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We present a stochastic variance-reduced heavy ball power iteration algorithm for solving PCA and provide a convergence analysis for it. The algorithm is an extension of heavy ball power iteration, incorporating a step size so that progress…

Optimization and Control · Mathematics 2019-01-25 Cheolmin Kim , Diego Klabjan

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

Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…

Information Theory · Computer Science 2014-06-19 Andrea Montanari , Emile Richard

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 a fundamental dimension reduction tool in statistics and machine learning. For large and high-dimensional data, computing the PCA (i.e., the singular vectors corresponding to a number of dominant…

Data Structures and Algorithms · Computer Science 2017-04-26 Wenjian Yu , Yu Gu , Jian Li , Shenghua Liu , Yaohang Li

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

Principal component analysis (PCA) is a classical dimension reduction method which projects data onto the principal subspace spanned by the leading eigenvectors of the covariance matrix. However, it behaves poorly when the number of…

Statistics Theory · Mathematics 2013-05-27 Zongming Ma

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

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…

Information Theory · Computer Science 2022-04-04 Zezhong Zhang , Guangxu Zhu , Rui Wang , Vincent K. N. Lau , Kaibin Huang

Principal component analysis (PCA) is a widespread technique for data analysis that relies on the covariance-correlation matrix of the analyzed data. However to properly work with high-dimensional data, PCA poses severe mathematical…

Quantitative Methods · Quantitative Biology 2018-10-18 Luigi Leonardo Palese

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

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

Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests.…

Optimization and Control · Mathematics 2017-10-09 Chris Junchi Li , Mengdi Wang , Han Liu , Tong Zhang

The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. The application of PCA in a financial setting is associated with several technical difficulties, such as numerical…

Statistical Finance · Quantitative Finance 2021-08-31 Paul Bilokon , David Finkelstein

Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…

Statistics Theory · Mathematics 2009-01-29 Iain M Johnstone , Arthur Yu Lu

Principal component analysis (PCA) is a dimensionality reduction method in data analysis that involves diagonalizing the covariance matrix of the dataset. Recently, quantum algorithms have been formulated for PCA based on diagonalizing a…

Quantum Physics · Physics 2022-10-26 Max Hunter Gordon , M. Cerezo , Lukasz Cincio , Patrick J. Coles

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

Data Structures and Algorithms · Computer Science 2021-06-07 Agniva Chowdhury , Petros Drineas , David P. Woodruff , Samson Zhou

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Computation · Statistics 2016-01-29 Qiaoya Zhang , Yiyuan She

Principal component analysis (PCA) is recognised as a quintessential data analysis technique when it comes to describing linear relationships between the features of a dataset. However, the well-known sensitivity of PCA to non-Gaussian…

Machine Learning · Statistics 2019-10-28 Jean P. Chereau , Bruno Scalzo Dees , Danilo P. Mandic

Principal component analysis (PCA) is a statistical technique commonly used in multivariate data analysis. However, PCA can be difficult to interpret and explain since the principal components (PCs) are linear combinations of the original…

Mathematical Software · Computer Science 2013-12-24 W. Liu , H. Zhang , D. Tao , Y. Wang , K. Lu
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