Graph Regularized Non-negative Reduced Biquaternion Matrix Factorization for Color Image Recognition
2026-06-02 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors improved a method called non-negative reduced biquaternion matrix factorization (NRBMF), which is used to analyze color images by keeping pixel values non-negative. They noticed NRBMF doesn’t consider how image data points relate to their neighbors, which can reduce how well the method distinguishes different images. To fix this, they added a graph-based regularization that encourages similar images to have similar feature representations while keeping all values non-negative. Their new model, GNRBMF, was tested and showed equal or better performance in recognizing color images. They also developed an algorithm to solve the math problems involved and studied why it works.
Non-negative matrix factorizationReduced biquaternion matricesColor image recognitionGraph Laplacian regularizationFeature representationAlternating projected gradientLocal geometric structureMatrix factorizationOptimization convergence
Authors
Hailang Wu, Yonghe Liu, Bingxuan Yu, Chaoqian Li
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.