# Deep matrix factorizations

arXiv: https://arxiv.org/abs/2010.00380 · HTML: https://mlsanity.com/paper/2010.00380/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2020.

## Built on by (most cited first, 9 of 9)

- [The Law of Parsimony in Gradient Descent for Learning Deep Linear Networks](https://mlsanity.com/paper/2306.01154/) (2023)
- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Rotation Synchronization via Deep Matrix Factorization](https://mlsanity.com/paper/2305.05268/) (2023)
- [Mixture of Mini Experts: Overcoming the Linear Layer Bottleneck in Multiple Instance Learning](https://mlsanity.com/paper/2603.22198/) (2026)
- [A consistent and flexible framework for deep matrix factorizations](https://mlsanity.com/paper/2206.10693/) (2022)
- [Neural Nonnegative Matrix Factorization for Hierarchical Multilayer Topic Modeling](https://mlsanity.com/paper/2303.00058/) (2023)
- [Advanced Unsupervised Learning: A Comprehensive Overview of Multi-View Clustering Techniques](https://mlsanity.com/paper/2512.05169/) (2025)
- [Evaluation of data driven low-rank matrix factorization for accelerated solutions of the Vlasov equation](https://mlsanity.com/paper/2501.04024/) (2024)
- [A Deep Latent Factor Graph Clustering with Fairness-Utility Trade-off Perspective](https://mlsanity.com/paper/2510.23507/) (2025)

## Abstract (arXiv)

Constrained low-rank matrix approximations have been known for decades as powerful linear dimensionality reduction techniques to be able to extract the information contained in large data sets in a relevant way. However, such low-rank approaches are unable to mine complex, interleaved features that underlie hierarchical semantics. Recently, deep matrix factorization (deep MF) was introduced to deal with the extraction of several layers of features and has been shown to reach outstanding performances on unsupervised tasks. Deep MF was motivated by the success of deep learning, as it is conceptually close to some neural networks paradigms. In this paper, we present the main models, algorithms, and applications of deep MF through a comprehensive literature review. We also discuss theoretical questions and perspectives of research.