Combining regression trees and radial basis function networks

A growing and pruning sequential learning algorithm of hyper basis function neural network for function approximation

Radial basis function (RBF) neural network is constructed of certain number of RBF neurons, and these networks are among the most used neural networks for modeling of various nonlinear problems in engineering. Conventional RBF neuron is usually based on Gaussian type of activation function with single width for each activation function. This feature restricts neuron performance for modeling the complex nonlinear problems. To accommodate limitation of a single scale, this paper presents neural network with similar but yet different activation function-hyper basis function (HBF). The HBF allows different scaling of input dimensions to provide better generalization property when dealing with complex nonlinear problems in engineering practice. The HBF is based on generalization of Gaussian type of neuron that applies Mahalanobis-like distance as a distance metrics between input training sample and prototype vector. Compared to the RBF, the HBF neuron has more parameters to optimize, but HBF neural network needs less number of HBF neurons to memorize relationship between input and output sets in order to achieve good generalization property. However, recent research results of HBF neural network performance have shown that optimal way of constructing this type of neural network is needed; this paper addresses this issue and modifies sequential learning algorithm for HBF neural network that exploits the concept of neuron's significance and allows growing and pruning of HBF neuron during learning process. Extensive experimental study shows that HBF neural network, trained with developed learning algorithm, achieves lower prediction error and more compact neural network.

RESPONSIVE NEUROMODULATORS BASED ON ARTIFICIAL NEURAL NETWORKS USED TO CONTROL SEIZURE-LIKE EVENTS IN A COMPUTATIONAL MODEL OF EPILEPSY

Deep brain stimulation (DBS) has been noted for its potential to suppress epileptic seizures. To date, DBS has achieved mixed results as a therapeutic approach to seizure control. Using a computational model, we demonstrate that high-complexity, biologically-inspired responsive neuromodulation is superior to periodic forms of neuromodulation (responsive and non-responsive) such as those implemented in DBS, as well as neuromodulation using random and random repetitive-interval stimulation. We configured radial basis function (RBF) networks to generate outputs modeling interictal time series recorded from rodent hippocampal slices that were perfused with low Mg2+/high K+solution. We then compared the performance of RBF-based interictal modulation, periodic biphasic-pulse modulation, random modulation and random repetitive modulation on a cognitive rhythm generator (CRG) model of spontaneous seizure-like events (SLEs), testing efficacy of SLE control. A statistically significant improvement in SLE mitigation for the RBF interictal modulation case versus the periodic and random cases was observed, suggesting that the use of biologically-inspired neuromodulators may achieve better results for the purpose of electrical control of seizures in a clinical setting.

ON DIFFERENT MODEL SELECTION CRITERIA IN A FORWARD AND BACKWARD REGRESSION HYBRID NETWORK

An assessment of the performance of a hybrid network with different model selection criteria is considered. These criteria are used in an automatic model selection algorithm for constructing a hybrid network of radial and perceptron hidden units for regression. A forward step builds the full hybrid network; a model selection criterion is used for controlling the network-size and another criterion is used for choosing the appropriate hidden unit for different regions of input space. This is followed by a conservative pruning step using Likelihood Ratio Test, Bayesian or Minimum Description Length, which leads to robust estimators with low variance. The result is a small architecture that performs well on difficult, realistic, benchmark data-sets of high dimensionality and small training size. Best results are obtained by using the Bayesian approach for the model selection.