Factorization of matrices with grades

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F16%3A33160375" target="_blank" >RIV/61989592:15310/16:33160375 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.sciencedirect.com/science/article/pii/S0165011415001694" target="_blank" >http://www.sciencedirect.com/science/article/pii/S0165011415001694</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.fss.2015.03.020" target="_blank" >10.1016/j.fss.2015.03.020</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Factorization of matrices with grades

Popis výsledku v původním jazyce

We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a product has a given feature, or a person performs well in a test. We assume that the grades are taken from bounded scales equipped with certain aggregation operators that are involved in the decompositions. Particular cases of the decompositions include the well-known Boolean matrix decomposition, and the sup-t-norm and inf-residuum decompositions. We consider the problem of decomposition of a given matrix into a product of two matrices with grades such that the number of factors, i.e. the inner dimension, be as small as possible. We observe that computing such decompositions is NP-hard and present a greedy approximation algorithm. Our algorithm is based on a geometric insight provided by a theorem identifying particular rectangular-shaped submatrices as optimal factors for the decompositions. These factors correspond to fixpoints of certain Galois connections associated with the input matrix, which are called formal concepts, and allow an easy interpretation of the decomposition. We present illustrative examples and experimental evaluation of the algorithm.

Název v anglickém jazyce

Factorization of matrices with grades

Popis výsledku anglicky

We present an approach to decomposition and factor analysis of matrices with ordinal data. The matrix entries are grades to which objects represented by rows satisfy attributes represented by columns, e.g. grades to which an image is red, a product has a given feature, or a person performs well in a test. We assume that the grades are taken from bounded scales equipped with certain aggregation operators that are involved in the decompositions. Particular cases of the decompositions include the well-known Boolean matrix decomposition, and the sup-t-norm and inf-residuum decompositions. We consider the problem of decomposition of a given matrix into a product of two matrices with grades such that the number of factors, i.e. the inner dimension, be as small as possible. We observe that computing such decompositions is NP-hard and present a greedy approximation algorithm. Our algorithm is based on a geometric insight provided by a theorem identifying particular rectangular-shaped submatrices as optimal factors for the decompositions. These factors correspond to fixpoints of certain Galois connections associated with the input matrix, which are called formal concepts, and allow an easy interpretation of the decomposition. We present illustrative examples and experimental evaluation of the algorithm.

Druh

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

CEP obor

IN - Informatika

OECD FORD obor

—

Projekt

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

Návaznosti

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

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název periodika

Fuzzy Sets and Systems

ISSN

0165-0114

e-ISSN

—

Svazek periodika

292

Číslo periodika v rámci svazku

JUN

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

13

Strana od-do

85-97

Kód UT WoS článku

000371786900006

EID výsledku v databázi Scopus

2-s2.0-84926659902