About: Discovery of optimal factors in binary data via a novel method of matrix decomposition

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We present a novel method of decomposition of an n xm binary matrix I into a Boolean product A ? B of an n x k binary matrix A and a k x m binary matrix B with k as small as possible. Attempts to solve this problem are known from Boolean factor analysis where I is interpreted as an object?attribute matrix, A and B are interpreted as object?factor and factor?attribute matrices, and the aim is to find a decomposition with a small number k of factors. The method presented here is based on a theorem proved in this paper. It says that optimal decompositions, i.e. those with the least number of factors possible, are those where factors are formal concepts in the sense of formal concept analysis. Finding an optimal decomposition is an NP-hard problem. However, we present an approximation algorithm for finding optimal decompositions which is based on the insight provided by the theorem. We present a novel method of decomposition of an n xm binary matrix I into a Boolean product A ? B of an n x k binary matrix A and a k x m binary matrix B with k as small as possible. Attempts to solve this problem are known from Boolean factor analysis where I is interpreted as an object?attribute matrix, A and B are interpreted as object?factor and factor?attribute matrices, and the aim is to find a decomposition with a small number k of factors. The method presented here is based on a theorem proved in this paper. It says that optimal decompositions, i.e. those with the least number of factors possible, are those where factors are formal concepts in the sense of formal concept analysis. Finding an optimal decomposition is an NP-hard problem. However, we present an approximation algorithm for finding optimal decompositions which is based on the insight provided by the theorem. (en)
Title	Discovery of optimal factors in binary data via a novel method of matrix decomposition Discovery of optimal factors in binary data via a novel method of matrix decomposition (en)
skos:prefLabel	Discovery of optimal factors in binary data via a novel method of matrix decomposition Discovery of optimal factors in binary data via a novel method of matrix decomposition (en)
skos:notation	RIV/61989592:15310/10:00010968!RIV11-MSM-15310___
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM6198959214)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2011
http://linked.open...aciTvurceVysledku	Vychodil, Vilém Bělohlávek, Radim
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Palackého v Olomouci / Přírodovědecká fakulta
http://linked.open...dnocenehoVysledku	254588
http://linked.open...ai/riv/idVysledku	RIV/61989592:15310/10:00010968
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Binary matrix decomposition, Factor analysis, Binary data, Formal concept analysis, Concept lattice (en)
http://linked.open.../riv/klicoveSlovo	Concept lattice Formal concept analysis Factor analysis Binary data Binary matrix decomposition
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[478C8C332D62]
http://linked.open...i/riv/nazevZdroje	Journal of Computer and System Sciences
http://linked.open...in/vavai/riv/obor	BD
http://linked.open...ichTvurcuVysledku	2 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2010
http://linked.open...v/svazekPeriodika	76
http://linked.open...iv/tvurceVysledku	Bělohlávek, Radim Vychodil, Vilém
http://linked.open...n/vavai/riv/zamer	Matematické modely a struktury
issn	0888-613X
number of pages	18 (xsd:int)
http://localhost/t...ganizacniJednotka	15310

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