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The article discusses selected problems related to both principal component analysis (PCA) and factor analysis (FA). In particular, both types of analysis were compared. A vector interpretation for both PCA and FA has also been proposed.…

Machine Learning · Computer Science 2021-10-22 Zenon Gniazdowski

The selection of best variables is a challenging problem in supervised and unsupervised learning, especially in high dimensional contexts where the number of variables is usually much larger than the number of observations. In this paper,…

Methodology · Statistics 2024-04-01 Benoit Liquet , Sarat Moka , Samuel Muller

This work addresses a procedure to estimate fundamental stellar parameters such as T eff , logg, [Fe/H], and v sin i using a dimensionality reduction technique called Principal Component Analysis (PCA), applied to a large database of…

Solar and Stellar Astrophysics · Physics 2015-08-18 W. Farah , M. Gebran , F. Paletou , R. Blomme

Principal component analysis (PCA) is routinely used in population genetics to assess genetic structure. With chromosomal reference genomes and population-scale whole genome-sequencing becoming increasingly accessible, contemporary studies…

Populations and Evolution · Quantitative Biology 2025-01-22 L. Moritz Blumer , Jeffrey M. Good , Richard Durbin

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to…

Data Structures and Algorithms · Computer Science 2016-07-13 Christos Boutsidis , David P. Woodruff , Peilin Zhong

Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…

Methodology · Statistics 2019-11-20 Yixuan Qiu , Jing Lei , Kathryn Roeder

A method of {\it topological grammars} is proposed for multidimensional data approximation. For data with complex topology we define a {\it principal cubic complex} of low dimension and given complexity that gives the best approximation for…

Neural and Evolutionary Computing · Computer Science 2007-05-23 A. N. Gorban , N. R. Sumner , A. Y. Zinovyev

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

Principal component analysis is a useful dimension reduction and data visualization method. However, in high dimension, low sample size asymptotic contexts, where the sample size is fixed and the dimension goes to infinity,a paradox has…

Applications · Statistics 2012-11-21 Dan Shen , Haipeng Shen , Hongtu Zhu , J. S. Marron

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

Methodology · Statistics 2025-08-22 Zhongyuan Lyu , Ming Yuan

Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…

Statistics Theory · Mathematics 2020-06-11 Kristoffer Hellton , Magne Thoresen

Principal component analysis (PCA), the most popular dimension-reduction technique, has been used to analyze high-dimensional data in many areas. It discovers the homogeneity within the data and creates a reduced feature space to capture as…

Methodology · Statistics 2026-03-24 Daning Bi , Le Chang , Yanrong Yang

The principal component analysis (PCA), a mathematical tool commonly used in statistics, has recently been employed to interpret the $p_T$-dependent fluctuations of harmonic flow $v_n$ in terms of leading and subleading flow modes in heavy…

Nuclear Experiment · Physics 2020-08-26 Ziming Liu , Arabinda Behera , Huichao Song , Jiangyong Jia

The principal component analysis (PCA) of different parameters affecting collectivity of nuclei predicted to be candidate of the interacting boson model dynamical symmetries are performed. The results show that, the use of PCA within…

Nuclear Theory · Physics 2015-06-24 A. Al-Sayed

The probabilistic principal component analysis (PPCA) is built upon a global linear mapping, with which it is insufficient to model complex data variation. This paper proposes a mixture of bilateral-projection probabilistic principal…

Computer Vision and Pattern Recognition · Computer Science 2016-01-08 Fujiao Ju , Yanfeng Sun , Junbin Gao , Simeng Liu , Yongli Hu

Principal Component Analysis (PCA) is known to be the most widely applied dimensionality reduction approach. A lot of improvements have been done on the traditional PCA, in order to obtain optimal results in the dimensionality reduction of…

Computer Vision and Pattern Recognition · Computer Science 2020-09-28 Chisom Ezinne Ogbuanya

We discuss the problem of estimating the number of principal components in Principal Com- ponents Analysis (PCA). Despite of the importance of the problem and the multitude of solutions proposed in the literature, it comes as a surprise…

Methodology · Statistics 2016-07-06 Piotr Sobczyk , Malgorzata Bogdan , Julie Josse

Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…

Statistics Theory · Mathematics 2017-10-30 Raphael Hauser , Raul Kangro , Jüri Lember , Heinrich Matzinger

Multidimensional functional data streams arise in diverse scientific fields, yet their analysis poses significant challenges. We propose a novel online framework for functional principal component analysis that enables efficient and…

Methodology · Statistics 2025-05-06 Muye Nanshan , Nan Zhang , Jiguo Cao

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