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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

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

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

Machine Learning · Statistics 2014-05-09 Dimitris S. Papailiopoulos , Alexandros G. Dimakis , Stavros Korokythakis

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

Our aim of this article is to reconstruct a signal from undersampled data in the situation that the signal is sparse in terms of a tight frame. We present a condition, which is independent of the coherence of the tight frame, to guarantee…

Numerical Analysis · Mathematics 2011-05-24 Song Li , Junhong Lin

We consider an online version of the robust Principle Component Analysis (PCA), which arises naturally in time-varying source separations such as video foreground-background separation. This paper proposes a compressive online robust PCA…

Information Theory · Computer Science 2017-05-30 Huynh Van Luong , Nikos Deligiannis , Jurgen Seiler , Soren Forchhammer , Andre Kaup

Motivated by applications such as sparse PCA, in this paper we present provably-accurate one-pass algorithms for the sparse approximation of the top eigenvectors of extremely massive matrices based on a single compact linear sketch. The…

Information Theory · Computer Science 2026-05-06 Edem Boahen , Simone Brugiapaglia , Hung-Hsu Chou , Mark Iwen , Felix Krahmer

Commonly used in computer vision and other applications, robust PCA represents an algorithmic attempt to reduce the sensitivity of classical PCA to outliers. The basic idea is to learn a decomposition of some data matrix of interest into…

Computer Vision and Pattern Recognition · Computer Science 2016-10-10 Tae-Hyun Oh , Yasuyuki Matsushita , In So Kweon , David Wipf

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…

Machine Learning · Computer Science 2026-03-10 Zhenyu Wang , Molei Liu , Jing Lei , Francis Bach , Zijian Guo

Compressed sensing (CS) is a sampling theory that allows reconstruction of sparse (or compressible) signals from an incomplete number of measurements, using of a sensing mechanism implemented by an appropriate projection matrix. The CS…

Computer Vision and Pattern Recognition · Computer Science 2017-08-29 Duc Minh Nguyen , Evaggelia Tsiligianni , Nikos Deligiannis

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

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…

Machine Learning · Statistics 2015-03-19 Teng Zhang , Gilad Lerman

Our interest lies in the recoverability properties of compressed tensors under the \textit{canonical polyadic decomposition} (CPD) model. The considered problem is well-motivated in many applications, e.g., hyperspectral image and video…

Signal Processing · Electrical Eng. & Systems 2020-08-26 Shahana Ibrahim , Xiao Fu , Xingguo Li

In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…

Information Theory · Computer Science 2015-06-19 Cesar F. Caiafa , Andrzej Cichocki

In this paper, we study the problem of matrix recovery, which aims to restore a target matrix of authentic samples from grossly corrupted observations. Most of the existing methods, such as the well-known Robust Principal Component Analysis…

Computer Vision and Pattern Recognition · Computer Science 2018-11-12 Xingyu Xie , Jianlong Wu , Guangcan Liu , Jun Wang

In this work, we study the robust subspace tracking (RST) problem and obtain one of the first two provable guarantees for it. The goal of RST is to track sequentially arriving data vectors that lie in a slowly changing low-dimensional…

Information Theory · Computer Science 2018-07-10 Praneeth Narayanamurthy , Namrata Vaswani

Robust PCA is a widely used statistical procedure to recover a underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank…

Machine Learning · Statistics 2017-09-04 Teng Zhang , Yi Yang

When deploying deep learning models to a device, it is traditionally assumed that available computational resources (compute, memory, and power) remain static. However, real-world computing systems do not always provide stable resource…

Machine Learning · Computer Science 2021-10-11 Elvis Nunez , Maxwell Horton , Anish Prabhu , Anurag Ranjan , Ali Farhadi , Mohammad Rastegari

Principal Components Analysis (PCA) is one of the most widely used dimension reduction techniques. Robust PCA (RPCA) refers to the problem of PCA when the data may be corrupted by outliers. Recent work by Cand{\`e}s, Wright, Li, and Ma…

Information Theory · Computer Science 2018-08-14 Namrata Vaswani , Praneeth Narayanamurthy

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