2020/07/31 by Changlin Wan, Wan, Changlin, Wennan Chang +7
Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2007.15821
openalex publication_date 2020/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.