Operators and spaces associated to matrices with grades and their decompositions

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F08%3A00005463" target="_blank" >RIV/61989592:15310/08:00005463 - 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

Operators and spaces associated to matrices with grades and their decompositions

Popis výsledku v původním jazyce

We present results on decompositions of matrices with grades, i.e. matrices I with entries from a bounded ordered set L such as the real unit interval [0, 1]. We consider decompositions of an n x m matrix I into a circular and triangular product A B of an n x k matrix A and a k x m matrix B with k as small as possible. This problem generalizes the decomposition problem of Boolean factor analysis in which a decomposition of a binary matrix is sought into two binary matrices and which is a particular caseof our setting when L has just two elements, namely 0 and 1. In our previous work, we proved that formal concepts of concept lattices associated to I are optimal factors for such decompositions. In this paper, we investigate concept-forming operators and concept lattices associated to decompositions of matrices and implications of these results.

Název v anglickém jazyce

Operators and spaces associated to matrices with grades and their decompositions

Popis výsledku anglicky

We present results on decompositions of matrices with grades, i.e. matrices I with entries from a bounded ordered set L such as the real unit interval [0, 1]. We consider decompositions of an n x m matrix I into a circular and triangular product A B of an n x k matrix A and a k x m matrix B with k as small as possible. This problem generalizes the decomposition problem of Boolean factor analysis in which a decomposition of a binary matrix is sought into two binary matrices and which is a particular caseof our setting when L has just two elements, namely 0 and 1. In our previous work, we proved that formal concepts of concept lattices associated to I are optimal factors for such decompositions. In this paper, we investigate concept-forming operators and concept lattices associated to decompositions of matrices and implications of these results.

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

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2008

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of The North American Fuzzy Information Processing Society

ISBN

978-1-4244-2351-4

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

1-6

Název nakladatele

IEEE Computer Society Press

Místo vydání

New York

Místo konání akce

Washinton

Datum konání akce

19. 5. 2008

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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