Complex Network for Complex Problems: A comparative study of CNN and Complex-valued CNN

TL;DR

This study compares real-valued CNNs, doubled-parameter CNNs, and complex-valued CNNs across brain MRI tasks, revealing that CV-CNNs outperform the others, highlighting their potential for complex data relationships.

Contribution

It provides the first large-scale comparison of CNN, CNNx2, and CV-CNN models across multiple brain MRI tasks, clarifying the benefits of complex-valued features.

Findings

CV-CNN outperforms CNN and CNNx2 in accuracy.

Complex-valued CNNs effectively learn complex relationships.

Doubling parameters alone does not match CV-CNN performance.

Abstract

Neural networks, especially convolutional neural networks (CNN), are one of the most common tools these days used in computer vision. Most of these networks work with real-valued data using real-valued features. Complex-valued convolutional neural networks (CV-CNN) can preserve the algebraic structure of complex-valued input data and have the potential to learn more complex relationships between the input and the ground-truth. Although some comparisons of CNNs and CV-CNNs for different tasks have been performed in the past, a large-scale investigation comparing different models operating on different tasks has not been conducted. Furthermore, because complex features contain both real and imaginary components, CV-CNNs have double the number of trainable parameters as real-valued CNNs in terms of the actual number of trainable parameters. Whether or not the improvements in performance with CV-CNN observed in the past have been because of the complex features or just because of having double the number of trainable parameters has not yet been explored. This paper presents a comparative study of CNN, CNNx2 (CNN with double the number of trainable parameters as the CNN), and CV-CNN. The experiments were performed using seven models for two different tasks - brain tumour classification and segmentation in brain MRIs. The results have revealed that the CV-CNN models outperformed the CNN and CNNx2 models.