Catálogo de publicaciones - libros

This chapter shifts attention to fuzzy ARTMAP classification which synthesises fuzzy logic and Adaptive Resonance Theory (ART) by exploiting the formal similarity between the computations of fuzzy subsets and the dynamics of category choice, search and learning. The contribution describes design features, system dynamics and simulation algorithms of this learning system, which is trained and tested for classification (with eight classes a priori given) of a Landsat-5 Thematic Mapper scene from the city of Vienna on a pixel-by-pixel basis. The performance of the fuzzy ARTMAP is compared with that of an error-based learning system based upon a single hidden layer feedforward network, and the Gaussian maximum likelihood classifier as conventional statistical benchmark on the same database. Both neural classifiers outperform the conventional classifier in terms of classification accuracy. Fuzzy ARTMAP leads to out-of-sample classification accuracies which are very close to maximum performance, while the backpropagation network — like the conventional classifier — has difficulty in distinguishing between some land use categories.

In this chapter a novel modular product unit neural network architecture is presented to model singly constrained spatial interaction flows. The efficacy of the model approach is demonstrated for the origin-constrained case of spatial interaction using Austrian interregional telecommunication traffic data. The model requires a global search procedure for parameter estimation, such as the Alopex procedure. A benchmark comparison against the standard origin-constrained gravity model and the two-stage neural network approach, suggested by Openshaw (1998), illustrates the superiority of the proposed model in terms of the generalisation performance measured by ARV and SRMSE.

This chapter views learning as an unconstrained nonlinear minimisation problem in which the objective function is defined by the negative log-likelihood function and the search space by the parameter space of an origin-constrained product unit neural spatial interaction model. We consider Alopex based global search, as opposed to local search based upon backpropagation of gradient descents, each in combination with the bootstrapping pairs approach to solve the maximum likelihood learning problem. Interregional telecommunication traffic flow data from Austria are used as test bed for comparing the performance of the two learning procedures. The study illustrates the superiority of Alopex based global search, measured in terms of Kullback and Leibler’s information criterion.

This paper attempts to develop a mathematically rigid and unified framework for neural spatial interaction modelling. Families of classical neural network models, but also less classical ones such as product unit neural network ones are considered for the cases of unconstrained and singly constrained spatial interaction flows. Current practice appears to suffer from least squares and normality assumptions that ignore the true integer nature of the flows and approximate a discrete-valued process by an almost certainly misrepresentative continuous distribution. To overcome this deficiency we suggest a more suitable estimation approach, maximum likelihood estimation under more realistic distributional assumptions of Poisson processes, and utilise a global search procedure, called Alopex, to solve the maximum likelihood estimation problem. To identify the transition from underfitting to overfitting we split the data into training, internal validation and test sets. The bootstrapping pairs approach with replacement is adopted to combine the purity of data splitting with the power of a resampling procedure to overcome the generally neglected issue of fixed data splitting and the problem of scarce data. In addition, the approach has power to provide a better statistical picture of the prediction variability. Finally, a benchmark comparison against the classical gravity models illustrates the superiority of both, the unconstrained and the origin-constrained neural network model versions in terms of generalisation performance measured by Kullback and Leibler’s information criterion.