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An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal…

Methodology · Statistics 2020-12-15 Jingxin Zhang , Hao Chen , Songhang Chen , Xia Hong

This paper proposes sparse and easy-to-interpret proximate factors to approximate statistical latent factors. Latent factors in a large-dimensional factor model can be estimated by principal component analysis (PCA), but are usually hard to…

Methodology · Statistics 2020-08-04 Markus Pelger , Ruoxuan Xiong

A general framework for principal component analysis (PCA) in the presence of heteroskedastic noise is introduced. We propose an algorithm called HeteroPCA, which involves iteratively imputing the diagonal entries of the sample covariance…

Statistics Theory · Mathematics 2021-04-02 Anru R. Zhang , T. Tony Cai , Yihong Wu

We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…

Machine Learning · Computer Science 2019-10-14 Jochen Görtler , Thilo Spinner , Dirk Streeb , Daniel Weiskopf , Oliver Deussen

Principal Component Analysis (PCA) finds the best linear representation of data, and is an indispensable tool in many learning and inference tasks. Classically, principal components of a dataset are interpreted as the directions that…

Optimization and Control · Mathematics 2019-12-24 Raphael A. Hauser , Armin Eftekhari

Foreground detection in a given video sequence is a pivotal step in many computer vision applications such as video surveillance system. Robust Principal Component Analysis (RPCA) performs low-rank and sparse decomposition and accomplishes…

Computer Vision and Pattern Recognition · Computer Science 2019-09-19 Amirhossein Khalilian-Gourtani , Shervin Minaee , Yao Wang

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample.…

Machine Learning · Statistics 2026-03-18 Javier Salazar Cavazos , Jeffrey A. Fessler , Laura Balzano

We study distributed principal component analysis (PCA) in high-dimensional settings under the spiked model. In such regimes, sample eigenvectors can deviate significantly from population ones, introducing a persistent bias. Existing…

Methodology · Statistics 2025-05-29 Weiming Li , Zeng Li , Siyu Wang , Yanqing Yin , Junpeng Zhu

Principal component analysis (PCA) has been widely used in analyzing high-dimensional data. It converts a set of observed data points of possibly correlated variables into a set of linearly uncorrelated variables via an orthogonal…

Optimization and Control · Mathematics 2024-03-06 Xin Liang , Zhen-Chen Guo , Li Wang , Ren-Cang Li , Wen-Wei Lin

Most anomaly detection systems try to model normal behavior and assume anomalies deviate from it in diverse manners. However, there may be patterns in the anomalies as well. Ideally, an anomaly detection system can exploit patterns in both…

Machine Learning · Computer Science 2023-05-23 Jonas Soenen , Elia Van Wolputte , Vincent Vercruyssen , Wannes Meert , Hendrik Blockeel

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…

Principal component analysis (PCA) is widely used for feature extraction and dimensionality reduction, with documented merits in diverse tasks involving high-dimensional data. Standard PCA copes with one dataset at a time, but it is…

Machine Learning · Computer Science 2019-01-30 Jia Chen , Gang Wang , Georgios B. Giannakis

We study a practical algorithm for sparse principal component analysis (PCA) of incomplete and noisy data. Our algorithm is based on the semidefinite program (SDP) relaxation of the non-convex $l_1$-regularized PCA problem. We provide…

Machine Learning · Statistics 2022-09-16 Hanbyul Lee , Qifan Song , Jean Honorio

Sparse principal component analysis (SPCA) methods have proven to efficiently analyze high-dimensional data. Among them, threshold-based SPCA (TSPCA) is computationally more cost-effective than regularized SPCA, based on L1 penalties. We…

Methodology · Statistics 2023-05-29 Kazuyoshi Yata , Makoto Aoshima

As a widely used method in machine learning, principal component analysis (PCA) shows excellent properties for dimensionality reduction. It is a serious problem that PCA is sensitive to outliers, which has been improved by numerous Robust…

Machine Learning · Computer Science 2020-11-24 Shenglan Liu , Yang Yu

Principal component analysis (PCA) is possibly one of the most widely used statistical tools to recover a low-rank structure of the data. In the high-dimensional settings, the leading eigenvector of the sample covariance can be nearly…

Statistics Theory · Mathematics 2015-04-06 Chao Gao , Harrison H. Zhou

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

We discuss spectral principal component analysis (SPCA) and show examples of its application in analyzing AGN spectra in both small and large samples. It can be used to identify peculiar spectra and classify AGN spectra. Its application to…

Astrophysics · Physics 2007-05-23 Zhaohui Shang , Beverley J. Wills

We introduce a novel algorithm that computes the $k$-sparse principal component of a positive semidefinite matrix $A$. Our algorithm is combinatorial and operates by examining a discrete set of special vectors lying in a low-dimensional…

Machine Learning · Statistics 2014-05-09 Dimitris S. Papailiopoulos , Alexandros G. Dimakis , Stavros Korokythakis

Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…

History and Overview · Mathematics 2016-04-19 Stephen Pankavich , Rebecca Swanson