  We present new results on Boolean matrix factorization and a new algorithm
based on these results. The results emphasize the significance of
factorizations that provide from-below approximations of the input matrix.
While the previously proposed algorithms do not consider the possibly different
significance of different matrix entries, our results help measure such
significance and suggest where to focus when computing factors. An experimental
evaluation of the new algorithm on both synthetic and real data demonstrates
its good performance in terms of good coverage by the first k factors as well
as a small number of factors needed for exact decomposition and indicates that
the algorithm outperforms the available ones in these terms. We also propose
future research topics.
