Complex-Valued vs. Real-Valued Neural Networks for Classification Perspectives: An Example on Non-Circular Data

TL;DR

This paper demonstrates that complex-valued neural networks outperform real-valued ones on non-circular complex data classification tasks, and provides a Python library for further research.

Contribution

It shows the advantages of CVNNs over RVNNs on non-circular data and releases a Python library for implementing CVNNs.

Findings

CVNNs outperform RVNNs on non-circular data.

CVNNs have higher mean and median accuracy with lower variance.

CVNNs exhibit less overfitting without regularization.

Abstract

The contributions of this paper are twofold. First, we show the potential interest of Complex-Valued Neural Network (CVNN) on classification tasks for complex-valued datasets. To highlight this assertion, we investigate an example of complex-valued data in which the real and imaginary parts are statistically dependent through the property of non-circularity. In this context, the performance of fully connected feed-forward CVNNs is compared against a real-valued equivalent model. The results show that CVNN performs better for a wide variety of architectures and data structures. CVNN accuracy presents a statistically higher mean and median and lower variance than Real-Valued Neural Network (RVNN). Furthermore, if no regularization technique is used, CVNN exhibits lower overfitting. The second contribution is the release of a Python library (Barrachina 2019) using Tensorflow as back-end that enables the implementation and training of CVNNs in the hopes of motivating further research on this area.