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The principal component analysis approach is employed to extract the principal components contained in nuclear mass models for the first time. The effects coming from different nuclear mass models are reintegrated and reorganized in the…

Nuclear Theory · Physics 2024-05-27 X. H. Wu , P. W. Zhao

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 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) is a widely used method for data processing, such as for dimension reduction and visualization. Standard PCA is known to be sensitive to outliers, and thus, various robust PCA methods have been proposed.…

Machine Learning · Statistics 2020-08-11 Keishi Sando , Hideitsu Hino

It is shown that Principal Component Analysis (PCA) applied to event-by-event single-particle distributions in A-A collisions allows establishing the most optimal basis for anisotropic flow studies from data itself, in contrast to manual…

Nuclear Theory · Physics 2020-12-01 Igor Altsybeev

Principal component analysis (PCA) represents a standard approach to identify collective variables $\{x_i\}\!=\!\boldsymbol{x}$, which can be used to construct the free energy landscape $\Delta G(\boldsymbol{x})$ of a molecular system.…

Biomolecules · Quantitative Biology 2019-05-30 Matthias Post , Steffen Wolf , Gerhard Stock

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

Functional principal component analysis (FPCA) is an important technique for dimension reduction in functional data analysis (FDA). Classical FPCA method is based on the Karhunen-Lo\`{e}ve expansion, which assumes a linear structure of the…

Methodology · Statistics 2023-06-27 Rou Zhong , Chunming Zhang , Jingxiao Zhang

The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more general objects. A particularly challenging…

Statistics Theory · Mathematics 2008-10-07 Burcu Aydin , Gabor Pataki , Haonan Wang , Elizabeth Bullitt , J. S. Marron

Deep neural networks show great success when input vectors are in an Euclidean space. However, those classical neural networks show a poor performance when inputs are phylogenetic trees, which can be written as vectors in the tropical…

Discrete Mathematics · Computer Science 2023-09-26 Ruriko Yoshida , Georgios Aliatimis , Keiji Miura

Motivation: Although principal component analysis (PCA) is widely used for the dimensional reduction of biomedical data, interpretation of PCA results remains daunting. Most existing methods attempt to explain each principal component (PC)…

Quantitative Methods · Quantitative Biology 2015-08-24 H. Robert Frost , Zhigang Li , Jason H. Moore

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

Machine Learning · Statistics 2017-08-16 Darren Homrighausen , Daniel J. McDonald

Principal component analysis is a statistical method, which lowers the number of important variables in a data set. The use of this method for the bursts' spectra and afterglows is discussed in this paper. The analysis indicates that three…

Astrophysics · Physics 2015-05-13 Z. Bagoly , I. Horvath , L. G. Balazs , L. Borgonovo , S. Larsson , A. Meszaros , F. Ryde

Principal Components Analysis (PCA) is a common way to study the sources of variation in a high-dimensional data set. Typically, the leading principal components are used to understand the variation in the data or to reduce the dimension of…

There is growing interest in using the close connection between differential geometry and statistics to model smooth manifold-valued data. In particular, much work has been done recently to generalize principal component analysis (PCA), the…

Other Statistics · Statistics 2016-10-07 Drew Lazar , Lizhen Lin

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Methodology · Statistics 2025-05-27 Si Cheng , Magali N. Blanco , Timothy V. Larson , Lianne Sheppard , Adam Szpiro , Ali Shojaie

Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…

Applications · Statistics 2018-06-18 Zhonghua Liu , Xihong Lin

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

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal…

Machine Learning · Computer Science 2019-07-02 Ami Tavory

Principal Component Analysis (PCA) is a well-known linear dimension-reduction technique designed for Euclidean data. In a wide spectrum of applied fields, however, it is common to observe multivariate circular data (also known as toroidal…

Methodology · Statistics 2023-08-22 Eduardo García-Portugués , Arturo Prieto-Tirado