Low Rank Support Quaternion Matrix Machine

TL;DR

The paper introduces LSQMM, a novel color image classification method that leverages quaternion algebra and low-rank regularization to improve accuracy and efficiency over existing techniques.

Contribution

It proposes a low-rank support quaternion matrix machine that models color channels as quaternions, incorporating quaternion nuclear norm regularization and an ADMM algorithm for enhanced classification.

Findings

Outperforms state-of-the-art methods in accuracy

Demonstrates robustness to noise and variations

Achieves computational efficiency in experiments

Abstract

Input features are conventionally represented as vectors, matrices, or third order tensors in the real field, for color image classification. Inspired by the success of quaternion data modeling for color images in image recovery and denoising tasks, we propose a novel classification method for color image classification, named as the Low-rank Support Quaternion Matrix Machine (LSQMM), in which the RGB channels are treated as pure quaternions to effectively preserve the intrinsic coupling relationships among channels via the quaternion algebra. For the purpose of promoting low-rank structures resulting from strongly correlated color channels, a quaternion nuclear norm regularization term, serving as a natural extension of the conventional matrix nuclear norm to the quaternion domain, is added to the hinge loss in our LSQMM model. An Alternating Direction Method of Multipliers (ADMM)-based iterative algorithm is designed to effectively resolve the proposed quaternion optimization model. Experimental results on multiple color image classification datasets demonstrate that our proposed classification approach exhibits advantages in classification accuracy, robustness and computational efficiency, compared to several state-of-the-art methods using support vector machines, support matrix machines, and support tensor machines.