Title: Graph-Regularized Non-Negative Reduced Biquaternion Matrix Factorization for Color Image Recognition

Abstract:

Non-negative reduced biquaternion matrix factorization (NRBMF) leverages the multiplication of reduced biquaternion (RB) matrices to embed the non-negativity constraints inherent in color image pixels directly into the factorization procedure. Nevertheless, NRBMF primarily prioritizes reconstruction fidelity, overlooking the local geometric structure of the image data. This oversight can potentially hinder the discriminative power of the resulting low-dimensional features. To overcome this limitation, we introduce a graph regularized non-negative reduced biquaternion matrix factorization (GNRBMF) framework tailored for color image recognition.

Our proposed approach integrates a graph Laplacian regularizer into the reduced biquaternion coefficient matrix. This mechanism ensures that samples located close to each other in the original data space are mapped to similar representations within the learned feature space. Furthermore, GNRBMF preserves the non-negativity characteristics of NRBMF within the reduced biquaternion domain. We have developed a component-wise alternating projected gradient algorithm to resolve the associated optimization problem and have rigorously analyzed its convergence properties. Empirical evaluations indicate that the GNRBMF model delivers recognition performance that is either competitive with or superior to existing methods across various tested scenarios.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC