English
Related papers

Related papers: Large-dimensional Factor Analysis with Weighted PC…

200 papers

In this brief note, we formulate Principal Component Analysis (PCA) over datasets consisting not of points but of distributions, characterized by their location and covariance. Just like the usual PCA on points can be equivalently derived…

Machine Learning · Statistics 2023-06-26 Vlad Niculae

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

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

Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…

Machine Learning · Computer Science 2017-10-27 Gang Wang , Jia Chen , Georgios B. Giannakis

Principal Component Analysis (PCA) is a ubiquitous tool with many applications in machine learning including feature construction, subspace embedding, and outlier detection. In this paper, we present an algorithm for computing the top…

Machine Learning · Computer Science 2013-10-25 Nikos Karampatziakis , Paul Mineiro

Efficient representations of data are essential for processing, exploration, and human understanding, and Principal Component Analysis (PCA) is one of the most common dimensionality reduction techniques used for the analysis of large,…

Computation · Statistics 2023-11-06 Olga Dorabiala , Aleksandr Aravkin , J. Nathan Kutz

Principal component analysis (PCA) is widely used to analyze high-dimensional data, but it is very sensitive to outliers. Robust PCA methods seek fits that are unaffected by the outliers and can therefore be trusted to reveal them. FastHCS…

Methodology · Statistics 2015-09-25 E. Schmitt , K. Vakili

Factor analysis (FA) and principal component analysis (PCA) are popular statistical methods for summarizing and explaining the variability in multivariate datasets. By default, FA and PCA assume the number of components or factors to be…

Methodology · Statistics 2022-05-17 Chetkar Jha , Ian Barnett

Early work established convergence of the principal component estimators of the factors and loadings up to a rotation for large dimensional approximate factor models with weak factors in that the factor loading $\Lambda^{(0)}$ scales…

Statistics Theory · Mathematics 2025-03-12 Yong He , Dong Liu , Yunjing Sun , Yalin Wang

Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…

Methodology · Statistics 2026-04-24 Tim Kutta , Nina Dörnemann , Piotr Kokoszka

Principal component analysis is a versatile tool to reduce dimensionality which has wide applications in statistics and machine learning. It is particularly useful for modeling data in high-dimensional scenarios where the number of…

Methodology · Statistics 2022-08-18 Xiaoyu Hu , Fang Yao

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

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 widely used dimension reduction method, but its performance is known to be non-robust to outliers. Recently, product-PCA (PPCA) has been shown to possess the efficiency-loss free ordering-robustness…

Statistics Theory · Mathematics 2024-12-17 Hung Hung , Chi-Chun Yeh , Su-Yun Huang

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

Recently years, the attempts on distilling mobile data into useful knowledge has been led to the deployment of machine learning algorithms at the network edge. Principal component analysis (PCA) is a classic technique for extracting the…

Information Theory · Computer Science 2022-04-04 Zezhong Zhang , Guangxu Zhu , Rui Wang , Vincent K. N. Lau , Kaibin Huang

Cellular Automata are discrete dynamical systems that evolve following simple and local rules. Despite of its local simplicity, knowledge discovery in CA is a NP problem. This is the main motivation for using data mining techniques for CA…

Discrete Mathematics · Computer Science 2007-05-23 Gilson A. Giraldi , Antonio A. F. Oliveira , Leonardo Carvalho

Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…

Methodology · Statistics 2023-08-22 Fei Ding , Shiyuan He , David E. Jones , Jianhua Z. Huang

We propose a new data-driven method to select the optimal number of relevant components in Principal Component Analysis (PCA). This new method applies to correlation matrices whose time autocorrelation function decays more slowly than an…

Statistical Finance · Quantitative Finance 2019-10-07 Anshul Verma , Pierpaolo Vivo , Tiziana Di Matteo

Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…

Methodology · Statistics 2023-11-28 Yiping Guo , Howard D. Bondell