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

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 exploit the local geometric structure of image data, which may limit the discriminative ability of the learned low-dimensional features. 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 representations in the learned feature space. Meanwhile, GNRBMF retains the non-negativity-preserving property of NRBMF in the reduced biquaternion domain. To solve the optimization problem, a component-wise alternating projected gradient algorithm is derived, and its convergence properties are analyzed. Experimental results demonstrate that the proposed GNRBMF model achieves competitive or superior recognition performance in some tested settings.