On the Learning Machine with Amplificatory Neuron in Complex Domain

The processing of complex-valued signals through neural networks is the important and challenging fields in image processing and digital signal processing. The networks with linear neurons in complex domain have been proposed in the various literatures, but its convergence capability and computational power are not up the mark. In the various researches, it has been mentioned that nonlinear aggregation of input signals provides better computational capability as compared to linear aggregation. These evidences motivated to design a new nonlinear aggregation operation. In this paper, a new artificial neuron structure based on nonlinear aggregation of complex-valued input signals is proposed. The learning rule of network with proposed neurons is also addressed to achieve faster learning and better computational power. Its aggregation operation is based on the product of different weighted arrangement of inputs with bias signals instead of summation. This product exhibits nonlinearity that amplifies the aggregation operation of the proposed new neuron and named as AMPlificatory neuron in Complex domain ( $${\mathbb {C}}$$ C -AMP). The training and testing processes of the three-layered network with $${\mathbb {C}}$$ C -AMP neurons are performed through standard classification, prediction, and function approximation problems for evaluating the computational capability of the proposed neuron and compared with existing neuron models. Results of training and testing processes for these problems through proposed work ensure better training, faster convergence, excellent generalization ability, and significant prediction accuracy with lesser network topology as compared to conventional neuron models. The excellent generalization for 2D transformation problems also shows the significant capability of $${\mathbb {C}}$$ C -AMP neuron.