mlsanityData to 7 Oct 2026

Low-Rank Matrix Completion: A Contemporary Survey

arXiv 1907.11705 ↗First posted 27 Jul 2019cs.DS cs.IT math.ITcited by 43

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Abstract (arXiv)

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 to grasp the essential knowledge from these studies. This is mainly because many of these works are highly theoretical or a proposal of new LRMC technique. In this paper, we give a contemporary survey on LRMC. In order to provide better view, insight, and understanding of potentials and limitations of LRMC, we present early scattered results in a structured and accessible way. Specifically, we classify the state-of-the-art LRMC techniques into two main categories and then explain each category in detail. We next discuss issues to be considered when one considers using LRMC techniques. These include intrinsic properties required for the matrix recovery and how to exploit a special structure in LRMC design. We also discuss the convolutional neural network (CNN) based LRMC algorithms exploiting the graph structure of a low-rank matrix. Further, we present the recovery performance and the computational complexity of the state-of-the-art LRMC techniques. Our hope is that this survey article will serve as a useful guide for practitioners and non-experts to catch the gist of LRMC.

Key facts. Cited by 43 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Jul 2019.

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Citing papers per year: 2021: 7; 2022: 7; 2023: 5; 2024: 10; 2025: 8; 2026: 6.

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  1. 2023Low Rank Matrix Completion via Robust Alternating Minimization in Nearly Linear Timecited by 31
  2. 2024Efficient Minimum Bayes Risk Decoding using Low-Rank Matrix Completion Algorithmscited by 13
  3. 2023Synthetic Combinations: A Causal Inference Framework for Combinatorial Interventionscited by 12
  4. 2021A new perspective on low-rank optimizationcited by 10
  5. 2021Multi-source Learning via Completion of Block-wise Overlapping Noisy Matricescited by 10
  6. 2021Temporal Graph Signal Decompositioncited by 8
  7. 2022Color Image Inpainting via Robust Pure Quaternion Matrix Completion: Error Bound and Weighted Losscited by 8
  8. 2024Higher-order Spatio-temporal Physics-incorporated Graph Neural Network for Multivariate Time Series Imputationcited by 8
  9. 2022Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recoverycited by 7
  10. 2023Rotation Synchronization via Deep Matrix Factorizationcited by 7
  11. 2022Matrix Completion with Hierarchical Graph Side Informationcited by 5
  12. 2022Accelerating nuclear-norm regularized low-rank matrix optimization through Burer-Monteiro decompositioncited by 5
31 more
  1. 2024Doubly Robust Inference in Causal Latent Factor Modelscited by 4
  2. 2024Symmetric Matrix Completion with ReLU Samplingcited by 4
  3. 2025An extrapolated and provably convergent algorithm for nonlinear matrix decomposition with the ReLU functioncited by 4
  4. 2024Multilinear Kernel Regression and Imputation via Manifold Learningcited by 3
  5. 20244CNet: A Diffusion Approach to Map Prediction for Decentralized Multi-Robot Explorationcited by 3
  6. 2025Theoretical Guarantees for Low-Rank Compression of Deep Neural Networkscited by 3
  7. 2021On the Fundamental Limits of Matrix Completion: Leveraging Hierarchical Similarity Graphscited by 2
  8. 2021Weighted Low-Rank Matrix Approximation: Acceleration and Applicationscited by 2
  9. 2021Gradual Federated Learning with Simulated Annealingcited by 2
  10. 2022Adaptive Sampling for Discoverycited by 2
  11. 2025Faster Convergence of Riemannian Stochastic Gradient Descent with Increasing Batch Sizecited by 2
  12. 2025A Taxonomy of Structure from Motion Methodscited by 2
  13. 2023Image Reconstruction using Superpixel Clustering and Tensor Completioncited by 1
  14. 2023Algorithmic Regularization in Tensor Optimization: Towards a Lifted Approach in Matrix Sensingcited by 1
  15. 2024Discrete Aware Matrix Completion via Convexized ℓ0-Norm Approximationcited by 1
  16. 2024Adaptive Retrieval and Scalable Indexing for k-NN Search with Cross-Encoderscited by 1
  17. 2024DKDL-Net: A Lightweight Bearing Fault Detection Model via Decoupled Knowledge Distillation and Low-Rank Adaptation Fine-tuningcited by 1
  18. 2025ClusterSC: Advancing Synthetic Control with Donor Selectioncited by 1
  19. 2025A Probabilistic Basis for Low-Rank Matrix Learningcited by 1
  20. 2021BERMo: What can BERT learn from ELMo?cited by 0
  21. 2022Hierarchical Clustering and Matrix Completion for the Reconstruction of World Input-Output Tablescited by 0
  22. 2022Introducing the Huber mechanism for differentially private low-rank matrix completioncited by 0
  23. 2024Predictive Low Rank Matrix Learning under Partial Observations: Mixed-Projection ADMMcited by 0
  24. 2025Robust Egoistic Rigid Body Localizationcited by 0
  25. 2025A Collaborative Process Parameter Recommender System for Fleets of Networked Manufacturing Machines -- with Application to 3D Printingcited by 0
  26. 2026Low Rank Tensor Completion via Adaptive ADMMcited by 0
  27. 2026Diffusion Models for Radio Map Estimation: Theoretical Performance Analysis and Sampling Rate Guidelinecited by 0
  28. 2026Compressing What Matters: Neuron Importance Meets Data-Aware Low Rank Approximation for Language Model Compressioncited by 0
  29. 2026Subzero matrix completion for sparse data analysis: large-scale learning of latent low-rank structurecited by 0
  30. 2026Synthetic Nearest Neighbors: Extending Synthetic Controls for Matrix Completion with Missing Not at Random Datacited by 0
  31. 2026CNA: An AI-Oriented Comprehensive Normalized Assessment for Healthy Status and Application to Optimize RRT Strategies by Reinforcement Learningcited by 0