  A novel approach to Boolean matrix factorization (BMF) is presented. Instead
of solving the BMF problem directly, this approach solves a nonnegative
optimization problem with the constraint over an auxiliary matrix whose Boolean
structure is identical to the initial Boolean data. Then the solution of the
nonnegative auxiliary optimization problem is thresholded to provide a solution
for the BMF problem. We provide the proofs for the equivalencies of the two
solution spaces under the existence of an exact solution. Moreover, the
nonincreasing property of the algorithm is also proven. Experiments on
synthetic and real datasets are conducted to show the effectiveness and
complexity of the algorithm compared to other current methods.
