Clustering Boolean Tensors

Abstract. Tensor factorizations are computationally hard problems, and in particular, often are significantly harder than their matrix counterparts. In case of Boolean tensor factorizations – where the input tensor and all the factors are required to be binary and we use Boolean algebra – much of that hardness comes from the possibility of overlapping components. Yet, in many applications we are perfectly happy to partition at least one of the modes. In this paper we investigate what consequences does this partitioning have on the computational complexity of the Boolean tensor factorizations and present a new algorithm for the resulting clustering problem. While future work aims at further tuning our algorithm for Boolean tensor clustering, it already now can obtain better results than algorithms solving different relaxations of the problem.