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Factorizing three-way ordinal data using triadic formal concepts

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F11%3A10225088" target="_blank" >RIV/61989592:15310/11:10225088 - isvavai.cz</a>

  • Result on the web

  • DOI - Digital Object Identifier

Alternative languages

  • Result language

    angličtina

  • Original language name

    Factorizing three-way ordinal data using triadic formal concepts

  • Original language description

    The paper presents a new approach to factor analysis of three-way ordinal data, i.e. data described by a 3-dimensional matrix I with values in an ordered scale. The matrix describes a relationship between objects, attributes, and conditions. The problemconsists in find- ing factors for I, i.e. finding a decomposition of I into three matrices, an object-factor matrix A, an attribute-factor matrix B, and a condition- factor matrix C, with the number of factors as small as possible. The difference from the decomposition-based methods of analysis of three- way data consists in the composition operator and the constraint on A, B, and C to be matrices with values in an ordered scale. We prove that optimal decompositions are achieved by using triadic concepts of I, developed within formal concept analysis, and provide results on natu- ral transformations between the space of attributes and conditions and the space of factors.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

  • CEP classification

    IN - Informatics

  • OECD FORD branch

Result continuities

  • Project

    <a href="/en/project/GAP202%2F10%2F0262" target="_blank" >GAP202/10/0262: Decompositions of matrices with binary and ordinal data: theory, algorithms, and complexity</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2011

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Lecture Notes in Artificial Intelligence

  • ISSN

    0302-9743

  • e-ISSN

  • Volume of the periodical

    7022

  • Issue of the periodical within the volume

  • Country of publishing house

    DE - GERMANY

  • Number of pages

    12

  • Pages from-to

    400-411

  • UT code for WoS article

  • EID of the result in the Scopus database