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A matrix completion problem is to recover the missing entries in a partially observed matrix. Most of the existing matrix completion methods assume a low rank structure of the underlying complete matrix. In this paper, we introduce an…

Machine Learning · Statistics 2020-11-16 Chencheng Cai , Rong Chen , Han Xiao

Low-rank matrix completion is the task of recovering unknown entries of a matrix by assuming that the true matrix admits a good low-rank approximation. Sometimes additional information about the variables is known, and incorporating this…

Machine Learning · Computer Science 2023-06-16 Benoît Loucheur , P. -A. Absil , Michel Journée

The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over…

Optimization and Control · Mathematics 2012-09-19 Bart Vandereycken

Low-rank matrix approximation (LRMA) has been arisen in many applications, such as dynamic MRI, recommendation system and so on. The alternating direction method of multipliers (ADMM) has been designed for the nuclear norm regularized least…

Optimization and Control · Mathematics 2023-12-05 Zekun Liu

Low-rank matrices play a fundamental role in modeling and computational methods for signal processing and machine learning. In many applications where low-rank matrices arise, these matrices cannot be fully sampled or directly observed, and…

Information Theory · Computer Science 2016-05-25 Mark A. Davenport , Justin Romberg

We consider a problem of significant practical importance, namely, the reconstruction of a low-rank data matrix from a small subset of its entries. This problem appears in many areas such as collaborative filtering, computer vision and…

Machine Learning · Computer Science 2009-11-04 Raghunandan H. Keshavan , Andrea Montanari , Sewoong Oh

We consider the problem of reconstructing a low rank matrix from a subset of its entries and analyze two variants of the so-called Alternating Minimization algorithm, which has been proposed in the past. We establish that when the…

Machine Learning · Statistics 2016-09-21 David Gamarnik , Sidhant Misra

We consider a generalization of low-rank matrix completion to the case where the data belongs to an algebraic variety, i.e. each data point is a solution to a system of polynomial equations. In this case the original matrix is possibly…

Machine Learning · Statistics 2017-03-29 Greg Ongie , Rebecca Willett , Robert D. Nowak , Laura Balzano

Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their…

Image and Video Processing · Electrical Eng. & Systems 2018-11-28 Yue Hu , Xiaohan Liu , Mathews Jacob

Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…

Multimedia · Computer Science 2016-02-22 Junhui Hou , Lap-Pui Chau , Nadia Magnenat-Thalmann , Ying He

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

Recent advances in matrix completion enable data imputation in full-rank matrices by exploiting low dimensional (nonlinear) latent structure. In this paper, we develop a new model for high rank matrix completion (HRMC), together with batch…

Machine Learning · Computer Science 2020-02-21 Jicong Fan , Madeleine Udell

Modern matrix completion problems often involve heterogeneous data whose rows simultaneously belong to many meta-categories, such as demographic and age groups in recommendation systems, or region and recording session labels in neural…

Machine Learning · Statistics 2026-05-21 Hamza Golubovic , Matthew Shen , Genevera I. Allen , Tarek M. Zikry

We give a new framework for solving the fundamental problem of low-rank matrix completion, i.e., approximating a rank-$r$ matrix $\mathbf{M} \in \mathbb{R}^{m \times n}$ (where $m \ge n$) from random observations. First, we provide an…

Machine Learning · Computer Science 2023-08-08 Jonathan A. Kelner , Jerry Li , Allen Liu , Aaron Sidford , Kevin Tian

In this paper, we propose an efficient and scalable low rank matrix completion algorithm. The key idea is to extend orthogonal matching pursuit method from the vector case to the matrix case. We further propose an economic version of our…

Machine Learning · Computer Science 2014-04-17 Zheng Wang , Ming-Jun Lai , Zhaosong Lu , Wei Fan , Hasan Davulcu , Jieping Ye

We consider the problem of reconstructing a low-rank matrix from a small subset of its entries. In this paper, we describe the implementation of an efficient algorithm called OptSpace, based on singular value decomposition followed by local…

Numerical Analysis · Computer Science 2013-01-30 Raghunandan H. Keshavan , Sewoong Oh

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple…

Computer Vision and Pattern Recognition · Computer Science 2015-11-24 Jie Chen , Haixian Zhang , Hua Mao , Yongsheng Sang , Zhang Yi

In many applications, e.g., recommender systems and traffic monitoring, the data comes in the form of a matrix that is only partially observed and low rank. A fundamental data-analysis task for these datasets is matrix completion, where the…

Machine Learning · Computer Science 2017-05-02 Natali Ruchansky , Mark Crovella , Evimaria Terzi

Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…

Machine Learning · Computer Science 2019-10-08 Abdallah Chehade , Zunya Shi

The low-rank matrix completion problem can be succinctly stated as follows: given a subset of the entries of a matrix, find a low-rank matrix consistent with the observations. While several low-complexity algorithms for matrix completion…

Information Theory · Computer Science 2010-06-11 Wei Dai , Ely Kerman , Olgica Milenkovic