Optimální triangulární dekompozice matic se stupni

Kód výsledku v 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>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Optimal triangular decompositions of matrices with grades

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

Optimal triangular decompositions of matrices with grades

Popis výsledku anglicky

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

Druh

D - Stať ve sborníku

CEP obor

BD - Teorie informace

OECD FORD obor

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Projekt

<a href="/cs/project/1ET101370417" target="_blank" >1ET101370417: Hierarchická analýza složitých dat</a><br>

Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2008

Kód důvěrnosti údajů

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

Název statě ve sborníku

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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Počet stran výsledku

10

Strana od-do

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Název nakladatele

University of Sfax

Místo vydání

Sfax, Tunisko

Místo konání akce

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Datum konání akce

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Typ akce podle státní příslušnosti

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Kód UT WoS článku

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