English
Related papers

Related papers: Fair Principal Component Analysis and Filter Desig…

200 papers

Robust Principal Component Analysis (RPCA) is a fundamental technique for decomposing data into low-rank and sparse components, which plays a critical role for applications such as image processing and anomaly detection. Traditional RPCA…

Machine Learning · Computer Science 2024-12-20 Kexin Li , You-wei Wen , Xu Xiao , Mingchao Zhao

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…

Machine Learning · Computer Science 2015-02-25 Malik Magdon-Ismail , Christos Boutsidis

Principal Component Analysis (PCA) is a popular method for dimension reduction and has attracted an unfailing interest for decades. More recently, kernel PCA (KPCA) has emerged as an extension of PCA but, despite its use in practice, a…

Machine Learning · Computer Science 2023-01-25 Maxime Haddouche , Benjamin Guedj , John Shawe-Taylor

Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…

Computation · Statistics 2010-06-04 Vladimir Rokhlin , Arthur Szlam , Mark Tygert

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

This paper presents new algorithms to solve the feature-sparsity constrained PCA problem (FSPCA), which performs feature selection and PCA simultaneously. Existing optimization methods for FSPCA require data distribution assumptions and are…

Machine Learning · Computer Science 2019-05-28 Lai Tian , Feiping Nie , Xuelong Li

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

This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between dimensionality-reduced conditional distributions of different protected classes. The incorporation of MMD naturally leads to…

Machine Learning · Statistics 2022-01-26 Junghyun Lee , Gwangsu Kim , Matt Olfat , Mark Hasegawa-Johnson , Chang D. Yoo

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

We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…

Machine Learning · Statistics 2020-12-10 Michael Weylandt

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

In the field of unsupervised feature selection, sparse principal component analysis (SPCA) methods have attracted more and more attention recently. Compared to spectral-based methods, SPCA methods don't rely on the construction of a…

Computer Vision and Pattern Recognition · Computer Science 2023-09-13 Junjing Zheng , Xinyu Zhang , Yongxiang Liu , Weidong Jiang , Kai Huo , Li Liu

Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…

Machine Learning · Statistics 2023-12-19 Xuan Ma , Jianhua Zhao , Yue Wang

Robust principal component analysis (RPCA) seeks a low-rank component and a sparse component from their summation. Yet, in many applications of interest, the sparse foreground actually replaces, or occludes, elements from the low-rank…

Computer Vision and Pattern Recognition · Computer Science 2026-04-23 Yinjian Wang , Wei Li , Yuanyuan Gui , James E. Fowler , Gemine Vivone

We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-08-16 Wenda Chu

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 (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

Methodology · Statistics 2025-08-22 Zhongyuan Lyu , Ming Yuan

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

Deep neural networks perform remarkably well on image classification tasks but remain vulnerable to carefully crafted adversarial perturbations. This work revisits linear dimensionality reduction as a simple, data-adapted defense. We…

Machine Learning · Computer Science 2025-10-08 Killian Steunou , Théo Druilhe , Sigurd Saue

In this paper, we consider a new variant for principal component analysis (PCA), aiming to capture the grouping and/or sparse structures of factor loadings simultaneously. To achieve these goals, we employ a non-convex truncated…

Methodology · Statistics 2022-09-14 Haiyan Jiang , Shanshan Qin , Oscar Hernan Madrid Padilla