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This paper considers the recovery of a low-rank matrix from an observed version that simultaneously contains both (a) erasures: most entries are not observed, and (b) errors: values at a constant fraction of (unknown) locations are…

Information Theory · Computer Science 2013-09-23 Yudong Chen , Ali Jalali , Sujay Sanghavi , Constantine Caramanis

In the low-rank matrix completion (LRMC) problem, the low-rank assumption means that the columns (or rows) of the matrix to be completed are points on a low-dimensional linear algebraic variety. This paper extends this thinking to cases…

Machine Learning · Statistics 2020-09-08 Greg Ongie , Daniel Pimentel-Alarcón , Laura Balzano , Rebecca Willett , Robert D. Nowak

Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…

Machine Learning · Computer Science 2014-09-04 Fanhua Shang , Yuanyuan Liu , Hanghang Tong , James Cheng , Hong Cheng

This paper provides the best bounds to date on the number of randomly sampled entries required to reconstruct an unknown low rank matrix. These results improve on prior work by Candes and Recht, Candes and Tao, and Keshavan, Montanari, and…

Information Theory · Computer Science 2009-10-21 Benjamin Recht

Low rank matrix recovery problems, including matrix completion and matrix sensing, appear in a broad range of applications. In this work we present GNMR -- an extremely simple iterative algorithm for low rank matrix recovery, based on a…

Optimization and Control · Mathematics 2022-04-28 Pini Zilber , Boaz Nadler

Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

Statistics Theory · Mathematics 2021-05-06 Yunhua Xiang , Tianyu Zhang , Xu Wang , Ali Shojaie , Noah Simon

As a paradigm to recover unknown entries of a matrix from partial observations, low-rank matrix completion (LRMC) has generated a great deal of interest. Over the years, there have been lots of works on this topic but it might not be easy…

Data Structures and Algorithms · Computer Science 2019-07-30 Luong Trung Nguyen , Junhan Kim , Byonghyo Shim

A Euclidean Distance Matrix (EDM) is a table of distance-square between points on a k- dimensional Euclidean space, with applications in many fields (e.g. engineering, geodesy, economics, genetics, biochemistry, psychology). A problem that…

Optimization and Control · Mathematics 2017-11-17 Nilson Moreira , Leonardo Duarte , Carlile Lavor , Cristiano Torezzan

In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…

Numerical Analysis · Mathematics 2019-05-28 Armenak Petrosyan , Hoang Tran , Clayton Webster

In this paper, we investigate the recovery of a sparse weight vector (parameters vector) from a set of noisy linear combinations. However, only partial information about the matrix representing the linear combinations is available. Assuming…

Machine Learning · Computer Science 2016-11-18 Ashkan Esmaeili , Arash Amini , Farokh Marvasti

Low-rank Matrix Completion (LRMC) describes the problem where we wish to recover missing entries of partially observed low-rank matrix. Most existing matrix completion work deals with sampling procedures that are independent of the…

Machine Learning · Computer Science 2025-04-15 Rishhabh Naik , Nisarg Trivedi , Davoud Ataee Tarzanagh , Laura Balzano

We present and analyze an efficient implementation of an iteratively reweighted least squares algorithm for recovering a matrix from a small number of linear measurements. The algorithm is designed for the simultaneous promotion of both a…

Numerical Analysis · Mathematics 2011-07-19 Massimo Fornasier , Holger Rauhut , Rachel Ward

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…

Numerical Analysis · Mathematics 2010-06-29 Rick Ma , Samuel Cheng

Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict…

Machine Learning · Computer Science 2013-06-05 Prateek Jain , Inderjit S. Dhillon

Matrix completion is a class of machine learning methods that concerns the prediction of missing entries in a partially observed matrix. This paper studies matrix completion for mixed data, i.e., data involving mixed types of variables…

Machine Learning · Statistics 2022-11-18 Yunxiao Chen , Xiaoou Li

Wisely utilizing the internal and external learning methods is a new challenge in super-resolution problem. To address this issue, we analyze the attributes of two methodologies and find two observations of their recovered details: 1) they…

Computer Vision and Pattern Recognition · Computer Science 2023-02-20 Shuang Wang , Bo Yue , Xuefeng Liang , Peiyuan Ji , Licheng Jiao

The inductive matrix completion (IMC) problem is to recover a low rank matrix from few observed entries while incorporating prior knowledge about its row and column subspaces. In this work, we make three contributions to the IMC problem:…

Machine Learning · Computer Science 2022-02-01 Pini Zilber , Boaz Nadler

Most recent results in matrix completion assume that the matrix under consideration is low-rank or that the columns are in a union of low-rank subspaces. In real-world settings, however, the linear structure underlying these models is…

Machine Learning · Statistics 2015-12-31 Ravi Ganti , Laura Balzano , Rebecca Willett

Robust matrix completion (RMC) is a widely used machine learning tool that simultaneously tackles two critical issues in low-rank data analysis: missing data entries and extreme outliers. This paper proposes a novel scalable and learnable…

Machine Learning · Computer Science 2026-05-22 HanQin Cai , Chandra Kundu , Jialin Liu , Wotao Yin

The matrix completion problem aims to reconstruct a low-rank matrix based on a revealed set of possibly noisy entries. Prior works consider completing the entire matrix with generalization error guarantees. However, the completion accuracy…

Machine Learning · Computer Science 2023-12-19 Elad Hazan , Adam Tauman Kalai , Varun Kanade , Clara Mohri , Y. Jennifer Sun