# Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition

arXiv: https://arxiv.org/abs/2606.03654 · HTML: https://mlsanity.com/paper/2606.03654/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 29 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Builds on (most cited first, 3 of 3)

- [Quaternion-based bilinear factor matrix norm minimization for color image inpainting](https://mlsanity.com/paper/2005.02886/) (2020)
- [Quasi Non-Negative Quaternion Matrix Factorization with Application to Color Face Recognition](https://mlsanity.com/paper/2211.16739/) (2022)
- [Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognition](https://mlsanity.com/paper/2408.05582/) (2024)

## Abstract (arXiv)

Non-negative reduced biquaternion matrix factorization (NRBMF) uses the product of reduced biquaternion (RB) matrices to incorporate the non-negativity constraints of color image pixels into the factorization process. However, NRBMF mainly focuses on reconstruction accuracy and does not explicitly exploit the local geometric structure of image data, which may limit the discriminative ability of the obtained low-dimensional coefficient representations. To address this issue, we propose a graph regularized non-negative reduced biquaternion matrix factorization (GNRBMF) model for color image recognition. The proposed model incorporates a graph Laplacian regularizer into the reduced biquaternion coefficient matrix, encouraging nearby samples in the original space to have similar coefficient representations. Meanwhile, GNRBMF retains the non-negativity property of NRBMF in the reduced biquaternion algebra. To solve the optimization problem, a component-wise alternating projected gradient algorithm is derived, and its convergence properties are analyzed. Experimental results on three color image datasets show that the proposed GNRBMF model achieves competitive or superior recognition performance compared with several methods in most tested settings.