Bruce Curry’s research while affiliated with University of Wales and other places

Neural networks can bring together psychometric and econometric approaches to the measurement of attitudes and emotions. This paper describes the analysis by neural network of consumer data gathered from car buyers, with the aim of investigating in detail the contribution made by explanatory variables to degree of satisfaction with last car bought and brand loyalty relating to car purchase. Nodes in the hidden layer of the network were labelled to represent respondents' less easily articulated attitudes or beliefs. Analysis of the findings shows clear differences in attitudes between male and female buyers.

This paper introduces an expert system model which is being developed with the objective of helping marketing managers to analyse the position of their company relative to their competitors, in a particular business or product area, and then suggesting ways in which this position might be improved. The authors also discuss a predevelopment test to assess management benefits, as well as the generation and elicitation of knowledge and expertise provided by managers themselves. In particular, this research considers the potential of an expert system to aid marketing managers in making competitive analysis evaluations.

This paper is a response to difficulties reported in applying feedforward neural networks (NNs) to seasonal data. The solution we propose is a modified network model which is pruned and optimised by means of Differential Evolution methods. The problem for NNs in the case of seasonality lies in the so-called 'universal approximation' property, which underpins the use of MLP networks as a vehicle for flexible non-linear regression. Our view is that seasonality is best modelled by using sinusoids, which permit the use of more powerful analytical tools without losing any generality as compared with dummy variables. However, the actual theorems supporting NN approximation specifically relate to functions possessing suitable properties of smoothness, in which case it is not surprising that NNs have difficulty with seasonality. Only a very 'short' sinusoid would be smooth enough. Our suggested solution is to transform the input variable so that instead of using a time variable alone we have sinusoids as inputs. In theoretical terms, this helps restore the approximation property, as can also be seen in our examples, which also serve to illustrate the strength of Differential Evolution methods.

This paper is a response to reports by a number of authors of difficulties in using feedforward neural networks (NNs) in the presence of seasonality. Such difficulties appear to contradict the well-known property of 'universal approximation', but arise in fact because the property only applies to suitably smooth functions. We report on what is an unexpected benefit of this limitation of NNs: although the network is unable to follow seasonal movements it can identify an underlying trend, through being forced to steer a middle course. We achieve such deseasonalisation through network pruning, which restricts the approximation capacity of the network by depriving it of connections. Although pruning is in general motivated by the search for the most parsimonious network, in our particular context it forces the network to ignore both seasonal movements and noise.

This paper deals with feedforward neural networks containing a single hidden layer and with sigmoid/logistic activation function. Training such a network is equivalent to implementing nonlinear regression using a flexible functional form, but the functional form in question is not easy to deal with. The Chebyshev polynomials are suggested as a way forward, providing an approximation to the network which is superior to Taylor series expansions. Application of these approximations suggests that the network is liable to a ‘naturally occurring’ parameter redundancy, which has implications for the training process as well as certain statistical implications. On the other hand, parameter redundancy does not appear to damage the fundamental property of universal approximation.

Debate continues regarding the capacity of feedforward neural networks (NNs) to deal with seasonality without pre-processing. The purpose of this paper is to provide, with examples, some theoretical perspective for the debate. In the first instance it considers possible specification errors arising through use of autoregressive forms. Secondly, it examines seasonal variation in the context of the so-called ‘universal approximation’ capabilities of NNs, finding that a short (bounded) sinusoidal series is easy for the network but that a series with many turning points becomes progressively more difficult. This follows from results contained in one of the seminal papers on NN approximation. It is confirmed in examples which also show that, to model seasonality with NNs, very large numbers of hidden nodes may be required.

This paper considers two related issues regarding feedforward Neural Networks (NNs). The first involves the question of whether the network weights corresponding to the best fitting network are unique. Our empirical tests suggest an answer in the negative, whether using standard Backpropagation algorithm or our preferred direct (non-gradient-based) search procedure. We also offer a theoretical analysis which suggests that there will almost inevitably be functional relationships between network weights. The second issue concerns the use of standard statistical approaches to testing the significance of weights or groups of weights. Treating feedforward NNs as an interesting way to carry out nonlinear regression suggests that statistical tests should be employed. According to our results, however, statistical tests can in practice be indeterminate. It is rather difficult to choose either the number of hidden layers or the number of nodes on this basis.

Rough Set Theory (RST) originated as an approach to approximating a given set, but has found its main applications in the statistical domain of classification problems. It generates classification rules, and can be seen in general terms as a technique for rule induction. Expositions of RST often stress that it is robust in requiring no (explicit) assumptions of a statistical nature. The argument here, however, is that this apparent strength is also a weakness which prevents establishment of general statistical properties and comparison with other methods. A sampling theory is developed for the first time, using both the original RST model and its probabilistic extension, Variable Precision Rough Sets. This is applied in the context of examples, one of which involves Fisher’s Iris data. Copyright Springer-Verlag Berlin/Heidelberg 2004

In a recent article in this journal Hwarng and Ang (HA) introduce what they describe as a 'simple' neural network for time series forecasting. It is argued here that the approach is better described as logistic regression applied in a time-series context. However, the HA model cannot be implemented through the standard LOGIT technique for handling qualitative dependent variables. Nor is it same as the logistic difference equation used in population biology. In fact, it seems to have no 'pedigree' in the time-series literature. The paper explores the dynamic properties of the model. Chaotic behaviour will not arise, and stability, especially in the first-order case, is quite likely.

This paper examines the technical foundations of the self-organising map (SOM). It compares Kohonen’s heuristic-based training algorithm with direct optimisation of a locally-weighted distortion index, also used by Kohonen. Direct optimisation is achieved through a genetic algorithm (GA). Although GAs have been used before with the SOM, this has not been done in conjunction with the distortion index. Comparing heuristic-based training and direct optimisation for the SOM is analogous to comparing the Backpropagation algorithm for feedforward networks with direct optimisation of RMS error. Our experiments reveal lower values of the distortion index with direct optimisation. As to whether the heuristic-based algorithm is able to provide an approximation to gradient descent, our results suggest the answer should be in the negative. Theorems for one-dimensional and for square maps indicate that different point densities will emerge for the two training approaches. Our findings are in accordance with these results.