Abstract
In this paper, we propose a complex-valued neural network based on the widely linear estimation taking advantage of its geometric structure, and show that it can learn geometric transformations that the conventional neural networks cannot. First we formulate a fully augmented complex-valued neuron model based on the widely linear estimation. It is a generalized complex-valued neuron model that includes a usual complex-valued neuron and a degenerated case called a degenerated fully augmented complex-valued neuron. A fully augmented complex-valued neural network consists of such fully augmented complex-valued neurons. Secondly, we derive the back-propagation learning algorithms for the multi-layered fully augmented complex-valued neural networks. Finally, we find out via experiments that the multi-layered fully augmented complex-valued neural network has the different ability to learn 2D affine transformation from that of the usual complex-valued neural network.
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