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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

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

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…

Methodology · Statistics 2015-08-20 Vincent Audigier , François Husson , Julie Josse

The study of stochastic variational principles involves the problem of constructing fixed-endpoint and adapted variations of semimartingales. We provide a detailed construction of variations of semimartingales that are not only fixed at…

Mathematical Physics · Physics 2025-09-11 Archishman Saha

Sparse versions of principal component analysis (PCA) have imposed themselves as simple, yet powerful ways of selecting relevant features of high-dimensional data in an unsupervised manner. However, when several sparse principal components…

Machine Learning · Statistics 2019-05-22 Charles Bouveyron , Pierre Latouche , Pierre-Alexandre Mattei

Principal Components Analysis (PCA) and Independent Component Analysis (ICA) are used to identify global patterns in solar and space data. PCA seeks orthogonal modes of the two-point correlation matrix constructed from a data set. It…

Astrophysics · Physics 2009-11-13 A. C. Cadavid , J. K. Lawrence , A. Ruzmaikin

Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary…

Statistics Theory · Mathematics 2012-02-24 Tom M. W. Nye

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

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

This paper describes some applications of an incremental implementation of the principal component analysis (PCA). The algorithm updates the transformation coefficients matrix on-line for each new sample, without the need to keep all the…

Machine Learning · Statistics 2019-08-14 Vittorio Lippi , Giacomo Ceccarelli

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

We explore the use of principal component analysis (PCA) to characterize high-fidelity simulations and interferometric observations of the millimeter emission that originates near the horizons of accreting black holes. We show…

Instrumentation and Methods for Astrophysics · Physics 2018-09-05 Lia Medeiros , Tod R. Lauer , Dimitrios Psaltis , Feryal Özel

Recently popularized randomized methods for principal component analysis (PCA) efficiently and reliably produce nearly optimal accuracy --- even on parallel processors --- unlike the classical (deterministic) alternatives. We adapt one of…

Computation · Statistics 2011-12-23 Nathan Halko , Per-Gunnar Martinsson , Yoel Shkolnisky , Mark Tygert

There are a number of well-established methods such as principal components analysis (PCA) for automatically capturing systematic variation due to latent variables in large-scale genomic data. PCA and related methods may directly provide a…

Methodology · Statistics 2015-03-05 Neo Christopher Chung , John D. Storey

Principal Component Analysis (PCA) has been widely used for dimensionality reduction and feature extraction. Robust PCA (RPCA), under different robust distance metrics, such as l1-norm and l2, p-norm, can deal with noise or outliers to some…

Machine Learning · Computer Science 2021-06-29 Zhao Kang , Hongfei Liu , Jiangxin Li , Xiaofeng Zhu , Ling Tian

We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of…

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

We extend the scope of differential machine learning and introduce a new breed of supervised principal component analysis to reduce dimensionality of Derivatives problems. Applications include the specification and calibration of pricing…

Computational Finance · Quantitative Finance 2025-03-19 Brian Huge , Antoine Savine

The study of stability and sensitivity of statistical methods or algorithms with respect to their data is an important problem in machine learning and statistics. The performance of the algorithm under resampling of the data is a…

Statistics Theory · Mathematics 2023-02-15 Haoyu Wang

This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…

Statistics Theory · Mathematics 2022-10-20 Elynn Y. Chen , Jianqing Fan