysis. In: Domenach, F., Ignatov, D.I., Poelmans, J. (eds) Formal Concept Analysis. ICFCA 2012. Lecture Notes in Computer Science(), vol 7278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29892-9_24

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  • DOI: https://doi.org/10.1007/978-3-642-29892-9_24

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29891-2

  • Online ISBN: 978-3-642-29892-9

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