Efficient Tensor Decomposition with Boolean Factors
This work addresses tensor decomposition for neuroscience applications, such as analyzing neural interactions in ECoG recordings, but it is incremental as it builds on existing matching pursuit strategies.
The paper tackled the problem of tensor decomposition with Boolean factors, which is challenging due to non-convex and combinatorial constraints, by proposing Binary Matching Pursuit (BMP), a novel method that efficiently decomposes tensors and recovers factors under mild conditions, with experiments showing superior performance over baselines on synthetic and real datasets.
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.