# Deep Nonnegative Matrix Factorization with Beta Divergences

arXiv: https://arxiv.org/abs/2309.08249 · HTML: https://mlsanity.com/paper/2309.08249/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 48 references that are in the map.
- First posted on arXiv 15 Sep 2023.

## Builds on (most cited first, 15 of 15)

- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Nonnegative Matrix Factorization for Signal and Data Analytics: Identifiability, Algorithms, and Applications](https://mlsanity.com/paper/1803.01257/) (2018)
- [On Identifiability of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1709.00614/) (2017)
- [Identifiability of the Simplex Volume Minimization Criterion for Blind Hyperspectral Unmixing: The No Pure-Pixel Case](https://mlsanity.com/paper/1406.5273/) (2014)
- [A deep matrix factorization method for learning attribute representations](https://mlsanity.com/paper/1509.03248/) (2015)
- [Simplex-Structured Matrix Factorization: Sparsity-based Identifiability and Provably Correct Algorithms](https://mlsanity.com/paper/2007.11446/) (2020)
- [Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence](https://mlsanity.com/paper/2010.01935/) (2020)
- [Nonlinear hyperspectral unmixing with robust nonnegative matrix factorization](https://mlsanity.com/paper/1401.5649/) (2014)
- [Blind Audio Source Separation with Minimum-Volume Beta-Divergence NMF](https://mlsanity.com/paper/1907.02404/) (2019)
- [An Inertial Block Majorization Minimization Framework for Nonsmooth Nonconvex Optimization](https://mlsanity.com/paper/2010.12133/) (2020)
- [Multiplicative Updates for NMF with β-Divergences under Disjoint Equality Constraints](https://mlsanity.com/paper/2010.16223/) (2020)
- [A Provable Splitting Approach for Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2301.10499/) (2023)
- [Deep Latent Factor Model for Collaborative Filtering](https://mlsanity.com/paper/1912.04754/) (2019)
- [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)

## Built on by (most cited first, 1 of 1)

- [What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?](https://mlsanity.com/paper/2409.07953/) (2024)

## Abstract (arXiv)

Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have primarily centered their evaluation on the least squares error, which may not be the most appropriate metric for assessing the quality of approximations on diverse datasets. For instance, when dealing with data types such as audio signals and documents, it is widely acknowledged that β-divergences offer a more suitable alternative. In this paper, we develop new models and algorithms for deep NMF using some β-divergences, with a focus on the Kullback-Leibler divergence. Subsequently, we apply these techniques to the extraction of facial features, the identification of topics within document collections, and the identification of materials within hyperspectral images.