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

Sungjae Cho
1/20/2025
math.NAcs.LG

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Abstract

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.

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Cite this paper

@article{cho2025seung,
  title  = {Lee and Seung (2000)'s Algorithms for Non-negative Matrix Factorization: A Supplementary Proof Guide},
  author = {Sungjae Cho},
  year   = {2025},
  eprint = {2501.11341},
  archivePrefix = {arXiv},
  url    = {http://arxiv.org/abs/2501.11341v2}
}

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