Geometric All-Way Boolean Tensor Decomposition

TL;DR

This paper introduces GETF, a fast and efficient geometric algorithm for Boolean tensor decomposition that improves accuracy and scalability over existing methods, enabling better analysis of high-dimensional logical data.

Contribution

The paper presents GETF, a novel geometric approach for all-order Boolean tensor decomposition that is computationally efficient and theoretically validated.

Findings

GETF significantly outperforms existing methods in reconstruction accuracy.

GETF is an order of magnitude faster than state-of-the-art algorithms.

Experiments show improved extraction of latent structures from real-world data.

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.