Optimal triangular decompositions of matrices with entries from residuated lattices

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F09%3A00010273" target="_blank" >RIV/61989592:15310/09:00010273 - 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 entries from residuated lattices

Popis výsledku v původním jazyce

We describe optimal decompositions of an n x m matrix I into a triangular product I 1/4 A / B of an n x k matrix A and a k x m matrix B. We assume that the matrix entries are elements of a residuated lattice, which leaves binary matrices or matrices which con- tain numbers from the unit interval [0,1] as special cases. The entries of I, A, and B 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 fixpoints of particular operators associated with I, which are studied in formal concept analysis, are optimal factors for decomposition of I in that they provide us withdecompositions I 1/4 A / B with the smallest number k of factors possible. Moreover, we describe transformations between the m- dimensional space of original attributes and the k-dimensional space of factors.We provide illustrative exampl

Název v anglickém jazyce

Optimal triangular decompositions of matrices with entries from residuated lattices

Popis výsledku anglicky

We describe optimal decompositions of an n x m matrix I into a triangular product I 1/4 A / B of an n x k matrix A and a k x m matrix B. We assume that the matrix entries are elements of a residuated lattice, which leaves binary matrices or matrices which con- tain numbers from the unit interval [0,1] as special cases. The entries of I, A, and B 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 fixpoints of particular operators associated with I, which are studied in formal concept analysis, are optimal factors for decomposition of I in that they provide us withdecompositions I 1/4 A / B with the smallest number k of factors possible. Moreover, we describe transformations between the m- dimensional space of original attributes and the k-dimensional space of factors.We provide illustrative exampl

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BD - Teorie informace

OECD FORD obor

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Projekt

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Návaznosti

Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

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

Název periodika

International Journal of Approximate Reasoning

ISSN

0888-613X

e-ISSN

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Svazek periodika

50

Číslo periodika v rámci svazku

8

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

9

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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