Particle swarm optimization aided orthogonal forward regression for unified data modeling

We propose a unified data modeling approach that is equally applicable to supervised regression and classification applications, as well as to unsupervised probability density function estimation. A particle swarm optimization (PSO) aided orthogonal forward regression (OFR) algorithm based on leave-one-out (LOO) criteria is developed to construct parsimonious radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines the center vector and diagonal covariance matrix of one RBF node by minimizing the LOO statistics. For regression applications, the LOO criterion is chosen to be the LOO mean square error, while the LOO misclassification rate is adopted in two-class classification applications. By adopting the Parzen window estimate as the desired response, the unsupervised density estimation problem is transformed into a constrained regression problem. This PSO aided OFR algorithm for tunable-node RBF networks is capable of constructing very parsimonious RBF models that generalize well, and our analysis and experimental results demonstrate that the algorithm is computationally even simpler than the efficient regularization assisted orthogonal least square algorithm based on LOO criteria for selecting fixed-node RBF models. Another significant advantage of the proposed learning procedure is that it does not have learning hyperparameters that have to be tuned using costly cross validation. The effectiveness of the proposed PSO aided OFR construction procedure is illustrated using several examples taken from regression and classification, as well as density estimation applications.

A stable one-step-ahead predictive control of non-linear systems

In this paper stability of one-step ahead predictive controllers based on non-linear models is established. It is shown that, under conditions which can be fulfilled by most industrial plants, the closed-loop system is robustly stable in the presence of plant uncertainties and input–output constraints. There is no requirement that the plant should be open-loop stable and the analysis is valid for general forms of non-linear system representation including the case out when the problem is constraint-free. The effectiveness of controllers designed according to the algorithm analyzed in this paper is demonstrated on a recognized benchmark problem and on a simulation of a continuous-stirred tank reactor (CSTR). In both examples a radial basis function neural network is employed as the non-linear system model.

Neural networks for linear control: an analysis

This paper considers the use of radial basis function and multi-layer perceptron networks for linear or linearizable, adaptive feedback control schemes in a discrete-time environment. A close look is taken at the model structure selected and the extent of the resulting parameterization. A comparison is made with standard, nonneural network algorithms, e.g. self-tuning control.

Variable selection algorithm for the construction of MIMO operating point dependent neurofuzzy networks

An input variable selection procedure is introduced for the identification and construction of multi-input multi-output (MIMO) neurofuzzy operating point dependent models. The algorithm is an extension of a forward modified Gram-Schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting. The proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice-based modeling algorithms such as radial basis function neurofuzzy networks, enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation. Some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm.

Givens rotation based fast backward elimination algorithm for RBF neural network pruning

A fast backward elimination algorithm is introduced based on a QR decomposition and Givens transformations to prune radial-basis-function networks. Nodes are sequentially removed using an increment of error variance criterion. The procedure is terminated by using a prediction risk criterion so as to obtain a model structure with good generalisation properties. The algorithm can be used to postprocess radial basis centres selected using a k-means routine and, in this mode, it provides a hybrid supervised centre selection approach.

Adaptive modelling with tunable RBF network using multi-innovation RLS algorithm assisted by swarm intelligence

In this paper, we propose a new on-line learning algorithm for the non-linear system identification: the swarm intelligence aided multi-innovation recursive least squares (SI-MRLS) algorithm. The SI-MRLS algorithm applies the particle swarm optimization (PSO) to construct a flexible radial basis function (RBF) model so that both the model structure and output weights can be adapted. By replacing an insignificant RBF node with a new one based on the increment of error variance criterion at every iteration, the model remains at a limited size. The multi-innovation RLS algorithm is used to update the RBF output weights which are known to have better accuracy than the classic RLS. The proposed method can produces a parsimonious model with good performance. Simulation result are also shown to verify the SI-MRLS algorithm.

A combined SMOTE and PSO based RBF classifier for two-class imbalanced problems

This contribution proposes a powerful technique for two-class imbalanced classification problems by combining the synthetic minority over-sampling technique (SMOTE) and the particle swarm optimisation (PSO) aided radial basis function (RBF) classifier. In order to enhance the significance of the small and specific region belonging to the positive class in the decision region, the SMOTE is applied to generate synthetic instances for the positive class to balance the training data set. Based on the over-sampled training data, the RBF classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier's structure and the parameters of RBF kernels are determined using a PSO algorithm based on the criterion of minimising the leave-one-out misclassification rate. The experimental results obtained on a simulated imbalanced data set and three real imbalanced data sets are presented to demonstrate the effectiveness of our proposed algorithm.

The control of dynamical systems by neural networks

In this paper the use of neural networks for the control of dynamical systems is considered. Both identification and feedback control aspects are discussed as well as the types of system for which neural networks can provide a useful technique. Multi-layer Perceptron and Radial Basis function neural network types are looked at, with an emphasis on the latter. It is shown how basis function centre selection is a critical part of the implementation process and that multivariate clustering algorithms can be an extremely useful tool for finding centres.

Practical neural networks in a computer control package

This paper deals with the integration of radial basis function (RBF) networks into the industrial software control package Connoisseur. The paper shows the improved modelling capabilities offered by RBF networks within the Connoisseur environment compared to linear modelling techniques such as recursive least squares. The paper also goes on to mention the way this improved modelling capability, obtained through the RBF networks will be utilised within Connoisseur.

Experimental separation of the coherent component of X-ray scattering prior to RDF analysis of non-crystalline polymers

An experimental method is described which enables the inelastically scattered X-ray component to be removed from diffractometer data prior to radial density function analysis. At each scattering angle an energy spectrum is generated from a Si(Li) detector combined with a multi-channel analyser from which the coherently scattered component is separated. The data obtained from organic polymers has an improved signal/noise ratio at high values of scattering angle, and a commensurate enhancement of resolution of the RDF at low r is demonstrated for the case of PMMA (ICI `Perspex'). The method obviates the need for the complicated correction for multiple scattering.

Parkinson’s Disease tremor classification – a comparison between Support Vector Machines and neural networks

Deep Brain Stimulation has been used in the study of and for treating Parkinson’s Disease (PD) tremor symptoms since the 1980s. In the research reported here we have carried out a comparative analysis to classify tremor onset based on intraoperative microelectrode recordings of a PD patient’s brain Local Field Potential (LFP) signals. In particular, we compared the performance of a Support Vector Machine (SVM) with two well known artificial neural network classifiers, namely a Multiple Layer Perceptron (MLP) and a Radial Basis Function Network (RBN). The results show that in this study, using specifically PD data, the SVM provided an overall better classification rate achieving an accuracy of 81% recognition.

Adaptive noise cancellation with fast tunable RBF network

This paper describes a novel adaptive noise cancellation system with fast tunable radial basis function (RBF). The weight coefficients of the RBF network are adapted by the multi-innovation recursive least square (MRLS) algorithm. If the RBF network performs poorly despite of the weight adaptation, an insignificant node with little contribution to the overall performance is replaced with a new node without changing the model size. Otherwise, the RBF network structure remains unchanged and only the weight vector is adapted. The simulation results show that the proposed approach can well cancel the noise in both stationary and nonstationary ANC systems.

Online modeling with tunable RBF network

In this paper, we propose a novel online modeling algorithm for nonlinear and nonstationary systems using a radial basis function (RBF) neural network with a fixed number of hidden nodes. Each of the RBF basis functions has a tunable center vector and an adjustable diagonal covariance matrix. A multi-innovation recursive least square (MRLS) algorithm is applied to update the weights of RBF online, while the modeling performance is monitored. When the modeling residual of the RBF network becomes large in spite of the weight adaptation, a node identified as insignificant is replaced with a new node, for which the tunable center vector and diagonal covariance matrix are optimized using the quantum particle swarm optimization (QPSO) algorithm. The major contribution is to combine the MRLS weight adaptation and QPSO node structure optimization in an innovative way so that it can track well the local characteristic in the nonstationary system with a very sparse model. Simulation results show that the proposed algorithm has significantly better performance than existing approaches.

Complex-valued b-spline neural networks for modelling and inverse of wiener systems

Communication signal processing applications often involve complex-valued (CV) functional representations for signals and systems. CV artificial neural networks have been studied theoretically and applied widely in nonlinear signal and data processing [1–11]. Note that most artificial neural networks cannot be automatically extended from the real-valued (RV) domain to the CV domain because the resulting model would in general violate Cauchy-Riemann conditions, and this means that the training algorithms become unusable. A number of analytic functions were introduced for the fully CV multilayer perceptrons (MLP) [4]. A fully CV radial basis function (RBF) nework was introduced in [8] for regression and classification applications. Alternatively, the problem can be avoided by using two RV artificial neural networks, one processing the real part and the other processing the imaginary part of the CV signal/system. A even more challenging problem is the inverse of a CV

PDFOS: PDF estimation based over-sampling for imbalanced two-class problems

This contribution proposes a novel probability density function (PDF) estimation based over-sampling (PDFOS) approach for two-class imbalanced classification problems. The classical Parzen-window kernel function is adopted to estimate the PDF of the positive class. Then according to the estimated PDF, synthetic instances are generated as the additional training data. The essential concept is to re-balance the class distribution of the original imbalanced data set under the principle that synthetic data sample follows the same statistical properties. Based on the over-sampled training data, the radial basis function (RBF) classifier is constructed by applying the orthogonal forward selection procedure, in which the classifier’s structure and the parameters of RBF kernels are determined using a particle swarm optimisation algorithm based on the criterion of minimising the leave-one-out misclassification rate. The effectiveness of the proposed PDFOS approach is demonstrated by the empirical study on several imbalanced data sets.