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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F10%3A00010968" target="_blank" >RIV/61989592:15310/10:00010968 - 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
Discovery of optimal factors in binary data via a novel method of matrix decomposition
Original language description
We present a novel method of decomposition of an n xm binary matrix I into a Boolean product A x 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 analysiswhere 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 provedin 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. The algorithm avoids the need to compute all formal concepts and significantly outperforms a greedy approxim
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BD - Information theory
OECD FORD branch
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Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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