About: Optimal triangular decompositions of matrices with grades

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We describe optimal decompositions of $n \times m$ matrix $I$ into triangular product $I=A\lp B$ of $n\times k$ matrix $A$ and $k\times m$ 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 We describe optimal decompositions of $n \times m$ matrix $I$ into triangular product $I=A\lp B$ of $n\times k$ matrix $A$ and $k\times m$ 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 (en)
Title	Optimal triangular decompositions of matrices with grades Optimal triangular decompositions of matrices with grades (en)
skos:prefLabel	Optimal triangular decompositions of matrices with grades Optimal triangular decompositions of matrices with grades (en)
skos:notation	RIV/61989592:15310/08:00005464!RIV10-MSM-15310___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(1ET101370417), Z(MSM6198959214)
http://linked.open...vai/riv/dodaniDat	2010
http://linked.open...aciTvurceVysledku	Bělohlávek, Radim
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Palackého v Olomouci / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	385080
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/08:00005464
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	matrix decompositions; fuzzy logic; Galois connection (en)
http://linked.open.../riv/klicoveSlovo	fuzzy logic Galois connection matrix decompositions
http://linked.open...ontrolniKodProRIV	[A30501B72C59]
http://linked.open...i/riv/mistoVydani	Sfax, Tunisko
http://linked.open...i/riv/nazevZdroje	International Conference on Relations, Orders and Graphs: Interaction with Computer Science
http://linked.open...in/vavai/riv/obor	BD
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Hierarchical analysis of complex data
http://linked.open...UplatneniVysledku	2008
http://linked.open...iv/tvurceVysledku	Bělohlávek, Radim
http://linked.open...n/vavai/riv/zamer	Matematické modely a struktury
number of pages	588 (xsd:int)
http://purl.org/ne...btex#hasPublisher	University of Sfax
https://schema.org/isbn	978-0-9809498-0-3
http://localhost/t...ganizacniJednotka	15310

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