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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…

Principal component analysis (PCA) is one of the most commonly used statistical procedures with a wide range of applications. This paper considers both minimax and adaptive estimation of the principal subspace in the high dimensional…

Statistics Theory · Mathematics 2014-01-08 T. Tony Cai , Zongming Ma , Yihong Wu

In recent years, the application of tensors has become more widespread in fields that involve data analytics and numerical computation. Due to the explosive growth of data, low-rank tensor decompositions have become a powerful tool to…

Numerical Analysis · Mathematics 2020-11-03 Lingjie Li , Wenjian Yu , Kim Batselier

When synthesizing multi-source high-dimensional data, a key objective is to extract low-dimensional representations that effectively approximate the original features across different sources. Such representations facilitate the discovery…

Machine Learning · Computer Science 2026-03-10 Zhenyu Wang , Molei Liu , Jing Lei , Francis Bach , Zijian Guo

The Principal Component Analysis (PCA) is a data dimensionality reduction technique well-suited for processing data from sensor networks. It can be applied to tasks like compression, event detection, and event recognition. This technique is…

Networking and Internet Architecture · Computer Science 2010-03-13 Yann-Aël Le Borgne , Sylvain Raybaud , Gianluca Bontempi

Robust principal component analysis (RPCA) is a well-studied problem with the goal of decomposing a matrix into the sum of low-rank and sparse components. In this paper, we propose a nonconvex feasibility reformulation of RPCA problem and…

Optimization and Control · Mathematics 2020-01-27 Aritra Dutta , Filip Hanzely , Peter Richtárik

Principal Component Analysis (PCA) is a very successful dimensionality reduction technique, widely used in predictive modeling. A key factor in its widespread use in this domain is the fact that the projection of a dataset onto its first…

Machine Learning · Statistics 2017-05-19 Xianghui Luo , Robert J. Durrant

We consider the Principal Component Analysis problem for large tensors of arbitrary order $k$ under a single-spike (or rank-one plus noise) model. On the one hand, we use information theory, and recent results in probability theory, to…

Machine Learning · Computer Science 2014-11-06 Andrea Montanari , Emile Richard

Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…

Statistics Theory · Mathematics 2019-06-14 David Hong , Laura Balzano , Jeffrey A. Fessler

Tensors, which give a faithful and effective representation to deliver the intrinsic structure of multi-dimensional data, play a crucial role in an increasing number of signal processing and machine learning problems. However, tensor data…

Machine Learning · Statistics 2026-02-17 Tong Wu

For very large datasets, random projections (RP) have become the tool of choice for dimensionality reduction. This is due to the computational complexity of principal component analysis. However, the recent development of randomized…

Machine Learning · Statistics 2019-01-04 Michael Wojnowicz , Di Zhang , Glenn Chisholm , Xuan Zhao , Matt Wolff

The problem of recovering a low-rank matrix from a set of observations corrupted with gross sparse error is known as the robust principal component analysis (RPCA) and has many applications in computer vision, image processing and web data…

Optimization and Control · Mathematics 2013-09-27 Necdet Serhat Aybat , Donald Goldfarb , Shiqian Ma

Principal component regression (PCR) is a simple, but powerful and ubiquitously utilized method. Its effectiveness is well established when the covariates exhibit low-rank structure. However, its ability to handle settings with noisy,…

Machine Learning · Computer Science 2021-05-20 Anish Agarwal , Devavrat Shah , Dennis Shen , Dogyoon Song

The research detailed in this paper scrutinizes Principal Component Analysis (PCA), a seminal method employed in statistics and machine learning for the purpose of reducing data dimensionality. Singular Value Decomposition (SVD) is often…

Methodology · Statistics 2024-04-02 Donggun Kim , Kisung You

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

Robust Principal Component Analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other…

Methodology · Statistics 2023-10-31 Xiaojun Zheng , Simon Mak , Liyan Xie , Yao Xie

Numerous applications in data mining and machine learning require recovering a matrix of minimal rank. Robust principal component analysis (RPCA) is a general framework for handling this kind of problems. Nuclear norm based convex surrogate…

Computer Vision and Pattern Recognition · Computer Science 2016-11-17 Zhao Kang , Chong Peng , Qiang Cheng

Recovering intrinsic low dimensional subspaces from data distributed on them is a key preprocessing step to many applications. In recent years, there has been a lot of work that models subspace recovery as low rank minimization problems. We…

Machine Learning · Computer Science 2014-12-09 Hongyang Zhang , Zhouchen Lin , Chao Zhang , Junbin Gao

Robust tensor recovery plays an instrumental role in robustifying tensor decompositions for multilinear data analysis against outliers, gross corruptions and missing values and has a diverse array of applications. In this paper, we study…

Machine Learning · Statistics 2014-08-26 Donald Goldfarb , Zhiwei Qin

Robust principal component analysis (RPCA) is a powerful method for learning low-rank feature representation of various visual data. However, for certain types as well as significant amount of error corruption, it fails to yield…

Computer Vision and Pattern Recognition · Computer Science 2018-01-24 Niannan Xue , Jiankang Deng , Shiyang Cheng , Yannis Panagakis , Stefanos Zafeiriou