# Randomized Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/1711.02037 · HTML: https://mlsanity.com/paper/1711.02037/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Nov 2017.

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

- [Probabilistic methods for approximate archetypal analysis](https://mlsanity.com/paper/2108.05767/) (2021)
- [Randomized Algorithms for Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2402.08134/) (2024)
- [Projection-based QLP Algorithm for Efficiently Computing Low-Rank Approximation of Matrices](https://mlsanity.com/paper/2103.07245/) (2021)
- [Learning nonnegative matrix factorizations from compressed data](https://mlsanity.com/paper/2409.04994/) (2024)

## Abstract (arXiv)

Nonnegative matrix factorization (NMF) is a powerful tool for data mining. However, the emergence of `big data' has severely challenged our ability to compute this fundamental decomposition using deterministic algorithms. This paper presents a randomized hierarchical alternating least squares (HALS) algorithm to compute the NMF. By deriving a smaller matrix from the nonnegative input data, a more efficient nonnegative decomposition can be computed. Our algorithm scales to big data applications while attaining a near-optimal factorization. The proposed algorithm is evaluated using synthetic and real world data and shows substantial speedups compared to deterministic HALS.