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Phylogenetic PCA (p-PCA) is a version of PCA for observations that are leaf nodes of a phylogenetic tree. P-PCA accounts for the fact that such observations are not independent, due to shared evolutionary history. The method works on…

Methodology · Statistics 2022-08-29 Morten Akhøj , Xavier Pennec , Stefan Sommer

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 components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

Machine Learning · Statistics 2015-05-06 Madeleine Udell , Corinne Horn , Reza Zadeh , Stephen Boyd

Principal component analysis (PCA) is a classical and widely used method for dimensionality reduction, with applications in data compression, computer vision, pattern recognition, and signal processing. However, PCA is designed for…

Methodology · Statistics 2025-10-01 Wenhui Wu , Changchun Shang , Jianhua Zhao , Xuan Ma , Yue Wang

The literature provides strong evidence that stock prices can be predicted from past price data. Principal component analysis (PCA) is a widely used mathematical technique for dimensionality reduction and analysis of data by identifying a…

Mathematical Finance · Quantitative Finance 2018-03-15 Mahsa Ghorbani , Edwin K. P. Chong

Revisiting PCA for Time Series Reduction in Temporal Dimension; Jiaxin Gao, Wenbo Hu, Yuntian Chen; Deep learning has significantly advanced time series analysis (TSA), enabling the extraction of complex patterns for tasks like…

Machine Learning · Computer Science 2024-12-30 Jiaxin Gao , Wenbo Hu , Yuntian Chen

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

Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…

Computer Vision and Pattern Recognition · Computer Science 2014-09-02 Quan Wang

Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…

Machine Learning · Computer Science 2017-07-11 Xiaojun Chang , Feiping Nie , Yi Yang , Heng Huang

This paper examines in detail the geometric structure of principal component analysis (PCA) by considering in detail the distributions of both unrotated and rotated MNIST digits in the space defined by the lowest order PCA components. Since…

Machine Learning · Computer Science 2025-10-02 David Yevick , Karolina Hutchison

Modal analysis techniques are used to identify patterns and develop reduced-order models in a variety of fluid applications. However, experimentally acquired flow fields may be corrupted with incorrect and missing entries, which may degrade…

In 2019, Yoshida et al. developed tropical Principal Component Analysis (PCA), that is, an analogue of the classical PCA in the setting of tropical geometry and applied it to visualize a set of gene trees over a space of phylogenetic trees…

Combinatorics · Mathematics 2025-05-23 Ruriko Yoshida

We explore the physical implications of applying principal component analysis (PCA) to translationally invariant classical systems defined on a $d$-dimensional hypercubic lattice. Using Rayleigh-Schr\"odinger perturbation theory, we…

Statistical Mechanics · Physics 2025-04-08 Su-Chan Park

Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be…

Machine Learning · Statistics 2012-10-29 Youwei Zhang , Laurent El Ghaoui

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

Recently, the robustification of principal component analysis has attracted lots of attention from statisticians, engineers and computer scientists. In this work we study the type of outliers that are not necessarily apparent in the…

Methodology · Statistics 2016-01-29 Yiyuan She , Shijie Li , Dapeng Wu

Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under…

Numerical Analysis · Mathematics 2025-04-28 Yangyang Xu , Kexin Li , Li Yang , You-Wei Wen

In this paper, we propose a novel approach named by Discriminative Principal Component Analysis which is abbreviated as Discriminative PCA in order to enhance separability of PCA by Linear Discriminant Analysis (LDA). The proposed method…

Computer Vision and Pattern Recognition · Computer Science 2019-03-13 Hanli Qiao

Principal Component Analysis (PCA) is a pivotal technique widely utilized in the realms of machine learning and data analysis. It aims to reduce the dimensionality of a dataset while minimizing the loss of information. In recent years,…

Cryptography and Security · Computer Science 2024-02-06 Xirong Ma

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an…

Image and Video Processing · Electrical Eng. & Systems 2021-03-02 Szu-Chi Chung , Shao-Hsuan Wang , Po-Yao Niu , Su-Yun Huang , Wei-Hau Chang , I-Ping Tu