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Tensor Robust Principal Component Analysis (TRPCA), which aims to recover a low-rank tensor corrupted by sparse noise, has attracted much attention in many real applications. This paper develops a new Global Weighted TRPCA method (GWTRPCA),…

Machine Learning · Computer Science 2023-01-06 Libin Wang , Yulong Wang , Shiyuan Wang , Youheng Liu , Yutao Hu , Longlong Chen , Hong Chen

Robust Principal Component Analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other…

Methodology · Statistics 2023-10-31 Xiaojun Zheng , Simon Mak , Liyan Xie , Yao Xie

We address the problem of tensor robust principal component analysis (TRPCA), which entails decomposing a given tensor into the sum of a low-rank tensor and a sparse tensor. By leveraging the tensor singular value decomposition (t-SVD), we…

Numerical Analysis · Mathematics 2025-05-08 Huiwen Zheng , Yifei Lou , Guoliang Tian , Chao Wang

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

Machine Learning · Statistics 2022-09-20 Yuefeng Han , Cun-Hui Zhang

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank…

Computer Vision and Pattern Recognition · Computer Science 2026-04-23 Yinjian Wang , Wei Li , Yuanyuan Gui , James E. Fowler , Gemine Vivone

Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by…

Machine Learning · Statistics 2018-11-13 Mehdi Bahri , Yannis Panagakis , Stefanos Zafeiriou

Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…

Methodology · Statistics 2026-03-17 Liangliang Yuan , Lei Wang , Quan Kong , Liuhua Peng

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and…

Optimization and Control · Mathematics 2020-01-27 Aritra Dutta , Filip Hanzely , Peter Richtárik

Tensor robust principal component analysis (TRPCA) is a classical way for low-rank tensor recovery, which minimizes the convex surrogate of tensor rank by shrinking each tensor singular value equally. However, for real-world visual data,…

Computer Vision and Pattern Recognition · Computer Science 2023-07-10 Xiaoyu Geng , Qiang Guo , Shuaixiong Hui , Ming Yang , Caiming Zhang

Tensor robust principal component analysis (TRPCA) has received a substantial amount of attention in various fields. Most existing methods, normally relying on tensor nuclear norm minimization, need to pay an expensive computational cost…

Numerical Analysis · Computer Science 2017-12-29 Jonathan Q. Jiang , Michael K. Ng

We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-16 Wenda Chu

The recently proposed tensor robust principal component analysis (TRPCA) methods based on tensor singular value decomposition (t-SVD) have achieved numerous successes in many fields. However, most of these methods are only applicable to…

Machine Learning · Computer Science 2023-11-13 Jianan Liu , Chunguang Li

This paper considers the use of Robust PCA in a CUR decomposition framework and applications thereof. Our main algorithms produce a robust version of column-row factorizations of matrices $\mathbf{D}=\mathbf{L}+\mathbf{S}$ where…

Computer Vision and Pattern Recognition · Computer Science 2023-02-28 HanQin Cai , Keaton Hamm , Longxiu Huang , Deanna Needell

In this paper, a new method is proposed for sparse PCA based on the recursive divide-and-conquer methodology. The main idea is to separate the original sparse PCA problem into a series of much simpler sub-problems, each having a closed-form…

Computer Vision and Pattern Recognition · Computer Science 2012-12-03 Qian Zhao , Deyu Meng , Zongben Xu

We design algorithms for Robust Principal Component Analysis (RPCA) which consists in decomposing a matrix into the sum of a low rank matrix and a sparse matrix. We propose a deep unrolled algorithm based on an accelerated alternating…

Signal Processing · Electrical Eng. & Systems 2023-07-13 Elizabeth Z. C. Tan , Caroline Chaux , Emmanuel Soubies , Vincent Y. F. Tan

This work studies the recursive robust principal components' analysis(PCA) problem. Here, "robust" refers to robustness to both independent and correlated sparse outliers. If the outlier is the signal-of-interest, this problem can be…

Information Theory · Computer Science 2014-08-20 Chenlu Qiu , Namrata Vaswani , Brian Lois , Leslie Hogben

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Machine Learning · Computer Science 2023-02-28 HanQin Cai , Jialin Liu , Wotao Yin

In this work, we study the online robust principal components' analysis (RPCA) problem. In recent work, RPCA has been defined as a problem of separating a low-rank matrix (true data), $L$, and a sparse matrix (outliers), $S$, from their…

Information Theory · Computer Science 2016-02-01 Jinchun Zhan , Brian Lois , Namrata Vaswani

Robust principal component analysis (RPCA) has drawn significant attentions due to its powerful capability in recovering low-rank matrices as well as successful appplications in various real world problems. The current state-of-the-art…

Machine Learning · Computer Science 2019-04-17 Chong Peng , Chenglizhao Chen , Zhao Kang , Jianbo Li , Qiang Cheng

The CUR decomposition provides an approximation of a matrix $X$ that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of $X$. In this regard, it appears to…

Data Structures and Algorithms · Computer Science 2010-11-02 Jacob Bien , Ya Xu , Michael W. Mahoney