Training reformulated radial basis function neural networks capable of identifying uncertainty in data classification

This paper introduces a learning algorithm that can be used for training reformulated radial basis function neural networks (RBFNNs) capable of identifying uncertainty in data classification. This learning algorithm trains a special class of reformulated RBFNNs, known as cosine RBFNNs, by updating selected adjustable parameters to minimize the class-conditional variances at the outputs of their radial basis functions (RBFs). The experiments verify that quantum neural networks (QNNs) and cosine RBFNNs trained by the proposed learning algorithm are capable of identifying uncertainty in data classification, a property that is not shared by cosine RBFNNs trained by the original learning algorithm and conventional feed-forward neural networks (FFNNs). Finally, this study leads to a simple classification strategy that can be used to improve the classification accuracy of QNNs and cosine RBFNNs by rejecting ambiguous feature vectors based on their responses.

Neuron Selection for RBF Neural Network Classifier Based on Data Structure Preserving Criterion

The central problem in training a radial basis function neural network is the selection of hidden layer neurons. In this paper, we propose to select hidden layer neurons based on data structure preserving criterion. Data structure denotes relative location of samples in the high-dimensional space. By preserving the data structure of samples including those that are close to separation boundaries between different classes, the neuron subset selected retains the separation margin underlying the full set of hidden layer neurons. As a direct result, the network obtained tends to generalize well.

Evolutionary Optimization of Radial Basis Function Classifiers for Data Mining Applications

In many data mining applications that address classification problems, feature and model selection are considered as key tasks. That is, appropriate input features of the classifier must be selected from a given (and often large) set of possible features and structure parameters of the classifier must be adapted with respect to these features and a given data set. This paper describes an evolutionary algorithm (EA) that performs feature and model selection simultaneously for radial basis function (RBF) classifiers. In order to reduce the optimization effort, various techniques are integrated that accelerate and improve the EA significantly: hybrid training of RBF networks, lazy evaluation, consideration of soft constraints by means of penalty terms, and temperature-based adaptive control of the EA. The feasibility and the benefits of the approach are demonstrated by means of four data mining problems: intrusion detection in computer networks, biometric signature verification, customer acquisition with direct marketing methods, and optimization of chemical production processes. It is shown that, compared to earlier EA-based RBF optimization techniques, the runtime is reduced by up to 99% while error rates are lowered by up to 86%, depending on the application. The algorithm is independent of specific applications so that many ideas and solutions can be transferred to other classifier paradigms.

A New Class of Wavelet Networks for Nonlinear System Identification

A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linear-in-the-parameter regressions, which can be solved using least-squares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linear-in-the-parameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions.