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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

Classical principal component analysis (PCA) is not robust to the presence of sparse outliers in the data. The use of the $\ell_1$ norm in the Robust PCA (RPCA) method successfully eliminates the weakness of PCA in separating the sparse…

Optimization and Control · Mathematics 2017-07-07 Aritra Dutta , Xin Li

Most high-dimensional matrix recovery problems are studied under the assumption that the target matrix has certain intrinsic structures. For image data related matrix recovery problems, approximate low-rankness and smoothness are the two…

Machine Learning · Statistics 2021-04-08 Long Feng , Junhui Wang

In this paper we present a comprehensive framework for learning robust low-rank representations by combining and extending recent ideas for learning fast sparse coding regressors with structured non-convex optimization techniques. This…

Machine Learning · Computer Science 2012-10-01 Pablo Sprechmann , Alex M. Bronstein , Guillermo Sapiro

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the…

Machine Learning · Statistics 2020-09-04 Young Woong Park , Diego Klabjan

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

In this paper, we propose a non-convex formulation to recover the authentic structure from the corrupted real data. Typically, the specific structure is assumed to be low rank, which holds for a wide range of data, such as images and…

Computer Vision and Pattern Recognition · Computer Science 2016-08-23 Jing Wang , Meng Wang , Xuegang Hu , Shuicheng Yan

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Machine Learning · Computer Science 2025-04-07 Long Chen , Xianchao Xiu

This paper studies the Tensor Robust Principal Component (TRPCA) problem which extends the known Robust PCA (Candes et al. 2011) to the tensor case. Our model is based on a new tensor Singular Value Decomposition (t-SVD) (Kilmer and Martin…

Computer Vision and Pattern Recognition · Computer Science 2018-05-29 Canyi Lu , Jiashi Feng , Yudong Chen , Wei Liu , Zhouchen Lin , Shuicheng Yan

Principal component analysis (PCA) frequently suffers from the disturbance of outliers and thus a spectrum of robust extensions and variations of PCA have been developed. However, existing extensions of PCA treat all samples equally even…

Machine Learning · Computer Science 2021-03-23 Rui Zhang , Hongyuan Zhang , Xuelong Li

Tensor, also known as multi-dimensional array, arises from many applications in signal processing, manufacturing processes, healthcare, among others. As one of the most popular methods in tensor literature, Robust tensor principal component…

Machine Learning · Statistics 2025-12-18 Bo Shen , Yutong Zhang , Zhenyu , Kong

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 seeks to recover a low-rank matrix from fully observed data with sparse corruptions. A scalable approach fits a low-rank factorization by minimizing the sum of entrywise absolute residuals, leading to a…

Optimization and Control · Mathematics 2026-01-30 Pinxi Gong , Lexiao Lai , Jianhao Ma

Robust principal component analysis (RPCA) is a widely used tool for dimension reduction. In this work, we propose a novel non-convex algorithm, coined Iterated Robust CUR (IRCUR), for solving RPCA problems, which dramatically improves the…

Machine Learning · Statistics 2021-02-09 HanQin Cai , Keaton Hamm , Longxiu Huang , Jiaqi Li , Tao Wang

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

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

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

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

This work studies the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is motivated by the recently proposed linear transforms based…

Machine Learning · Computer Science 2019-07-22 Canyi Lu , Pan Zhou

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Machine Learning · Computer Science 2012-06-22 Alfredo Kalaitzis , Neil Lawrence