T-product based ℓ1-norm tensor principal component analysis and a finite-step convergence algorithm

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-09-26 DOI:10.1016/j.aml.2024.109318

Xianpeng Mao , Yuning Yang

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引用次数: 0

Abstract

T-product based tensor principal component analysis (

ℓ_{2}

-tPCA) was used for dimensionality reduction, data preprocessing, compression, and visualization of multivariate data. However,

ℓ_{2}

-tPCA may amplify the influence of outliers and large-magnitude noise. To explore robustness against heavily corrupted third-order data, we consider the

ℓ_{1}

-norm tPCA model (

ℓ_{1}

-tPCA). We develop an effective proximal alternating maximization method and prove that within finitely many steps, the algorithm stops at a point satisfying certain optimality conditions. Numerical experiments on color face reconstruction and recognition demonstrate the efficiency of the proposed algorithms, confirming that

ℓ_{1}

-tPCA is more resilient to outliers compared to

ℓ_{2}

-tPCA.

查看原文本刊更多论文

基于 T 产物的 ℓ1 准则张量主成分分析和有限步收敛算法

基于 T-Product 的张量主成分分析（ℓ2-tPCA）被用于多变量数据的降维、数据预处理、压缩和可视化。然而，ℓ2-tPCA 可能会放大异常值和大振幅噪声的影响。为了探索对严重破坏的三阶数据的鲁棒性，我们考虑了 ℓ1-norm tPCA 模型（ℓ1-tPCA）。我们开发了一种有效的近似交替最大化方法，并证明在有限步内，算法会在满足特定最优条件的点上停止。对彩色人脸重建和识别的数值实验证明了所提算法的高效性，并证实与 ℓ2-tPCA 相比，ℓ1-tPCA 对异常值的抵抗力更强。

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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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.