"15310" . "Z(MSM6198959214)" . . . "18"^^ . . "76" . . . . "B\u011Blohl\u00E1vek, Radim" . "RIV/61989592:15310/10:00010968" . "1" . "Binary matrix decomposition, Factor analysis, Binary data, Formal concept analysis, Concept lattice"@en . "Discovery of optimal factors in binary data via a novel method of matrix decomposition" . "RIV/61989592:15310/10:00010968!RIV11-MSM-15310___" . . . . "2"^^ . "Vychodil, Vil\u00E9m" . "2"^^ . "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." . . "[478C8C332D62]" . "Discovery of optimal factors in binary data via a novel method of matrix decomposition"@en . . . . "Journal of Computer and System Sciences" . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . "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 . . "Discovery of optimal factors in binary data via a novel method of matrix decomposition"@en . "Discovery of optimal factors in binary data via a novel method of matrix decomposition" . "254588" . . . "0888-613X" .