# Algorithms, Initializations, and Convergence for the Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/1407.7299 · HTML: https://mlsanity.com/paper/1407.7299/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2014.

## Built on by (most cited first, 9 of 9)

- [Graph-based Neural Acceleration for Nonnegative Matrix Factorization](https://mlsanity.com/paper/2202.00264/) (2022)
- [Adaptive and Implicit Regularization for Matrix Completion](https://mlsanity.com/paper/2208.05640/) (2022)
- [Initialization for Nonnegative Matrix Factorization: a Comprehensive Review](https://mlsanity.com/paper/2109.03874/) (2021)
- [No Pattern, No Recognition: a Survey about Reproducibility and Distortion Issues of Text Clustering and Topic Modeling](https://mlsanity.com/paper/2208.01712/) (2022)
- [Extending the Unmixing methods to Multispectral Images](https://mlsanity.com/paper/2111.11893/) (2021)
- [AIR-Net: Adaptive and Implicit Regularization Neural Network for Matrix Completion](https://mlsanity.com/paper/2110.07557/) (2021)
- [n-stage Latent Dirichlet Allocation: A Novel Approach for LDA](https://mlsanity.com/paper/2110.08591/) (2021)
- [Binary Orthogonal Non-negative Matrix Factorization](https://mlsanity.com/paper/2210.10660/) (2022)
- [Rank Suggestion in Non-negative Matrix Factorization: Residual Sensitivity to Initial Conditions (RSIC)](https://mlsanity.com/paper/2410.14838/) (2024)

## Abstract (arXiv)

It is well known that good initializations can improve the speed and accuracy of the solutions of many nonnegative matrix factorization (NMF) algorithms. Many NMF algorithms are sensitive with respect to the initialization of W or H or both. This is especially true of algorithms of the alternating least squares (ALS) type, including the two new ALS algorithms that we present in this paper. We compare the results of six initialization procedures (two standard and four new) on our ALS algorithms. Lastly, we discuss the practical issue of choosing an appropriate convergence criterion.