A fully complex-valued radial basis function network and its learning algorithm

• Published in: International journal of neural systems Vol. 19; no. 4; p. 253
• Main Authors: Savitha, R, Suresh, S, Sundararajan, N
• Format: Journal Article
• Language: English
• Published: Singapore 01.08.2009
• Subjects: Algorithms; Artificial Intelligence; Humans; Neural Networks (Computer); Signal Processing, Computer-Assisted
• ISSN: 0129-0657
• DOI: 10.1142/S0129065709002026

In this paper, a fully complex-valued radial basis function (FC-RBF) network with a fully complex-valued activation function has been proposed, and its complex-valued gradient descent learning algorithm has been developed. The fully complex activation function, sech(.) of the proposed network, satisfies all the properties needed for a complex-valued activation function and has Gaussian-like characteristics. It maps C(n) --> C, unlike the existing activation functions of complex-valued RBF network that maps C(n) --> R. Since the performance of the complex-RBF network depends on the number of neurons and initialization of network parameters, we propose a K-means clustering based neuron selection and center initialization scheme. First, we present a study on convergence using complex XOR problem. Next, we present a synthetic function approximation problem and the two-spiral classification problem. Finally, we present the results for two practical applications, viz., a non-minimum phase equalization and an adaptive beam-forming problem. The performance of the network was compared with other well-known complex-valued RBF networks available in literature, viz., split-complex CRBF, CMRAN and the CELM. The results indicate that the proposed fully complex-valued network has better convergence, approximation and classification ability.