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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

Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…

Optimization and Control · Mathematics 2025-12-02 Ryan Cory-Wright , Jean Pauphilet

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 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

Principal component analysis (PCA) is known to be sensitive to outliers, so that various robust PCA variants were proposed in the literature. A recent model, called REAPER, aims to find the principal components by solving a convex…

Numerical Analysis · Mathematics 2021-03-19 Robert Beinert , Gabriele Steidl

Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

Machine Learning · Computer Science 2017-07-11 Xiaojun Chang , Feiping Nie , Yi Yang , Heng Huang

Mining useful clusters from high dimensional data has received significant attention of the computer vision and pattern recognition community in the recent years. Linear and non-linear dimensionality reduction has played an important role…

Computer Vision and Pattern Recognition · Computer Science 2016-05-25 Nauman Shahid , Nathanael Perraudin , Vassilis Kalofolias , Gilles Puy , Pierre Vandergheynst

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

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In…

Machine Learning · Computer Science 2015-08-03 Ohad Shamir

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of…

Optimization and Control · Mathematics 2010-10-27 Dimitris Bertsimas , David B. Brown , Constantine Caramanis

This work addresses integrating probabilistic propositional logic constraints into the distribution encoded by a probabilistic circuit (PC). PCs are a class of tractable models that allow efficient computations (such as conditional and…

Machine Learning · Computer Science 2024-03-21 Soroush Ghandi , Benjamin Quost , Cassio de Campos

Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…

Numerical Analysis · Mathematics 2019-07-12 Jared Tanner , Andrew Thompson , Simon Vary

The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods. We show how computing the leading principal component could be reduced to solving a \textit{small} number of well-conditioned {\it…

Optimization and Control · Mathematics 2015-11-26 Dan Garber , Elad Hazan

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

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 propose a new method for robust PCA -- the task of recovering a low-rank matrix from sparse corruptions that are of unknown value and support. Our method involves alternating between projecting appropriate residuals onto the set of…

Information Theory · Computer Science 2014-10-29 Praneeth Netrapalli , U N Niranjan , Sujay Sanghavi , Animashree Anandkumar , Prateek Jain

Principal component analysis (PCA) is widely used to analyze high-dimensional data, but it is very sensitive to outliers. Robust PCA methods seek fits that are unaffected by the outliers and can therefore be trusted to reveal them. FastHCS…

Methodology · Statistics 2015-09-25 E. Schmitt , K. Vakili

Stochastic algorithms are well-known for their performance in the era of big data. In convex optimization, stochastic algorithms have been studied in depth and breadth. However, the current body of research on stochastic algorithms for…

Optimization and Control · Mathematics 2021-08-06 Hoai An Le Thi , Hoang Phuc Hau Luu , Tao Pham Dinh

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

Machine Learning · Statistics 2014-08-26 Donald Goldfarb , Zhiwei Qin

Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this…

Optimization and Control · Mathematics 2018-01-19 Bo Jiang , Tianyi Lin , Shiqian Ma , Shuzhong Zhang