Quantitative Concept Analysis

Dusko Pavlovic

    Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

    7 Citations (Scopus)
    82 Downloads (Pure)

    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.
    Original languageEnglish
    Title of host publicationFormal Concept Analysis
    Subtitle of host publication10th International Conference, ICFCA 2012, Leuven, Belgium, May 7-10, 2012. Proceedings
    EditorsFlorent Domenach, Dmitry I. Ignatov, Jonas Poelmans
    Place of PublicationBerlin, Heidelberg
    PublisherSpringer
    Pages260-277
    Number of pages18
    ISBN (Electronic)978-3-642-29892-9
    ISBN (Print)978-3-642-29891-2
    DOIs
    Publication statusPublished - 7 May 2012
    Event10th International Conference on Formal Concept Analysis, ICFCA 2012 - Leuven, Belgium
    Duration: 7 May 201210 May 2012
    Conference number: 10

    Publication series

    NameLecture Notes in Computer Science
    PublisherSpringer Verlag
    Volume7278
    ISSN (Print)0302-9743

    Conference

    Conference10th International Conference on Formal Concept Analysis, ICFCA 2012
    Abbreviated titleICFCA
    CountryBelgium
    CityLeuven
    Period7/05/1210/05/12

    Keywords

    • Concept analysis
    • Universal property
    • Enriched category
    • Semantic completion

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