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
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DOI - Digital Object Identifier
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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
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
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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
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Volume of the periodical
7022
Issue of the periodical within the volume
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Country of publishing house
DE - GERMANY
Number of pages
12
Pages from-to
400-411
UT code for WoS article
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EID of the result in the Scopus database
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