塔克格式张量流式低秩逼近的多线性奈斯特伦连续算法

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-08-17 DOI:10.1016/j.aml.2024.109271

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引用次数: 0

摘要

我们提出了多线性 Nyström 算法的顺序版本，该算法适用于以流式格式给出的张量的低阶塔克逼近。该算法完全通过原始数据的随机草图访问张量 A，有效地利用了张量 A 中的结构，如低阶性和线性组合。我们对该算法进行了确定性分析，并在数值实验（包括视频处理中的应用）中展示了其优越的速度和效率。

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A sequential multilinear Nyström algorithm for streaming low-rank approximation of tensors in Tucker format

We present a sequential version of the multilinear Nyström algorithm which is suitable for low-rank Tucker approximation of tensors given in a streaming format. Accessing the tensor $A$ exclusively through random sketches of the original data, the algorithm effectively leverages structures in $A$ , such as low-rankness, and linear combinations. We present a deterministic analysis of the algorithm and demonstrate its superior speed and efficiency in numerical experiments including an application in video processing.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.