  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 \textit{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.
