Neural Networks with Complex and Quaternion Inputs

Many neural network architectures operate only on real data and simple complex inputs. But there are applications where considerations of complex and quaternion inputs are quite desirable. Prior complex neural network models have generalized the Hopfield model, backpropagation and the perceptron learning rule to handle complex inputs. The Hopfield model for inputs and outputs falling on the unit circle in the complex plane was formulated by Noest [15, 16, 17]. Georgiou [2, 3, 12, 14] described the complex perceptron learning rule and the complex domain backpropagation algorithm. Li, Liao and Yu [13] used digital filter theory to perform fast training of complex-valued recurrent neural networks. Recent work by Rajagopal [21] has used Kak’s instantaneously trained networks to handle complex inputs.