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Related papers: Learning Robust Low-Rank Representations

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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

The common task in matrix completion (MC) and robust principle component analysis (RPCA) is to recover a low-rank matrix from a given data matrix. These problems gained great attention from various areas in applied sciences recently,…

Information Theory · Computer Science 2012-01-06 Hui Zhang , Jian-Feng Cai , Lizhi Cheng , Jubo Zhu

The robust principal component analysis (RPCA) decomposes a data matrix into a low-rank part and a sparse part. There are mainly two types of algorithms for RPCA. The first type of algorithm applies regularization terms on the singular…

Numerical Analysis · Mathematics 2021-02-02 Ningyu Sha , Lei Shi , Ming Yan

Matrix low rank approximation including the classical PCA and the robust PCA (RPCA) method have been applied to solve the background modeling problem in video analysis. Recently, it has been demonstrated that a special weighted low rank…

Optimization and Control · Mathematics 2017-03-21 Aritra Dutta , Xin Li

Deep unfolded neural networks are designed by unrolling the iterations of optimization algorithms. They can be shown to achieve faster convergence and higher accuracy than their optimization counterparts. This paper proposes a new…

Machine Learning · Computer Science 2020-10-05 Huynh Van Luong , Boris Joukovsky , Yonina C. Eldar , Nikos Deligiannis

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

This paper studies tensor-based Robust Principal Component Analysis (RPCA) using atomic-norm regularization. Given the superposition of a sparse and a low-rank tensor, we present conditions under which it is possible to exactly recover the…

Optimization and Control · Mathematics 2019-01-31 Derek Driggs , Stephen Becker , Jordan Boyd-Graber

Deep neural networks perform remarkably well on image classification tasks but remain vulnerable to carefully crafted adversarial perturbations. This work revisits linear dimensionality reduction as a simple, data-adapted defense. We…

Machine Learning · Computer Science 2025-10-08 Killian Steunou , Théo Druilhe , Sigurd Saue

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

Recent research on problem formulations based on decomposition into low-rank plus sparse matrices shows a suitable framework to separate moving objects from the background. The most representative problem formulation is the Robust Principal…

Computer Vision and Pattern Recognition · Computer Science 2016-11-29 Thierry Bouwmans , Andrews Sobral , Sajid Javed , Soon Ki Jung , El-Hadi Zahzah

Robust Principal Component Analysis (RPCA) aims to recover a low-rank structure from noisy, partially observed data that is also corrupted by sparse, potentially large-magnitude outliers. Traditional RPCA models rely on convex relaxations,…

Machine Learning · Statistics 2025-10-07 Kun Zhao , Haoke Zhang , Jiayi Wang , Yifei Lou

We introduce a novel framework for an approxi- mate recovery of data matrices which are low-rank on graphs, from sampled measurements. The rows and columns of such matrices belong to the span of the first few eigenvectors of the graphs…

Machine Learning · Computer Science 2016-10-05 Nauman Shahid , Nathanael Perraudin , Gilles Puy , Pierre Vandergheynst

We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…

Machine Learning · Computer Science 2012-06-22 Alex Bronstein , Pablo Sprechmann , Guillermo Sapiro

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…

Machine Learning · Statistics 2017-09-15 Niannan Xue , Jiankang Deng , Yannis Panagakis , Stefanos Zafeiriou

We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their sum. In this work, we propose a fast non-convex algorithm,…

Machine Learning · Computer Science 2021-10-13 HanQin Cai , Zehan Chao , Longxiu Huang , Deanna Needell

We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given tensor into an underlying low-rank component and a sparse…

Numerical Analysis · Mathematics 2024-01-30 HanQin Cai , Zehan Chao , Longxiu Huang , Deanna Needell

Unified representation learning for multi-source data integration faces two important challenges: blockwise missingness and blockwise signal heterogeneity. The former arises from sources observing different, yet potentially overlapping,…

Methodology · Statistics 2026-02-13 Ziqi Liu , Ye Tian , Weijing Tang

We propose a low-rank transformation-learning framework to robustify subspace clustering. Many high-dimensional data, such as face images and motion sequences, lie in a union of low-dimensional subspaces. The subspace clustering problem has…

Computer Vision and Pattern Recognition · Computer Science 2013-08-02 Qiang Qiu , Guillermo Sapiro