Geometric All-Way Boolean Tensor Decomposition

• URL: http://arxiv.org/abs/2007.15821v2
• Date: Mon, 26 Oct 2020 19:21:59 GMT
• Title: Geometric All-Way Boolean Tensor Decomposition
• Authors: Changlin Wan, Wennan Chang, Tong Zhao, Sha Cao, Chi Zhang
• Abstract summary: We present GETF, which sequentially identifies the rank-1 basis for a tensor from a geometric perspective. 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.
• Score: 14.065968221500246
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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