Boolean CP Decomposition of Binary Tensors: Uniqueness and Algorithm

We propose an algorithm to perform the low-rank Boolean Canonical Polyadic Decomposition (BCPD) of a binary tensor. The proposed approach is based on the AO-ADMM strategy introduced in [1] and uses a post-nonlinear mixture model for binary sources. We show that this new method is better suited for low-rank approximation of binary tensors compared to other similar methods. We also provide an easy-to-check uniqueness condition for the BCPD. This is the first time that such a condition is derived for Boolean decompositions.