A new algorithm for Boolean matrix factorization which admits overcovering

We present a new algorithm for general Boolean matrix factorization. The algorithm is based on two key ideas. First, it utilizes formal concepts of the factorized matrix as crucial components of constructed factors. Second, it performs steps back during the construction of factors to see if some of the already constructed factors may be improved or even eliminated in view of the subsequently added factors. The second idea is inspired by 8M-an old, previously incompletely described and virtually unknown factorization algorithm, which we analyze and describe in detail. We provide experimental evaluation of the new algorithm and compare it to 8M and two other well-known algorithms. The results demonstrate that our algorithm outperforms these algorithms in terms of quality of the decompositions as well in its robustness with respect to small changes in data.