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

2026-06-02

AI Summary

This work addresses the limitation of existing non-negative reduced biquaternion matrix factorization methods, which neglect the local geometric structure of images and thereby constrain the discriminative power of low-dimensional features. To overcome this, the paper introduces, for the first time, a graph Laplacian regularizer into the non-negative matrix factorization framework within the reduced biquaternion domain. This approach preserves pixel non-negativity while encouraging neighboring samples in the original space to exhibit similar representations in the feature space, effectively integrating the algebraic structure of color images with manifold geometric information. The proposed method is optimized through reduced biquaternion representation, graph regularization constraints, and a component-wise alternating projected gradient algorithm, achieving performance on multiple color image recognition tasks that is either superior or comparable to state-of-the-art methods.

Abstract

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.

Problem

• color image recognition
• non-negative matrix factorization
• local geometric structure
• discriminative features
• reduced biquaternion

Innovation

• graph regularization
• non-negative matrix factorization
• reduced biquaternion
• color image recognition
• manifold learning