# Quasi Non-Negative Quaternion Matrix Factorization with Application to Color Face Recognition

arXiv: https://arxiv.org/abs/2211.16739 · HTML: https://mlsanity.com/paper/2211.16739/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 41 references that are in the map.
- First posted on arXiv 30 Nov 2022.

## Builds on (most cited first, 6 of 6)

- [Accelerating Nonnegative Matrix Factorization Algorithms using Extrapolation](https://mlsanity.com/paper/1805.06604/) (2018)
- [Quaternion Non-negative Matrix Factorization: definition, uniqueness and algorithm](https://mlsanity.com/paper/1903.10593/) (2019)
- [A Low Rank Quaternion Decomposition Algorithm and Its Application in Color Image Inpainting](https://mlsanity.com/paper/2009.12203/) (2020)
- [Low Rank Pure Quaternion Approximation for Pure Quaternion Matrices](https://mlsanity.com/paper/2012.15138/) (2020)
- [Advanced Variations of Two-Dimensional Principal Component Analysis for Face Recognition](https://mlsanity.com/paper/1912.09970/) (2019)
- [NMF with Sparse Regularizations in Transformed Domains](https://mlsanity.com/paper/1407.7691/) (2014)

## Built on by (most cited first, 3 of 3)

- [Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognition](https://mlsanity.com/paper/2408.05582/) (2024)
- [A Theoretically Guaranteed Quaternion Weighted Schatten p-norm Minimization Method for Color Image Restoration](https://mlsanity.com/paper/2307.12656/) (2023)
- [Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition](https://mlsanity.com/paper/2606.03654/) (2026)

## Abstract (arXiv)

To address the non-negativity dropout problem of quaternion models, a novel quasi non-negative quaternion matrix factorization (QNQMF) model is presented for color image processing. To implement QNQMF, the quaternion projected gradient algorithm and the quaternion alternating direction method of multipliers are proposed via formulating QNQMF as the non-convex constraint quaternion optimization problems. Some properties of the proposed algorithms are studied. The numerical experiments on the color image reconstruction show that these algorithms encoded on the quaternion perform better than these algorithms encoded on the red, green and blue channels. Furthermore, we apply the proposed algorithms to the color face recognition. Numerical results indicate that the accuracy rate of face recognition on the quaternion model is better than on the red, green and blue channels of color image as well as single channel of gray level images for the same data, when large facial expressions and shooting angle variations are presented.