# Initialization for Nonnegative Matrix Factorization: a Comprehensive Review

arXiv: https://arxiv.org/abs/2109.03874 · HTML: https://mlsanity.com/paper/2109.03874/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 102 references that are in the map.
- First posted on arXiv 8 Sep 2021.

## Builds on (most cited first, 8 of 8)

- [Structured Graph Learning for Scalable Subspace Clustering: From Single-view to Multi-view](https://mlsanity.com/paper/2102.07943/) (2021)
- [Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization](https://mlsanity.com/paper/1407.7299/) (2014)
- [Compressed Nonnegative Matrix Factorization is Fast and Accurate](https://mlsanity.com/paper/1505.04650/) (2015)
- [Nonnegative Matrix Factorization with Local Similarity Learning](https://mlsanity.com/paper/1907.04150/) (2019)
- [Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering](https://mlsanity.com/paper/2005.09229/) (2020)
- [Improved SVD-based Initialization for Nonnegative Matrix Factorization using Low-Rank Correction](https://mlsanity.com/paper/1807.04020/) (2018)
- [Matrix Approximation under Local Low-Rank Assumption](https://mlsanity.com/paper/1301.3192/) (2013)
- [Rank-One NMF-Based Initialization for NMF and Relative Error Bounds under a Geometric Assumption](https://mlsanity.com/paper/1612.08549/) (2016)

## Built on by (most cited first, 4 of 4)

- [A Holistic Approach to Unifying Automatic Concept Extraction and Concept Importance Estimation](https://mlsanity.com/paper/2306.07304/) (2023)
- [GSVD-NMF: Recovering Missing Features in Non-negative Matrix Factorization](https://mlsanity.com/paper/2408.08260/) (2024)
- [An Exterior Method for Nonnegative Matrix Factorization](https://mlsanity.com/paper/2605.19325/) (2026)
- [Sparse Network Inference under Imperfect Detection and its Application to Ecological Networks](https://mlsanity.com/paper/2604.18820/) (2026)

## Abstract (arXiv)

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.