利用优化切片/特征选择的离散经验插值法进行稳健的低管阶张量恢复

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2024-04-06 DOI:10.1007/s10444-024-10117-8

Salman Ahmadi-Asl, Anh-Huy Phan, Cesar F. Caiafa, Andrzej Cichocki

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引用次数: 0

摘要

在本文中，我们将离散经验插值法（DEIM）扩展到基于 t 积的三阶张量情况，并用它来选择重要/显著的横向和水平切片/特征。对所提出的 Tubal DEIM（TDEIM）进行了理论和数值研究。特别是，得出了拟议的 TDEIM 方法的误差边界细节。实验结果表明，与现有方法相比，TDEIM 可以提供更精确的近似值。此外，还介绍了所提方法在监督分类任务中的应用。

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Robust low tubal rank tensor recovery using discrete empirical interpolation method with optimized slice/feature selection

In this paper, we extend the Discrete Empirical Interpolation Method (DEIM) to the third-order tensor case based on the t-product and use it to select important/significant lateral and horizontal slices/features. The proposed Tubal DEIM (TDEIM) is investigated both theoretically and numerically. In particular, the details of the error bounds of the proposed TDEIM method are derived. The experimental results show that the TDEIM can provide more accurate approximations than the existing methods. An application of the proposed method to the supervised classification task is also presented.

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.