Initialization for Nonnegative Matrix Factorization: a Comprehensive Review

TL;DR

This paper reviews various initialization methods for non-negative matrix factorization (NMF), highlighting their advantages and disadvantages, and presents numerical results to compare their performance.

Contribution

It provides a comprehensive overview of existing NMF initialization techniques, analyzing their effectiveness and practical implications.

Findings

Different initialization methods significantly impact NMF convergence.

Numerical experiments illustrate the strengths and weaknesses of each method.

No single initialization method is universally optimal.

Abstract

Non-negative matrix factorization (NMF) has become a popular method for representing meaningful data by extracting a non-negative basis feature from an observed non-negative data matrix. Some of the unique features of this method in identifying hidden data put this method amongst the powerful methods in the machine learning area. The NMF is a known non-convex optimization problem and the initial point has a significant effect on finding an efficient local solution. In this paper, we investigate the most popular initialization procedures proposed for NMF so far. We describe each method and present some of their advantages and disadvantages. Finally, some numerical results to illustrate the performance of each algorithm are presented.