The universal approximation theorem for complex-valued neural networks

Complex-Valued Neural Networks

The usual real-valued artificial neural networks have been applied to various fields such as telecommunications, robotics, bioinformatics, image processing and speech recognition, in which complex numbers (two dimensions) are often used with the Fourier transformation. This indicates the usefulness of complex-valued neural networks whose input and output signals and parameters such as weights a...

Complex-Valued Neural Networks

Neural Networks for Quaternion-valued Function Approximation

In the paper a new structure of Multi-Layer Perceptron, able to deal with quaternion-valued signal, is proposed. A learning algorithm for the proposed Quaternion MLP (QMLP) is also derived. Such a neural network allows to interpolate functions of quaternion variable with a smaller number of connections with respect to the corresponding real valued MLP. INTRODUCTION In the last few years, neural...

Novel Complex Valued Neural Networks

In view of many applications, in recent years, there has been increasing interest in complex valued neural networks. In this paper, it is reasoned that transforming real valued signals into complex valued signals (using Discrete Fourier Transform) and processing them in that domain is equivalent to processing real valued signals. This approach could have many advantages. Also neural networks ba...

On Universal Approximation Using Neural Networks