Scalable Binary CUR Low-Rank Approximation Algorithm

TL;DR

This paper introduces a scalable binary CUR low-rank approximation algorithm that efficiently processes large matrices using parallel and adaptive strategies, achieving significant speed-ups with maintained accuracy.

Contribution

It presents a novel parallel, deterministic algorithm for binary CUR low-rank approximation that improves scalability and efficiency for large-scale matrices.

Findings

Achieves near-linear speed-up with increased processes

Maintains high reconstruction accuracy on large matrices

Reduces computational time significantly in experiments

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 $16,384 \times 16,384$ matrices demonstrate a good speed-up, 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 of different size across various sizes demonstrate an near-optimal reconstruction accuracy.