Optimal Decompositions of Matrices with Grades into Binary and Graded Matrices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F08%3A00005380" target="_blank" >RIV/61989592:15310/08:00005380 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Optimal Decompositions of Matrices with Grades into Binary and Graded Matrices
Original language description
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.
Czech name
Optimální rozklady matic se stupni na binární matice a matice se stupni
Czech description
Článek popisuje optimální rozklady matic se stupni na binární matice a matice se stupni a algoritmus, který tyto rozklady počítá.

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2008
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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