Optimal decompositions of matrices with entries from residuated lattices

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F12%3A33147464" target="_blank" >RIV/61989592:15310/12:33147464 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1093/logcom/exr023" target="_blank" >http://dx.doi.org/10.1093/logcom/exr023</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/logcom/exr023" target="_blank" >10.1093/logcom/exr023</a>

Result language
angličtina
Original language name
Optimal decompositions of matrices with entries from residuated lattices
Original language description
We describe optimal decompositions of matrices whose entries are elements of a residuated lattice L, such as L=[0, 1]. Such matrices represent relationships between objects and attributes with the entries representing degrees to which attributes represented by columns apply to objects represented by rows. Given such an n x m object-attribute matrix I, we look for a decomposition of I into a product A * B of an n x k object-factor matrix A and a k x m factor-attribute matrix B with entries from L with the number k of factors as small as possible. We show that formal concepts of I, which play a central role in the Port-Royal approach to logic and which are the fixpoints of particular Galois connections associated to I, are optimal factors for decomposition of I in that they provide us with decompositions with the smallest number of factors. Moreover, we describe transformations between the space of original attributes and the space of factors induced by a decomposition I = A * B. The art
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
IN - Informatics
OECD FORD branch
—

Project
<a href="/en/project/GAP202%2F10%2F0262" target="_blank" >GAP202/10/0262: Decompositions of matrices with binary and ordinal data: theory, algorithms, and complexity</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)