Non-Negative Reduced Biquaternion Matrix Factorization with Applications in Color Face Recognition

TL;DR

This paper introduces a non-negative reduced biquaternion matrix factorization model tailored for color image processing, especially effective in color face recognition, by leveraging quaternion algebra properties and an efficient optimization algorithm.

Contribution

It proposes the first non-negative RB matrix factorization model for color images and develops an RB-ANNLS algorithm with convergence analysis for this purpose.

Findings

Effective in color face recognition tasks

Outperforms existing methods in accuracy

Validated through extensive experiments

Abstract

Reduced biquaternion (RB), as a four-dimensional algebra highly suitable for representing color pixels, has recently garnered significant attention from numerous scholars. In this paper, for color image processing problems, we introduce a concept of the non-negative RB matrix and then use the multiplication properties of RB to propose a non-negative RB matrix factorization (NRBMF) model. The NRBMF model is introduced to address the challenge of reasonably establishing a non-negative quaternion matrix factorization model, which is primarily hindered by the multiplication properties of traditional quaternions. Furthermore, this paper transforms the problem of solving the NRBMF model into an RB alternating non-negative least squares (RB-ANNLS) problem. Then, by introducing a method to compute the gradient of the real function with RB matrix variables, we solve the RB-ANNLS optimization problem using the RB projected gradient algorithm and conduct a convergence analysis of the algorithm. Finally, we validate the effectiveness and superiority of the proposed NRBMF model in color face recognition.