English
Related papers

Related papers: Projected Robust PCA with Application to Smooth Im…

200 papers

Robust Principal Component Analysis (RPCA) via rank minimization is a powerful tool for recovering underlying low-rank structure of clean data corrupted with sparse noise/outliers. In many low-level vision problems, not only it is known…

Computer Vision and Pattern Recognition · Computer Science 2019-02-18 Tae-Hyun Oh , Yu-Wing Tai , Jean-Charles Bazin , Hyeongwoo Kim , In So Kweon

PCA is one of the most widely used dimension reduction techniques. A related easier problem is "subspace learning" or "subspace estimation". Given relatively clean data, both are easily solved via singular value decomposition (SVD). The…

Information Theory · Computer Science 2020-06-25 Namrata Vaswani , Thierry Bouwmans , Sajid Javed , Praneeth Narayanamurthy

Robust principal component analysis (RPCA) has been widely used for recovering low-rank matrices in many data mining and machine learning problems. It separates a data matrix into a low-rank part and a sparse part. The convex approach has…

Computer Vision and Pattern Recognition · Computer Science 2016-09-29 Chong Peng , Zhao Kang , Qiang Chen

We introduce a reformulation of regularized low-rank recovery models to take advantage of GPU, multiple CPU, and hybridized architectures. Low-rank recovery often involves nuclear-norm minimization through iterative thresholding of singular…

Optimization and Control · Mathematics 2017-10-05 Derek Driggs , Stephen Becker , Aleksandr Aravkin

Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…

Numerical Analysis · Mathematics 2021-01-14 Alberto García-González , Antonio Huerta , Sergio Zlotnik , Pedro Díez

Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…

Machine Learning · Computer Science 2023-01-25 Arpita Gang , Waheed U. Bajwa

Robust tensor principal component analysis (RTPCA) aims to separate the low-rank and sparse components from multi-dimensional data, making it an essential technique in the signal processing and computer vision fields. Recently emerging…

Computer Vision and Pattern Recognition · Computer Science 2025-01-20 Lanlan Feng , Ce Zhu , Yipeng Liu , Saiprasad Ravishankar , Longxiu Huang

Registration involving one or more images containing pathologies is challenging, as standard image similarity measures and spatial transforms cannot account for common changes due to pathologies. Low-rank/Sparse (LRS) decomposition removes…

Computer Vision and Pattern Recognition · Computer Science 2017-04-04 Xu Han , Xiao Yang , Stephen Aylward , Roland Kwitt , Marc Niethammer

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product…

Machine Learning · Statistics 2019-03-11 Canyi Lu , Jiashi Feng , Yudong Chen , Wei Liu , Zhouchen Lin , Shuicheng Yan

Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by…

Machine Learning · Statistics 2018-11-13 Mehdi Bahri , Yannis Panagakis , Stefanos Zafeiriou

Principal Component Analysis (PCA) is a dimension reduction technique. It produces inconsistent estimators when the dimensionality is moderate to high, which is often the problem in modern large-scale applications where algorithm…

Computation · Statistics 2016-01-29 Qiaoya Zhang , Yiyuan She

Modal analysis techniques are used to identify patterns and develop reduced-order models in a variety of fluid applications. However, experimentally acquired flow fields may be corrupted with incorrect and missing entries, which may degrade…

Recent research on problem formulations based on decomposition into low-rank plus sparse matrices shows a suitable framework to separate moving objects from the background. The most representative problem formulation is the Robust Principal…

Computer Vision and Pattern Recognition · Computer Science 2016-11-29 Thierry Bouwmans , Andrews Sobral , Sajid Javed , Soon Ki Jung , El-Hadi Zahzah

We propose a unified framework to solve general low-rank plus sparse matrix recovery problems based on matrix factorization, which covers a broad family of objective functions satisfying the restricted strong convexity and smoothness…

Machine Learning · Statistics 2018-02-21 Xiao Zhang , Lingxiao Wang , Quanquan Gu

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

We revisit the problem of robust principal component analysis with features acting as prior side information. To this aim, a novel, elegant, non-convex optimization approach is proposed to decompose a given observation matrix into a…

Machine Learning · Statistics 2017-09-15 Niannan Xue , Jiankang Deng , Yannis Panagakis , Stefanos Zafeiriou

Sparse principal component analysis (PCA) is a popular dimensionality reduction technique for obtaining principal components which are linear combinations of a small subset of the original features. Existing approaches cannot supply…

Optimization and Control · Mathematics 2022-02-22 Dimitris Bertsimas , Ryan Cory-Wright , Jean Pauphilet

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

Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

Applications · Statistics 2025-06-25 Theodosios Papazoglou , Guosheng Yin

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the…

Machine Learning · Computer Science 2012-06-22 Alfredo Kalaitzis , Neil Lawrence