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

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.

Gerardo Altamirano-Gómez, Carlos Gershenson · 2024