基于块Krylov迭代的快速准确的低秩逼近频繁方向算法

Qianxin Yi, Chenhao Wang, Xiuwu Liao, Yao Wang
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引用次数: 0

摘要

频繁方向(FD)是一种常用的求解低秩近似的确定性矩阵素描技术。然而,FD及其随机化变体在处理大规模数据集时往往存在计算成本高或计算不稳定的问题,限制了其在实际中的应用。为了解决这些问题,本文旨在提高FD的效率和有效性。具体而言,利用块克雷洛夫迭代和计数草图技术的力量,我们提出了一种快速准确的FD算法,称为BKICS-FD。我们推导了所提出的BKICS-FD的误差界,然后进行了大量的数值实验,以说明它在计算速度和精度方面优于几种流行的FD算法。
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A Fast and Accurate Frequent Directions Algorithm for Low Rank Approximation via Block Krylov Iteration
It is known that frequent directions (FD) is a popular deterministic matrix sketching technique for low rank approximation. However, FD and its randomized variants usually meet high computational cost or computational instability in dealing with large-scale datasets, which limits their use in practice. To remedy such issues, this paper aims at improving the efficiency and effectiveness of FD. Specifically, by utilizing the power of Block Krylov Iteration and count sketch techniques, we propose a fast and accurate FD algorithm dubbed as BKICS-FD. We derive the error bound of the proposed BKICS-FD and then carry out extensive numerical experiments to illustrate its superiority over several popular FD algorithms, both in terms of computational speed and accuracy.
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