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

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