Wan, ChanglinChang, WennanZhao, TongCao, ShaZhang, Chi2022-02-012022-02-012020Wan, C., Chang, W., Zhao, T., Cao, S., & Zhang, C. (2020). Geometric All-way Boolean Tensor Decomposition. Advances in Neural Information Processing Systems, 33, 2848–2857. https://proceedings.neurips.cc/paper/2020/hash/1def1713ebf17722cbe300cfc1c88558-Abstract.htmlhttps://hdl.handle.net/1805/27638Boolean 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.enPublisher PolicyBoolean Tensor DecompositionGeometric Expansion for all-order Tensor FactorizationArticle