Optimal triangular decompositions of matrices with grades
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F08%3A00005464" target="_blank" >RIV/61989592:15310/08:00005464 - 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
Optimal triangular decompositions of matrices with grades
Original language description
We describe optimal decompositions of $n times m$ matrix $I$ into triangular product $I=Alp B$ of $ntimes k$ matrix $A$ and $ktimes m$ matrix $B$. $I$, $A$, and $B$ represent relationships between objects and attributes, objects and factors, and factors and attributes, respectively. We assume that the matrix entries are elements of a complete residuated lattice, which leaves binary matrices or matrices which contain numbers from unit interval $[0,1]$ as special cases. The entries of $I$, $A$, and $B$ are meant to represent grades to which objects have attributes, factors apply to objects, and attributes are particular manifestations of factors, respectively. This way, the decomposition provides a model for factor analysis of graded data. We prove that optimal decompositions of $I$, i.e. with the number $k$ of factors as small as possible, are those which use fixpoints of particular operators associated to $I$ as factors. The operators form isotone
Czech name
Optimální triangulární dekompozice matic se stupni
Czech description
Článek popisuje optimální dekompozice matic, které obsahují jako položky matic stupně.
Classification
Type
D - Article in proceedings
CEP classification
BD - Information theory
OECD FORD branch
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Result continuities
Project
<a href="/en/project/1ET101370417" target="_blank" >1ET101370417: Hierarchical analysis of complex data</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
International Conference on Relations, Orders and Graphs: Interaction with Computer Science
ISBN
978-0-9809498-0-3
ISSN
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e-ISSN
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Number of pages
10
Pages from-to
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Publisher name
University of Sfax
Place of publication
Sfax, Tunisko
Event location
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Event date
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Type of event by nationality
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UT code for WoS article
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