Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of multiple rank-1 tensors, which is an NP-hard problem. Existing BTD methods have been limited by their high computational cost, in applications to large scale or higher order tensors. In this work, we presented a computationally efficient BTD algorithm, namely Geometric Expansion for all-order Tensor Factorization (GETF), that sequentially identifies the rank-1 basis components for a tensor from a geometric perspective. We conducted rigorous theoretical analysis on the validity as well as algorithemic efficiency of GETF in decomposing all-order tensor. Experiments on both synthetic and real-world data demonstrated that GETF has significantly improved performance in reconstruction accuracy, extraction of latent structures and it is an order of magnitude faster than other state-of-the-art methods.

Weaknesses: There exist several limitations in experiments which are summarized as follows: 1-Authors need to show useful scenarios where binary representation is the best way to model the tensor. For instance, it seems count representation makes more sense rather than the binary representation. By binary representation, the quantity of crimes is ignored. For figures 6c, 6I, it is better to specify the number of patterns. Why not showing the scalability of GETF and other baselines as we increase 1- number of patterns 2- the size of a tensor dimension, and 3- number of non-zero elements in the tenor.

This paper presents a greedy sequential algorithm for decomposing a Boolean Nth-order tensor into a Boolean sum of rank 1 components, using Left-Triangular-like and geometric considerations. The paper includes detailed theory, algorithm development and some experiments. This makes the exposition rather dense but the authors have clearly invested a lot time and effort in the work. The task is interesting and the rank-1 pattern revealing algorithm looks nice and intriguing. The work received divergent scores with the main points of disagreement being the difficulty of following the exposition, the practical need for special methods dedicated to Boolean tensors, and the lack of comparative experiments with other algorithms and with (NP hard) exact minimal decompositions.

Boolean tensor has been broadly utilized in representing high dimensional logical data collected on spatial, temporal and/or other relational domains. Boolean Tensor Decomposition (BTD) factorizes a binary tensor into the Boolean sum of multiple rank-1 tensors, which is an NP-hard problem. Existing BTD methods have been limited by their high computational cost, in applications to large scale or higher order tensors. In this work, we presented a computationally efficient BTD algorithm, namely Geometric Expansion for all-order Tensor Factorization (GETF), that sequentially identifies the rank-1 basis components for a tensor from a geometric perspective. We conducted rigorous theoretical analysis on the validity as well as algorithemic efficiency of GETF in decomposing all-order tensor.