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Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called…

Machine Learning · Computer Science 2019-04-19 Jicong Fan , Tommy W. S. Chow

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

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

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Machine Learning · Computer Science 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

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

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Machine Learning · Computer Science 2024-12-20 Kexin Li , You-wei Wen , Xu Xiao , Mingchao Zhao

Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local…

Data Analysis, Statistics and Probability · Physics 2013-12-09 Daniel N. Kaslovsky , Francois G. Meyer

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

It is well known that Principal Component Analysis (PCA) is strongly affected by outliers and a lot of effort has been put into robustification of PCA. In this paper we present a new algorithm for robust PCA minimizing the trimmed…

Machine Learning · Statistics 2015-06-02 Anastasia Podosinnikova , Simon Setzer , Matthias Hein

Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…

Machine Learning · Statistics 2013-10-01 Gonzalo Mateos , Georgios B. Giannakis

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

Tensor robust principal component analysis (RPCA), which seeks to separate a low-rank tensor from its sparse corruptions, has been crucial in data science and machine learning where tensor structures are becoming more prevalent. While…

Machine Learning · Statistics 2022-12-23 Harry Dong , Megna Shah , Sean Donegan , Yuejie Chi

We propose a robust principal component analysis (RPCA) framework to recover low-rank and sparse matrices from temporal observations. We develop an online version of the batch temporal algorithm in order to process larger datasets or…

Machine Learning · Statistics 2022-08-04 Hong-Lan Botterman , Julien Roussel , Thomas Morzadec , Ali Jabbari , Nicolas Brunel

Robust Principal Component Analysis (RPCA) aims at recovering a low-rank subspace from grossly corrupted high-dimensional (often visual) data and is a cornerstone in many machine learning and computer vision applications. Even though RPCA…

Computer Vision and Pattern Recognition · Computer Science 2017-03-29 Niannan Xue , Yannis Panagakis , Stefanos Zafeiriou

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

Machine Learning · Statistics 2019-08-21 Genevera I. Allen , Michael Weylandt

The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data…

Optimization and Control · Mathematics 2013-09-27 Necdet Serhat Aybat , Donald Goldfarb , Shiqian Ma

An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key…

Machine Learning · Statistics 2023-02-23 Harry Dong , Tian Tong , Cong Ma , Yuejie Chi

Foreground detection in a given video sequence is a pivotal step in many computer vision applications such as video surveillance system. Robust Principal Component Analysis (RPCA) performs low-rank and sparse decomposition and accomplishes…

Computer Vision and Pattern Recognition · Computer Science 2019-09-19 Amirhossein Khalilian-Gourtani , Shervin Minaee , Yao Wang

This paper is about a curious phenomenon. Suppose we have a data matrix, which is the superposition of a low-rank component and a sparse component. Can we recover each component individually? We prove that under some suitable assumptions,…

Information Theory · Computer Science 2009-12-21 Emmanuel J. Candes , Xiaodong Li , Yi Ma , John Wright

In this paper we develop a new approach to sparse principal component analysis (sparse PCA). We propose two single-unit and two block optimization formulations of the sparse PCA problem, aimed at extracting a single sparse dominant…

Optimization and Control · Mathematics 2008-12-01 Michel Journée , Yurii Nesterov , Peter Richtárik , Rodolphe Sepulchre
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