Optimální rozklady matic se stupni na binární matice a matice se stupni

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Optimal Decompositions of Matrices with Grades into Binary and Graded Matrices

Popis výsledku v původním jazyce

The paper contributes to factor analysis of relational data. We study the problem of decomposition of object-attribute matrices with grades, i.e. matrices whose entries contain degrees to which objects have attributes. The degrees are taken from a bounded partially ordered scale. Examples of such matrices are binary matrices, matrices with entries from a finite chain, or matrices with entries from the unit interval [0, 1]. We study the problem of decomposition of a given object-attribute matrix I with grades into an object-factor matrix A and a binary factorattribute matrix B, with the number of factors as small as possible. We present a theorem describing optimal decompositions. The theorem shows that decompositions which use as factors particular formal concepts associated to I are optimal in that the number of factors involved is the smallest possible. Furthermore, we present an approximation algorithm for finding those decompositions and illustrative examples.

Název v anglickém jazyce

Optimal Decompositions of Matrices with Grades into Binary and Graded Matrices

Popis výsledku anglicky

The paper contributes to factor analysis of relational data. We study the problem of decomposition of object-attribute matrices with grades, i.e. matrices whose entries contain degrees to which objects have attributes. The degrees are taken from a bounded partially ordered scale. Examples of such matrices are binary matrices, matrices with entries from a finite chain, or matrices with entries from the unit interval [0, 1]. We study the problem of decomposition of a given object-attribute matrix I with grades into an object-factor matrix A and a binary factorattribute matrix B, with the number of factors as small as possible. We present a theorem describing optimal decompositions. The theorem shows that decompositions which use as factors particular formal concepts associated to I are optimal in that the number of factors involved is the smallest possible. Furthermore, we present an approximation algorithm for finding those decompositions and illustrative examples.

Druh

D - Stať ve sborníku

CEP obor

BD - Teorie informace

OECD FORD obor

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Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

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

Concept Lattices and Their Applications 2008

ISBN

978-80-244-2111-7

ISSN

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e-ISSN

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Počet stran výsledku

12

Strana od-do

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Název nakladatele

Univerzita Palackého

Místo vydání

Olomouc

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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