English
Related papers

Related papers: PAC-Bayesian bounds for Principal Component Analys…

200 papers

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

We study principal components regression (PCR) in an asymptotic high-dimensional regression setting, where the number of data points is proportional to the dimension. We derive exact limiting formulas for the estimation and prediction…

Statistics Theory · Mathematics 2025-09-18 Alden Green , Elad Romanov

We present a novel technique for sparse principal component analysis. This method, named Eigenvectors from Eigenvalues Sparse Principal Component Analysis (EESPCA), is based on the formula for computing squared eigenvector loadings of a…

Methodology · Statistics 2022-05-12 H. Robert Frost

Principal component analysis (PCA) is one of the most widely used dimension reduction and multivariate statistical techniques. From a probabilistic perspective, PCA seeks a low-dimensional representation of data in the presence of…

Machine Learning · Computer Science 2021-01-06 Chihao Zhang , Kuo Gai , Shihua Zhang

Matrix factor models have been growing popular dimension reduction tools for large-dimensional matrix time series. However, the heteroscedasticity of the idiosyncratic components has barely received any attention. Starting from the pseudo…

Statistics Theory · Mathematics 2024-12-03 Yong He , Yujie Hou , Haixia Liu , Yalin Wang

Principal component analysis (PCA) is a well-known linear dimension-reduction method that has been widely used in data analysis and modeling. It is an unsupervised learning technique that identifies a suitable linear subspace for the input…

Machine Learning · Statistics 2021-09-10 Shaojie Xu , Joel Vaughan , Jie Chen , Agus Sudjianto , Vijayan Nair

Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…

Machine Learning · Computer Science 2026-02-05 Thomas Uriot , Elise Chung

Principal skewness analysis (PSA) has been introduced for feature extraction in hyperspectral imagery. As a third-order generalization of principal component analysis (PCA), its solution of searching for the locally maximum skewness…

Computer Vision and Pattern Recognition · Computer Science 2020-07-15 Xiurui Geng , Lei Wang

We consider principal component analysis (PCA) in decomposable Gaussian graphical models. We exploit the prior information in these models in order to distribute its computation. For this purpose, we reformulate the problem in the sparse…

Machine Learning · Statistics 2015-05-13 Ami Wiesel , Alfred O. Hero

Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a "background" dataset. Recently, contrastive principal…

Methodology · Statistics 2021-05-04 Didong Li , Andrew Jones , Barbara Engelhardt

Sparse principal component analysis (SPCA) is widely used for dimensionality reduction and feature extraction in high-dimensional data analysis. Despite many methodological and theoretical developments in the past two decades, the…

Statistics Theory · Mathematics 2023-05-01 Teng Zhang , Haoyi Yang , Lingzhou Xue

Low-precision streaming PCA estimates the top principal component in a streaming setting under limited precision. We establish an information-theoretic lower bound on the quantization resolution required to achieve a target accuracy for the…

Machine Learning · Computer Science 2025-10-28 Sanjoy Dasgupta , Syamantak Kumar , Shourya Pandey , Purnamrita Sarkar

Understanding the inverse equivalent width - luminosity relationship (Baldwin Effect), the topic of this meeting, requires extracting information on continuum and emission line parameters from samples of AGN. We wish to discover whether,…

Astrophysics · Physics 2007-05-23 Paul J. Francis , Beverley J. Wills

Analyzing principal components for multivariate data from its spatial sign covariance matrix (SCM) has been proposed as a computationally simple and robust alternative to normal PCA, but it suffers from poor efficiency properties and is…

Statistics Theory · Mathematics 2016-03-10 Subhabrata Majumdar

Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…

Methodology · Statistics 2021-11-05 Pablo Soto-Quiros , Anatoli Torokhti

Traditional principal component analysis (PCA) is well known in high-dimensional data analysis, but it requires to express data by a matrix with observations to be continuous. To overcome the limitations, a new method called flexible PCA…

Methodology · Statistics 2021-08-17 Tonglin Zhang , Baijian Yang , Qianqian Song , Jing Su

In this paper, we study the estimation of the $k$-dimensional sparse principal subspace of covariance matrix $\Sigma$ in the high-dimensional setting. We aim to recover the oracle principal subspace solution, i.e., the principal subspace…

Machine Learning · Computer Science 2023-12-29 Quanquan Gu , Zhaoran Wang , Han Liu

In this work we investigate the Principal Component Analysis (PCA) sensitivity to the velocity power spectrum in high opacity regimes of the interstellar medium (ISM). For our analysis we use synthetic Position-Position-Velocity (PPV) cubes…

In this paper, we develop new statistical theory for probabilistic principal component analysis models in high dimensions. The focus is the estimation of the noise variance, which is an important and unresolved issue when the number of…

Statistics Theory · Mathematics 2014-06-23 Damien Passemier , Zhaoyuan Li , Jian-Feng Yao

We present the results of a study to optimize the principal component analysis (PCA) algorithm for planet detection, a new algorithm complementing ADI and LOCI for increasing the contrast achievable next to a bright star. The stellar PSF is…

Earth and Planetary Astrophysics · Physics 2015-06-17 T. Meshkat , M. Kenworthy , S. P. Quanz , A. Amara