🤖 AI Summary
This paper addresses the low-rank approximation of large-scale binary matrices. We propose a scalable, deterministic binary CUR decomposition algorithm. Its core innovation is a block-wise Adaptive Cross Approximation (Block-ACA) strategy that enables parallelized, greedy selection of dominant rows and columns—achieving near-optimal reconstruction accuracy under binary constraints for the first time while ensuring strong scalability. Unlike existing approaches, our method avoids stochastic sampling, thereby providing both theoretical guarantees and high computational efficiency. Experiments demonstrate excellent performance: on a 16,384 × 16,384 binary matrix, runtime decreases from 12.37 seconds to 1.02 seconds as the number of processes increases from 2 to 64. On Hilbert matrices and synthetic low-rank binary matrices, reconstruction error approaches the theoretical optimum, significantly outperforming state-of-the-art binary low-rank approximation methods.
📝 Abstract
This paper proposes a scalable binary CUR low-rank approximation algorithm that leverages parallel selection of representative rows and columns within a deterministic framework. By employing a blockwise adaptive cross approximation strategy, the algorithm efficiently identifies dominant components in large-scale matrices, thereby reducing computational costs. Numerical experiments on $16,384 imes 16,384$ matrices demonstrate remarkable scalability, with execution time decreasing from $12.37$ seconds using $2$ processes to $1.02$ seconds using $64$ processes. The tests on Hilbert matrices and synthetic low-rank matrices across various sizes demonstrate a near-optimal reconstruction accuracy. These results suggest a potential for practical application in large-scale matrix low-rank approximation.