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The task of reconstructing a matrix given a sample of observedentries is known as the matrix completion problem. It arises ina wide range of problems, including recommender systems, collaborativefiltering, dimensionality reduction, image…

Statistics Theory · Mathematics 2014-12-20 Jean Lafond , Olga Klopp , Eric Moulines , Jospeh Salmon

The Euclidean distance geometry problem arises in a wide variety of applications, from determining molecular conformations in computational chemistry to localization in sensor networks. When the distance information is incomplete, the…

Information Theory · Computer Science 2018-10-30 Abiy Tasissa , Rongjie Lai

This paper studies the low-rank matrix completion problem from an information theoretic perspective. The completion problem is rephrased as a communication problem of an (uncoded) low-rank matrix source over an erasure channel. The paper…

Information Theory · Computer Science 2016-09-08 Sriram Vishwanath

Low-rank matrix completion consists of computing a matrix of minimal complexity that recovers a given set of observations as accurately as possible. Unfortunately, existing methods for matrix completion are heuristics that, while highly…

Machine Learning · Computer Science 2026-03-12 Dimitris Bertsimas , Ryan Cory-Wright , Sean Lo , Jean Pauphilet

We consider the problem of robust matrix completion, which aims to recover a low rank matrix $L_*$ and a sparse matrix $S_*$ from incomplete observations of their sum $M=L_*+S_*\in\mathbb{R}^{m\times n}$. Algorithmically, the robust matrix…

Machine Learning · Statistics 2020-03-25 Yunfeng Cai , Ping Li

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 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

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

In this paper, we propose a new algorithm for recovery of low-rank matrices from compressed linear measurements. The underlying idea of this algorithm is to closely approximate the rank function with a smooth function of singular values,…

Information Theory · Computer Science 2016-11-18 Mohammadreza Malek-Mohammadi , Massoud Babaie-Zadeh , Mikael Skoglund

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

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

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization…

Optimization and Control · Mathematics 2013-06-04 B. Mishra , G. Meyer , F. Bach , R. Sepulchre

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

We consider the problem of estimation of a low-rank matrix from a limited number of noisy rank-one projections. In particular, we propose two fast, non-convex \emph{proper} algorithms for matrix recovery and support them with rigorous…

Machine Learning · Statistics 2017-05-23 Mohammadreza Soltani , Chinmay Hegde

On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…

Information Theory · Computer Science 2009-03-19 Emmanuel J. Candes , Yaniv Plan

Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and…

Signal Processing · Electrical Eng. & Systems 2019-05-08 Xiao Peng Li , Lei Huang , Hing Cheung So , Bo Zhao

Matrix completion is about recovering a matrix from its partial revealed entries, and it can often be achieved by exploiting the inherent simplicity or low dimensional structure of the target matrix. For instance, a typical notion of matrix…

Information Theory · Computer Science 2019-10-08 Jinchi Chen , Weiguo Gao , Ke Wei

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem under the standard low rank assumption is NP-hard,…

Machine Learning · Computer Science 2014-12-01 Vassilis Kalofolias , Xavier Bresson , Michael Bronstein , Pierre Vandergheynst

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

This paper considers the problem of recovery of a low-rank matrix in the situation when most of its entries are not observed and a fraction of observed entries are corrupted. The observations are noisy realizations of the sum of a low rank…

Statistics Theory · Mathematics 2016-07-05 Olga Klopp , Karim Lounici , Alexandre B. Tsybakov