Efficient Tensor Decomposition with Boolean Factors

TL;DR

This paper introduces BMP, a new tensor decomposition method with Boolean factors, leveraging a greedy approach and MAXCUT-like optimization, demonstrating improved performance and applications in neuroscience data analysis.

Contribution

We propose BMP, a novel tensor decomposition algorithm with Boolean factors that guarantees convergence and effective factor recovery, suitable for neuroscience applications.

Findings

BMP outperforms baseline methods on synthetic datasets.

BMP effectively recovers neural interaction factors.

Demonstrated application in analyzing ECoG recordings.

Abstract

Tensor decomposition has been extensively used as a tool for exploratory analysis. Motivated by neuroscience applications, we study tensor decomposition with Boolean factors. The resulting optimization problem is challenging due to the non-convex objective and the combinatorial constraints. We propose Binary Matching Pursuit (BMP), a novel generalization of the matching pursuit strategy to decompose the tensor efficiently. BMP iteratively searches for atoms in a greedy fashion. The greedy atom search step is solved efficiently via a MAXCUT-like boolean quadratic program. We prove that BMP is guaranteed to converge sublinearly to the optimal solution and recover the factors under mild identifiability conditions. Experiments demonstrate the superior performance of our method over baselines on synthetic and real datasets. We also showcase the application of BMP in quantifying neural interactions underlying high-resolution spatiotemporal ECoG recordings.