Efficient Tensor Decomposition with Boolean Factors

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 propo...

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Bibliographic Details
Published inarXiv.org
Main Authors Sung-En Chang, Zheng, Xun, Yen, Ian E H, Ravikumar, Pradeep, Yu, Rose
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 11.11.2020
Subjects
Binary codes
Boolean
Boolean algebra
Combinatorial analysis
Decomposition
Hyperspectral imaging
Learning
Mathematical analysis
Optimization
Tensors
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Summary: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.
ISSN:2331-8422