# Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting

arXiv: https://arxiv.org/abs/1611.01408 · HTML: https://mlsanity.com/paper/1611.01408/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2016.

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

- [Quantum Multi-Model Fitting](https://mlsanity.com/paper/2303.15444/) (2023)
- [Multi-Model 3D Registration: Finding Multiple Moving Objects in Cluttered Point Clouds](https://mlsanity.com/paper/2402.10865/) (2024)
- [MultiLink: Multi-class Structure Recovery via Agglomerative Clustering and Model Selection](https://mlsanity.com/paper/2505.10874/) (2025)
- [Outlier-Robust Multi-Model Fitting on Quantum Annealers](https://mlsanity.com/paper/2504.13836/) (2025)

## Abstract (arXiv)

In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are interesting as, compared to traditional NMF, they present additional sparsity and part-based behavior, explaining unique data features. To show these features in practice, we first present an application to the analysis of climate data. We then present an NMU-based algorithm to robustly fit multiple parametric models to a dataset. The proposed approach delivers state-of-the-art results for the estimation of multiple fundamental matrices and homographies, outperforming other alternatives in the literature and exemplifying the use of efficient NMU computations.