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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

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

In this short note we extend some of the recent results on matrix completion under the assumption that the columns of the matrix can be grouped (clustered) into subspaces (not necessarily disjoint or independent). This model deviates from…

Information Theory · Computer Science 2017-08-04 Vaneet Aggarwal , Shuchin Aeron

Low-rank matrix completion addresses the problem of completing a matrix from a certain set of generic specified entries. Over the complex numbers a matrix with a given entry pattern can be uniquely completed to a specific rank, called the…

Algebraic Geometry · Mathematics 2025-03-13 Mareike Dressler , Robert Krone

The core of the general recommender systems lies in learning high-quality embedding representations of users and items to investigate their positional relations in the feature space. Unfortunately, data sparsity caused by…

Information Retrieval · Computer Science 2025-04-24 Yi Zhang , Yiwen Zhang

Similarity matrix serves as a fundamental tool at the core of numerous downstream machine-learning tasks. However, missing data is inevitable and often results in an inaccurate similarity matrix. To address this issue, Similarity Matrix…

Machine Learning · Computer Science 2024-10-01 Changyi Ma , Runsheng Yu , Xiao Chen , Youzhi Zhang

In this paper, we show that the low rank matrix completion problem can be reduced to the problem of finding the rank of a certain tensor.

Optimization and Control · Mathematics 2013-07-24 Harm Derksen

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

Matrices of (approximate) low rank are pervasive in data science, appearing in recommender systems, movie preferences, topic models, medical records, and genomics. While there is a vast literature on how to exploit low rank structure in…

Machine Learning · Computer Science 2018-05-31 Madeleine Udell , Alex Townsend

We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…

Numerical Analysis · Mathematics 2020-06-23 Melanie Beckerleg , Andrew Thompson

Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…

Numerical Analysis · Mathematics 2016-06-07 Victor Y. Pan , Liang Zhao

Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix.…

Machine Learning · Computer Science 2021-06-08 Amit Boyarski , Sanketh Vedula , Alex Bronstein

The low-rank matrix completion problem can be solved by Riemannian optimization on a fixed-rank manifold. However, a drawback of the known approaches is that the rank parameter has to be fixed a priori. In this paper, we consider the…

Optimization and Control · Mathematics 2022-02-21 Bin Gao , P. -A. Absil

With the huge influx of various data nowadays, extracting knowledge from them has become an interesting but tedious task among data scientists, particularly when the data come in heterogeneous form and have missing information. Many data…

Machine Learning · Computer Science 2017-05-11 Tsuyoshi Kato , Rachelle Rivero

The problem of completing a large matrix with lots of missing entries has received widespread attention in the last couple of decades. Two popular approaches to the matrix completion problem are based on singular value thresholding and…

Statistics Theory · Mathematics 2022-04-25 Sohom Bhattacharya , Sourav Chatterjee

A new message-passing (MP) method is considered for the matrix completion problem associated with recommender systems. We attack the problem using a (generative) factor graph model that is related to a probabilistic low-rank matrix…

Information Theory · Computer Science 2010-07-06 Byung-Hak Kim , Arvind Yedla , Henry D. Pfister

Noisy matrix completion has attracted significant attention due to its applications in recommendation systems, signal processing and image restoration. Most existing works rely on (weighted) least squares methods under various low-rank…

Machine Learning · Statistics 2024-12-17 Ziyuan Chen , Fang Yao

We study the problem of exact completion for $m \times n$ sized matrix of rank $r$ with the adaptive sampling method. We introduce a relation of the exact completion problem with the sparsest vector of column and row spaces (which we call…

Machine Learning · Computer Science 2022-03-08 Ilqar Ramazanli , Barnabas Poczos

Matrix completion is fundamental for predicting missing data with a wide range of applications in personalized healthcare, e-commerce, recommendation systems, and social network analysis. Traditional matrix completion approaches typically…

Machine Learning · Computer Science 2025-03-19 Patrick Hytla , Tran T. A. Nghia , Duy Nhat Phan , Andrew Rice

We consider the problem of recovering a low-rank matrix from its clipped observations. Clipping is conceivable in many scientific areas that obstructs statistical analyses. On the other hand, matrix completion (MC) methods can recover a…

Machine Learning · Computer Science 2019-03-05 Takeshi Teshima , Miao Xu , Issei Sato , Masashi Sugiyama