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The contributions of this paper are twofold. First, we show the potentialinterest of Complex-Valued Neural Network (CVNN) on classification tasks forcomplex-valued datasets. To highlight this assertion, we investigate an exampleof complex-valued data in which the real and imaginary parts are statisticallydependent through the property of non-circularity. In this context, theperformance of fully connected feed-forward CVNNs is compared against areal-valued equivalent model. The results show that CVNN performs better for awide variety of architectures and data structures. CVNN accuracy presents astatistically higher mean and median and lower variance than Real-Valued NeuralNetwork (RVNN). Furthermore, if no regularization technique is used, CVNNexhibits lower overfitting. The second contribution is the release of a Pythonlibrary (Barrachina 2019) using Tensorflow as back-end that enables theimplementation and training of CVNNs in the hopes of motivating furtherresearch on this area.

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