# Survey of Matrix Completion Algorithms

arXiv: https://arxiv.org/abs/2204.01532 · HTML: https://mlsanity.com/paper/2204.01532/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 23 references that are in the map.
- First posted on arXiv 1 Apr 2022.

## Builds on (most cited first, 10 of 10)

- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Low-Rank Matrix and Tensor Completion via Adaptive Sampling](https://mlsanity.com/paper/1304.4672/) (2013)
- [On the Power of Adaptivity in Matrix Completion and Approximation](https://mlsanity.com/paper/1407.3619/) (2014)
- [Noise-Tolerant Life-Long Matrix Completion via Adaptive Sampling](https://mlsanity.com/paper/1612.00100/) (2016)
- [Matrix completion with queries](https://mlsanity.com/paper/1705.00399/) (2017)
- [Adaptive Consensus ADMM for Distributed Optimization](https://mlsanity.com/paper/1706.02869/) (2017)
- [Optimal Exact Matrix Completion Under new Parametrization](https://mlsanity.com/paper/2002.02431/) (2020)
- [Lifelong Matrix Completion with Sparsity-Number](https://mlsanity.com/paper/2203.07637/) (2022)
- [Adaptive Noisy Matrix Completion](https://mlsanity.com/paper/2203.08340/) (2022)
- [Matrix Completion with Heterogonous Cost](https://mlsanity.com/paper/2203.12120/) (2022)

## Built on by (most cited first, 2 of 2)

- [Optimal Transfer Learning for Missing Not-at-Random Matrix Completion](https://mlsanity.com/paper/2503.00174/) (2025)
- [Alliance Beats Isolation: Unifying Heterogeneous Allied Datasets Improves Classifier Performance](https://mlsanity.com/paper/2609.19748/) (2026)

## Abstract (arXiv)

Matrix completion problem has been investigated under many different conditions since Netflix announced the Netflix Prize problem. Many research work has been done in the field once it has been discovered that many real life dataset could be estimated with a low-rank matrix. Since then compressed sensing, adaptive signal detection has gained the attention of many researchers. In this survey paper we are going to visit some of the matrix completion methods, mainly in the direction of passive and adaptive directions. First, we discuss passive matrix completion methods with convex optimization, and the second active matrix completion techniques with adaptive signal detection methods. Traditionally many machine learning problems are solved in passive environment. However, later it has been observed that adaptive sensing algorithms many times performs more efficiently than former algorithms. Hence algorithms in this setting has been extensively studied. Therefore, we are going to present some of the latest adaptive matrix completion algorithms in this paper meanwhile providing passive methods.