Matrix Completion With Cross-Concentrated Sampling: Bridging Uniform Sampling and CUR Sampling [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022 While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples.
Hanqin Cai +3 more
semanticscholar +1 more source
Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Loss [PDF]
SIAM Journal of Imaging Sciences, 2022 In this paper, we study color image inpainting as a pure quaternion matrix completion problem. In the literature, the theoretical guarantee for quaternion matrix completion is not well-established.
Junren Chen, Michael K. Ng
semanticscholar +1 more source
Orthogonal Inductive Matrix Completion [PDF]
IEEE Transactions on Neural Networks and Learning Systems, 2023 To appear in Transactions of Neural Networks and Learning Systems (TNNLS)
Antoine Ledent +2 more
openaire +4 more sources
Quaternion Matrix Factorization for Low-Rank Quaternion Matrix Completion
Mathematics, 2023 The main aim of this paper is to study quaternion matrix factorization for low-rank quaternion matrix completion and its applications in color image processing.
Jiang-Feng Chen +3 more
doaj +1 more source
Matrix Completion via Non-Convex Relaxation and Adaptive Correlation Learning [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022 The existing matrix completion methods focus on optimizing the relaxation of rank function such as nuclear norm, Schatten-$p$p norm, etc. They usually need many iterations to converge.
Xuelong Li, Hongyuan Zhang, Rui Zhang
semanticscholar +1 more source
Structured Gradient Descent for Fast Robust Low-Rank Hankel Matrix Completion [PDF]
SIAM Journal on Scientific Computing, 2022 We study the robust matrix completion problem for the low-rank Hankel matrix, which detects the sparse corruptions caused by extreme outliers while we try to recover the original Hankel matrix from the partial observation.
Hanqin Cai, Jian-Feng Cai, Juntao You
semanticscholar +1 more source
Simple, fast, and flexible framework for matrix completion with infinite width neural networks. [PDF]
Proc Natl Acad Sci U S A, 2022 Significance Matrix completion is a fundamental problem in machine learning that arises in various applications. We envision that our infinite width neural network framework for matrix completion will be easily deployable and produce strong baselines for
Radhakrishnan A +3 more
europepmc +3 more sources
A Singular Value Thresholding Algorithm for Matrix Completion [PDF]
SIAM Journal on Optimization, 2008 This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem and arises in many ...
Jian-Feng Cai, E. Candès, Zuowei Shen
semanticscholar +1 more source
Exact Matrix Completion via Convex Optimization [PDF]
Foundations of Computational Mathematics, 2008 We consider a problem of considerable practical interest: the recovery of a data matrix from a sampling of its entries. Suppose that we observe m entries selected uniformly at random from a matrix M.
E. Candès, B. Recht
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Robust Matrix Completion with Heavy-Tailed Noise [PDF]
Journal of the American Statistical Association, 2022 This article studies noisy low-rank matrix completion in the presence of heavy-tailed and possibly asymmetric noise, where we aim to estimate an underlying low-rank matrix given a set of highly incomplete noisy entries.
Bingyan Wang, Jianqing Fan
semanticscholar +1 more source