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Principal component analysis (PCA) is a classical and ubiquitous method for reducing data dimensionality, but it is suboptimal for heterogeneous data that are increasingly common in modern applications. PCA treats all samples uniformly so…

Statistics Theory · Mathematics 2021-12-02 David Hong , Kyle Gilman , Laura Balzano , Jeffrey A. Fessler

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Numerical Analysis · Mathematics 2021-01-14 Alberto García-González , Antonio Huerta , Sergio Zlotnik , Pedro Díez

Principal Component Analysis (PCA) is a well-known multivariate technique used to decorrelate a set of vectors. PCA has been extensively applied in the past to the classification of stellar and galaxy spectra. Here we apply PCA to the…

Astrophysics · Physics 2007-05-23 I. Ferreras , B. Rogers , O. Lahav , .

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

Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as…

Machine Learning · Statistics 2019-03-28 Shixiang Chen , Shiqian Ma , Lingzhou Xue , Hui Zou

Principal components analysis (PCA) is a widely used dimension reduction technique with an extensive range of applications. In this paper, an online distributed algorithm is proposed for recovering the principal eigenspaces. We further…

Machine Learning · Statistics 2019-05-20 Davoud Ataee Tarzanagh , Mohamad Kazem Shirani Faradonbeh , George Michailidis

We provide a probabilistic and infinitesimal view of how the principal component analysis procedure (PCA) can be generalized to analysis of nonlinear manifold valued data. Starting with the probabilistic PCA interpretation of the Euclidean…

Statistics Theory · Mathematics 2018-06-26 Stefan Sommer

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…

Methodology · Statistics 2018-01-08 Jianqing Fan , Qiang Sun , Wen-Xin Zhou , Ziwei Zhu

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

Statistics Theory · Mathematics 2019-06-14 David Hong , Laura Balzano , Jeffrey A. Fessler

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

Sparse principal component analysis (SPCA) has emerged as a powerful technique for modern data analysis, providing improved interpretation of low-rank structures by identifying localized spatial structures in the data and disambiguating…

Principal component analysis (PCA) is a powerful standard tool for reducing the dimensionality of data. Unfortunately, it is sensitive to outliers so that various robust PCA variants were proposed in the literature. This paper addresses the…

Numerical Analysis · Mathematics 2019-02-13 Sebastian Neumayer , Max Nimmer , Simon Setzer , Gabriele Steidl

Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works…

Machine Learning · Statistics 2017-09-19 Clément Elvira , Pierre Chainais , Nicolas Dobigeon

Principal Component Analysis (PCA) is a commonly used tool for dimension reduction in analyzing high dimensional data; Multilinear Principal Component Analysis (MPCA) has the potential to serve the similar function for analyzing tensor…

Statistics Theory · Mathematics 2011-04-29 Hung Hung , Pei-Shien Wu , I-Ping Tu , Su-Yun Huang

Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…

Methodology · Statistics 2021-11-05 Pablo Soto-Quiros , Anatoli Torokhti

Principal component analysis (PCA) has achieved great success in unsupervised learning by identifying covariance correlations among features. If the data collection fails to capture the covariance information, PCA will not be able to…

Computational Physics · Physics 2021-08-24 Ziming Liu , Sitian Qian , Yixuan Wang , Yuxuan Yan , Tianyi Yang

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

Statistics Theory · Mathematics 2021-04-02 Anru R. Zhang , T. Tony Cai , Yihong Wu

Methods for supervised principal component analysis (SPCA) aim to incorporate label information into principal component analysis (PCA), so that the extracted features are more useful for a prediction task of interest. Prior work on SPCA…

Machine Learning · Statistics 2022-08-18 Alexander Ritchie , Laura Balzano , Daniel Kessler , Chandra S. Sripada , Clayton Scott

Principal component analysis (PCA) is a standard dimensionality reduction technique used in various research and applied fields. From an algorithmic point of view, classical PCA can be formulated in terms of operations on a multivariate…

Methodology · Statistics 2022-11-08 Ayisha Fayomi , Yannis Pantazis , Michail Tsagris , Andrew T. A. Wood

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