Multilinear Robust Principal Component Analysis

SHI Jia-rong; ZHOU Shui-sheng; ZHENG Xiu-yun

doi:10.3969/j.issn.0372-2112.2014.08.004

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Multilinear Robust Principal Component Analysis

更新时间：2025-07-16

- Multilinear Robust Principal Component Analysis
- Acta Electronica Sinica Vol. 42, Issue 8, Pages: 1480-1486(2014)
- 作者机构：
  
  1. 西安建筑科技大学理学院,陕西,西安,710055
  2. 西安电子科技大学数学与统计学院,陕西,西安,710071
  3. 西安建筑科技大学理学院,陕西,西安,710055
  4. 西安电子科技大学数学与统计学院,陕西,西安,710071
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61179040);Research Project of Education Department of Shaanxi Province (No.2013JK0587, No.2013JK0588);Natural Science Basic Research Program of Shaanxi Province (No.2014JQ8323)
- DOI：10.3969/j.issn.0372-2112.2014.08.004
  CLC： TP391
- Published：2014
- 稿件说明：
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SHI Jia-rong, ZHOU Shui-sheng, ZHENG Xiu-yun. Multilinear Robust Principal Component Analysis[J]. Acta Electronica Sinica, 2014, 42(8): 1480-1486.
DOI：

SHI Jia-rong, ZHOU Shui-sheng, ZHENG Xiu-yun. Multilinear Robust Principal Component Analysis[J]. Acta Electronica Sinica, 2014, 42(8): 1480-1486. DOI： 10.3969/j.issn.0372-2112.2014.08.004.

摘要

鲁棒主成分分析（RPCA）是恢复低秩与稀疏成分的一种非常有效的方法.本文将RPCA推广到张量情形，提出了多线性鲁棒主成分分析（MRPCA）框架.首先建立了MRPCA模型，即最小化张量核范数与

范数的加权组合.然后使用增广拉格朗日乘子法求解上述张量核范数优化问题.实验结果证实：对于具有多线性结构的数据，MRPCA比RPCA更加鲁棒.

Abstract

Robust principal component analysis(RPCA)is a very effective method to recover both the low-rank and sparse components.This paper extends RPCA to the case of tensor and proposes a framework of multilinear robust principal component analysis(MRPCA).First

it establishes the model of MRPCA which minimizes a weighted combination of the tensor nuclear norm and

norm.Then

it employs the augmented Lagrange multipliers algorithm to solve the above nuclear norm optimization problem.Experimental results demonstrate that MRPCA is more robust than RPCA for the data with multilinear structure.

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