Statistical Analysis of the Impact of Quaternion Components in Convolutional Neural Networks

TL;DR

This paper analyzes how different component choices in Quaternion-Valued CNNs affect image classification performance and introduces a new Fully Quaternion ReLU activation function to enhance model effectiveness.

Contribution

It provides a statistical comparison of quaternion components and proposes a novel Fully Quaternion ReLU activation function for QCNNs.

Findings

Component selection significantly influences QCNN performance

The new Fully Quaternion ReLU improves classification accuracy

Statistical analysis clarifies component interactions in QCNNs

Abstract

In recent years, several models using Quaternion-Valued Convolutional Neural Networks (QCNNs) for different problems have been proposed. Although the definition of the quaternion convolution layer is the same, there are different adaptations of other atomic components to the quaternion domain, e.g., pooling layers, activation functions, fully connected layers, etc. However, the effect of selecting a specific type of these components and the way in which their interactions affect the performance of the model still unclear. Understanding the impact of these choices on model performance is vital for effectively utilizing QCNNs. This paper presents a statistical analysis carried out on experimental data to compare the performance of existing components for the image classification problem. In addition, we introduce a novel Fully Quaternion ReLU activation function, which exploits the unique properties of quaternion algebra to improve model performance.