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

TL;DR

This paper provides detailed explanations and supplementary proof derivations for Lee and Seung's 2000 algorithms for non-negative matrix factorization, clarifying their formulation and theoretical basis.

Contribution

It offers a comprehensive supplementary proof guide that clarifies the derivation and formulation of Lee and Seung's NMF algorithms, which were previously lacking in detail.

Findings

Clarified the derivation of NMF algorithms

Enhanced understanding of algorithm formulation

Supported the original algorithms with detailed proofs

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.