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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

Principal component analysis (PCA) is one of the most powerful tools in machine learning. The simplest method for PCA, the power iteration, requires $\mathcal O(1/\Delta)$ full-data passes to recover the principal component of a matrix with…

Optimization and Control · Mathematics 2017-07-11 Christopher De Sa , Bryan He , Ioannis Mitliagkas , Christopher Ré , Peng Xu

Principal component analysis (PCA) is perhaps the most widely used method for data dimensionality reduction. A key question in PCA is deciding how many factors to retain. This manuscript describes a new approach to automatically selecting…

Methodology · Statistics 2026-02-10 Enes Makalic , Daniel F. Schmidt

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…

History and Overview · Mathematics 2016-04-19 Stephen Pankavich , Rebecca Swanson

Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…

Methodology · Statistics 2014-01-15 Ngoc Mai Tran , Maria Osipenko , Wolfgang Karl Haerdle

Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…

Optimization and Control · Mathematics 2009-07-14 Zhaosong Lu , Yong Zhang

Most of machine learning deals with vector parameters. Ideally we would like to take higher order information into account and make use of matrix or even tensor parameters. However the resulting algorithms are usually inefficient. Here we…

Machine Learning · Computer Science 2015-07-27 Wojciech Kotłowski , Manfred K. Warmuth

Principal Subspace Analysis (PSA) -- and its sibling, Principal Component Analysis (PCA) -- is one of the most popular approaches for dimensionality reduction in signal processing and machine learning. But centralized PSA/PCA solutions are…

Machine Learning · Computer Science 2021-11-25 Arpita Gang , Bingqing Xiang , Waheed U. Bajwa

Principal Component Analysis (PCA) is a popular tool for dimensionality reduction and feature extraction in data analysis. There is a probabilistic version of PCA, known as Probabilistic PCA (PPCA). However, standard PCA and PPCA are not…

Machine Learning · Computer Science 2019-04-16 Bowen Zhao , Xi Xiao , Wanpeng Zhang , Bin Zhang , Shutao Xia

Principal component analysis (PCA) is widely used for dimension reduction and embedding of real data in social network analysis, information retrieval, and natural language processing, etc. In this work we propose a fast randomized PCA…

Machine Learning · Computer Science 2018-10-17 Xu Feng , Yuyang Xie , Mingye Song , Wenjian Yu , Jie Tang

Principal Component Analysis (PCA) is one of the most commonly used statistical methods for data exploration, and for dimensionality reduction wherein the first few principal components account for an appreciable proportion of the…

Methodology · Statistics 2024-01-11 Caren Marzban , Ulvi Yurtsever , Michael Richman

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

Machine Learning · Statistics 2021-09-10 Shaojie Xu , Joel Vaughan , Jie Chen , Agus Sudjianto , Vijayan Nair

Missing data is a commonly occurring problem in practice. Many imputation methods have been developed to fill in the missing entries. However, not all of them can scale to high-dimensional data, especially the multiple imputation…

Machine Learning · Computer Science 2023-03-21 Thu Nguyen , Hoang Thien Ly , Michael Alexander Riegler , Pål Halvorsen , Hugo L. Hammer

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Computation · Statistics 2010-06-04 Vladimir Rokhlin , Arthur Szlam , Mark Tygert

Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

Applications · Statistics 2025-06-25 Theodosios Papazoglou , Guosheng Yin

Conventional principal component analysis (PCA) finds a principal vector that maximizes the sum of second powers of principal components. We consider a generalized PCA that aims at maximizing the sum of an arbitrary convex function of…

Machine Learning · Computer Science 2019-11-19 Samuele Battaglino , Erdem Koyuncu

Principal Component Analysis (PCA) and its nonlinear extension Kernel PCA (KPCA) are widely used across science and industry for data analysis and dimensionality reduction. Modern deep learning tools have achieved great empirical success,…

Machine Learning · Computer Science 2023-02-23 Francesco Tonin , Qinghua Tao , Panagiotis Patrinos , Johan A. K. Suykens

We study the distributed computing setting in which there are multiple servers, each holding a set of points, who wish to compute functions on the union of their point sets. A key task in this setting is Principal Component Analysis (PCA),…

Machine Learning · Computer Science 2014-12-24 Maria-Florina Balcan , Vandana Kanchanapally , Yingyu Liang , David Woodruff

We present a federated, asynchronous, and $(\varepsilon, \delta)$-differentially private algorithm for PCA in the memory-limited setting. Our algorithm incrementally computes local model updates using a streaming procedure and adaptively…

Machine Learning · Computer Science 2020-10-26 Andreas Grammenos , Rodrigo Mendoza-Smith , Jon Crowcroft , Cecilia Mascolo

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Machine Learning · Computer Science 2019-01-08 Jian Vora