Frequency-Domain and Spatial-Domain MLMVN-Based Convolutional Neural Networks

Abstract

This paper presents a detailed analysis of a convolutional neural network based on multi-valued neurons (CNNMVN) and a fully connected multilayer neural network based on multi-valued neurons (MLMVN), employed here as a convolutional neural network in the frequency domain. We begin by providing an overview of the fundamental concepts underlying CNNMVN, focusing on the organization of convolutional layers and the CNNMVN learning algorithm. The error backpropagation rule for this network is justified and presented in detail. Subsequently, we consider how MLMVN can be used as a convolutional neural network in the frequency domain. It is shown that each neuron in the first hidden layer of MLMVN may work as a frequency-domain convolutional kernel, utilizing the Convolution Theorem. Essentially, these neurons create Fourier transforms of the feature maps that would have resulted from the convolutions in the spatial domain performed in regular convolutional neural networks. Furthermore, we discuss optimization techniques for both networks and compare the resulting convolutions to explore which features they extract from images. Finally, we present experimental results showing that both approaches can achieve high accuracy in image recognition.