# Lee and Seung (2000)'s Algorithms for Non-negative Matrix Factorization: A Supplementary Proof Guide

arXiv: https://arxiv.org/abs/2501.11341 · HTML: https://mlsanity.com/paper/2501.11341/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 11 references that are in the map.
- First posted on arXiv 20 Jan 2025.

## Builds on (most cited first, 1 of 1)

- [Nonnegative Matrix Factorization in Dimensionality Reduction: A Survey](https://mlsanity.com/paper/2405.03615/) (2024)

## Abstract (arXiv)

Lee and Seung (2000) introduced numerical solutions for non-negative matrix factorization (NMF) using iterative multiplicative update algorithms. These algorithms have been actively utilized as dimensionality reduction tools for high-dimensional non-negative data and learning algorithms for artificial neural networks. Despite a considerable amount of literature on the applications of the NMF algorithms, detailed explanations about their formulation and derivation are lacking. This report provides supplementary details to help understand the formulation and derivation of the proofs as used in the original paper.