用于低多线性秩逼近的黎曼预条件坐标后退法

IF 1.5 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Matrix Analysis and Applications Pub Date : 2024-05-21 DOI:10.1137/21m1463896

Mohammad Hamed, Reshad Hosseini

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引用次数: 0

摘要

SIAM 矩阵分析与应用期刊》，第 45 卷，第 2 期，第 1054-1075 页，2024 年 6 月。摘要本文提出了一种内存高效的一阶方法，用于高阶高维张量的低多线性秩逼近。在我们的方法中，我们利用代价函数和约束条件的二阶信息，在格拉斯曼流形上提出了一个新的黎曼度量。我们使用黎曼坐标下降法来解决问题，并提供了与欧几里得坐标下降法相匹配的全局收敛分析。我们还证明，我们方法中单位步长的每一步实际上都是正交迭代算法的一步。实验结果表明，我们的方法对高维张量具有计算优势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Riemannian Preconditioned Coordinate Descent for Low Multilinear Rank Approximation

SIAM Journal on Matrix Analysis and Applications, Volume 45, Issue 2, Page 1054-1075, June 2024.
Abstract. This paper presents a memory-efficient, first-order method for low multilinear rank approximation of high-order, high-dimensional tensors. In our method, we exploit the second-order information of the cost function and the constraints to suggest a new Riemannian metric on the Grassmann manifold. We use a Riemmanian coordinate descent method for solving the problem and also provide a global convergence analysis matching that of the coordinate descent method in the Euclidean setting. We also show that each step of our method with the unit step size is actually a step of the orthogonal iteration algorithm. Experimental results show the computational advantage of our method for high-dimensional tensors.

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来源期刊

SIAM Journal on Matrix Analysis and Applications 数学-应用数学

CiteScore

2.90

自引率

6.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Matrix Analysis and Applications contains research articles in matrix analysis and its applications and papers of interest to the numerical linear algebra community. Applications include such areas as signal processing, systems and control theory, statistics, Markov chains, and mathematical biology. Also contains papers that are of a theoretical nature but have a possible impact on applications.