Abstract: A complex valued neural network is a neural network, which consists of complex valued input and/or weights and/or thresholds and/or activation functions. Complex-valued neural networks have been widening the scope of applications not only in electronics and informatics, but also in social systems. One of the most important applications of the complex valued neural network is in image and vision processing. In Neural networks, radial basis functions are often used for interpolation in multidimensional space. A Radial Basis function is a function, which has built into it a distance criterion with respect to a centre. Radial basis functions have often been applied in the area of neural networks where they may be used as a replacement for the sigmoid hidden layer transfer characteristic in multi-layer perceptron. This paper aims to present exhaustive results of using RBF units in a complex-valued neural network model that uses the back-propagation algorithm (called 'Complex-BP') for learning. Our experiments results demonstrate the effectiveness of a Radial basis function in a complex valued neural network in image recognition over a real valued neural network. We have studied and stated various observations like effect of learning rates, ranges of the initial weights randomly selected, error functions used and number of iterations for the convergence of error on a neural network model with RBF units. Some inherent properties of this complex back propagation algorithm are also studied and discussed.
Abstract: A complex valued neural network is a neural network
which consists of complex valued input and/or weights and/or thresholds
and/or activation functions. Complex-valued neural networks
have been widening the scope of applications not only in electronics
and informatics, but also in social systems. One of the most important
applications of the complex valued neural network is in signal
processing. In Neural networks, generalized mean neuron model
(GMN) is often discussed and studied. The GMN includes a new
aggregation function based on the concept of generalized mean of all
the inputs to the neuron. This paper aims to present exhaustive results
of using Generalized Mean Neuron model in a complex-valued neural
network model that uses the back-propagation algorithm (called
-Complex-BP-) for learning. Our experiments results demonstrate the
effectiveness of a Generalized Mean Neuron Model in a complex
plane for signal processing over a real valued neural network. We
have studied and stated various observations like effect of learning
rates, ranges of the initial weights randomly selected, error functions
used and number of iterations for the convergence of error required on
a Generalized Mean neural network model. Some inherent properties
of this complex back propagation algorithm are also studied and
discussed.