# Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognition

arXiv: https://arxiv.org/abs/2408.05582 · HTML: https://mlsanity.com/paper/2408.05582/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 10 Aug 2024.

## Builds on (most cited first, 9 of 9)

- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [Color image recovery using low-rank quaternion matrix completion algorithm](https://mlsanity.com/paper/1909.06567/) (2019)
- [Quaternion-based bilinear factor matrix norm minimization for color image inpainting](https://mlsanity.com/paper/2005.02886/) (2020)
- [Non-negative Matrix Factorization: Robust Extraction of Extended Structures](https://mlsanity.com/paper/1712.10317/) (2017)
- [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)
- [Quaternion-based dynamic mode decomposition for background modeling in color videos](https://mlsanity.com/paper/2112.13982/) (2021)
- [Quasi Non-Negative Quaternion Matrix Factorization with Application to Color Face Recognition](https://mlsanity.com/paper/2211.16739/) (2022)

## Built on by (most cited first, 1 of 1)

- [Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition](https://mlsanity.com/paper/2606.03654/) (2026)

## Abstract (arXiv)

Reduced biquaternion (RB), as a four-dimensional algebra highly suitable for representing color pixels, has recently garnered significant attention from numerous scholars. In this paper, for color image processing problems, we introduce a concept of the non-negative RB matrix and then use the multiplication properties of RB to propose a non-negative RB matrix factorization (NRBMF) model. The NRBMF model is introduced to address the challenge of reasonably establishing a non-negative quaternion matrix factorization model, which is primarily hindered by the multiplication properties of traditional quaternions. Furthermore, this paper transforms the problem of solving the NRBMF model into an RB alternating non-negative least squares (RB-ANNLS) problem. Then, by introducing a method to compute the gradient of the real function with RB matrix variables, we solve the RB-ANNLS optimization problem using the RB projected gradient algorithm and conduct a convergence analysis of the algorithm. Finally, we validate the effectiveness and superiority of the proposed NRBMF model in color face recognition.