English
Related papers

Related papers: Learning Robust Low-Rank Representations

200 papers

Reduced-rank regression estimates regression coefficients by imposing a low-rank constraint on the matrix of regression coefficients, thereby accounting for correlations among response variables. To further improve predictive accuracy and…

Methodology · Statistics 2026-01-14 Kanji Goto , Shintaro Yuki , Kensuke Tanioka , Hiroshi Yadohisa

Tensor Robust Principal Component Analysis (TRPCA) is a fundamental technique for decomposing multi-dimensional data into a low-rank tensor and an outlier tensor, yet existing methods relying on sparse outlier assumptions often fail under…

Numerical Analysis · Mathematics 2025-04-28 Yangyang Xu , Kexin Li , Li Yang , You-Wei Wen

The robust PCA problem, wherein, given an input data matrix that is the superposition of a low-rank matrix and a sparse matrix, we aim to separate out the low-rank and sparse components, is a well-studied problem in machine learning. One…

Machine Learning · Computer Science 2017-07-06 U. N. Niranjan , Arun Rajkumar , Theja Tulabandhula

In autonomous driving, radar systems play an important role in detecting targets such as other vehicles on the road. Radars mounted on different cars can interfere with each other, degrading the detection performance. Deep learning methods…

Signal Processing · Electrical Eng. & Systems 2021-04-20 Nicolae-Cătălin Ristea , Andrei Anghel , Radu Tudor Ionescu , Yonina C. Eldar

Reed-Muller (RM) codes achieve the capacity of general binary-input memoryless symmetric channels and are conjectured to have a comparable performance to that of random codes in terms of scaling laws. However, such results are established…

Information Theory · Computer Science 2023-08-02 Mohammad Vahid Jamali , Xiyang Liu , Ashok Vardhan Makkuva , Hessam Mahdavifar , Sewoong Oh , Pramod Viswanath

Deep learning algorithms for video Snapshot Compressive Imaging (SCI) have achieved great success, yet they predominantly focus on reconstructing from clean measurements. This overlooks a critical real-world challenge: the captured signal…

Computer Vision and Pattern Recognition · Computer Science 2026-03-17 Hao Wang , Zhankuo Xu , Jiong Ni , Xing Liu , Haoyang Liu , Xin Yuan

It is always demanding to learn robust visual representation for various learning problems; however, this learning and maintenance process usually suffers from noise, incompleteness or knowledge domain mismatch. Thus, robust representation…

Machine Learning · Computer Science 2020-04-28 Zhengming Ding , Ming Shao , Handong Zhao , Sheng Li

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…

Machine Learning · Statistics 2015-03-19 Teng Zhang , Gilad Lerman

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

A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The…

Computer Vision and Pattern Recognition · Computer Science 2014-03-11 Qiang Qiu , Guillermo Sapiro

Robust Principal Component Analysis (PCA) (Candes et al., 2011) and low-rank matrix completion (Recht et al., 2010) are extensions of PCA to allow for outliers and missing entries respectively. It is well-known that solving these problems…

Numerical Analysis · Mathematics 2019-07-12 Jared Tanner , Andrew Thompson , Simon Vary

Robust principal component analysis seeks to recover a low-rank matrix from fully observed data with sparse corruptions. A scalable approach fits a low-rank factorization by minimizing the sum of entrywise absolute residuals, leading to a…

Optimization and Control · Mathematics 2026-01-30 Pinxi Gong , Lexiao Lai , Jianhao Ma

This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…

Machine Learning · Computer Science 2020-05-05 Sandor Szedmak , Anna Cichonska , Heli Julkunen , Tapio Pahikkala , Juho Rousu

In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…

Statistics Theory · Mathematics 2017-07-18 Yiyuan She , Kun Chen

In this paper, we propose a robust representation learning model called Adaptive Structure-constrained Low-Rank Coding (AS-LRC) for the latent representation of data. To recover the underlying subspaces more accurately, AS-LRC seamlessly…

Computer Vision and Pattern Recognition · Computer Science 2019-08-23 Zhao Zhang , Lei Wang , Sheng Li , Yang Wang , Zheng Zhang , Zhengjun Zha , Meng Wang

Representation learning stands as one of the critical machine learning techniques across various domains. Through the acquisition of high-quality features, pre-trained embeddings significantly reduce input space redundancy, benefiting…

Machine Learning · Computer Science 2023-12-19 Suiyao Chen , Jing Wu , Naira Hovakimyan , Handong Yao

Dynamic robust PCA refers to the dynamic (time-varying) extension of robust PCA (RPCA). It assumes that the true (uncorrupted) data lies in a low-dimensional subspace that can change with time, albeit slowly. The goal is to track this…

Information Theory · Computer Science 2019-02-26 Praneeth Narayanamurthy , Namrata Vaswani

Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…

Machine Learning · Statistics 2015-05-06 Madeleine Udell , Corinne Horn , Reza Zadeh , Stephen Boyd

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional…

Computer Vision and Pattern Recognition · Computer Science 2016-11-16 Ping Li , Jun Yu , Meng Wang , Luming Zhang , Deng Cai , Xuelong Li

Tensor Robust Principal Component Analysis (TRPCA) holds a crucial position in machine learning and computer vision. It aims to recover underlying low-rank structures and to characterize the sparse structures of noise. Current approaches…

Numerical Analysis · Mathematics 2026-01-15 Chao Wang , Huiwen Zheng , Raymond Chan , Youwei Wen