A Parallel and Hierarchical Markovian RBF Neural Network: Preliminary Performance Evaluation

This paper presents a hierarchical Markovian Radial Basis Function (RBF) Neural Network, having embedded nature with many levels. The hidden RBF neurons in all the tree nodes of the hierarchy are composed of fully functional RBF Neural Networks that have the classical two synaptic link sets, one for the RBF centers and the other for the linear output weights. The Markov chain rule is specifically used in the RBF summations and permits this hierarchical functionality in a fractal-like fashion which supports a clear recursion. Thus the Neural Network operation is exactly the same at all levels. We further analyze the general framework where classical RBF Neural Network training algorithms can be applied, specifically for finding the centers and calculating the linear output weights. This framework is fast, simple and facilitates easy parallel implementations which are the main targets of this study.

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