Catálogo de publicaciones - libros

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.

The proliferation and dissemination of digital spatial databases, coupled with the ever wider use of Geographic Information Systems (GISystems or briefly GIS), is stimulating increasing interest in spatial analysis from outside the spatial sciences. The recognition of the spatial dimension in social science research sometimes yields different and more meaningful results than analysis that ignores it. Spatial analysis is a research paradigm that provides a unique set of techniques and methods for analysing events — events in a very general sense — that are located in geographical space (see Table 1). Spatial analysis involves spatial modelling, which includes models of location-allocation, spatial interaction, spatial choice and search, spatial optimisation, and space-time. This article concentrates on spatial data analysis, the heart of spatial analysis.

Many of the more sophisticated techniques and algorithms to process spatial data in spatial models are currently not or hardly available in GISystems. This raises the question of how spatial models should be integrated with GISystems. This chapter discusses possibilities and problems of interfacing spatial interaction models and GISystems from a conceptual rather than a technical point of view. The contribution illustrates that the integration between spatial analysis/modelling and GIS opens up tremendous opportunities for the development of new, highly visual, interactive and computational techniques for the analysis of spatial flow data. Using the Spatial Interaction Modelling [SIM] software package as an example, the chapter suggests that in spatial interaction modelling GIS functionalities are especially useful in three steps of the modelling process: zone design, matrix building and visualisation.

This chapter discusses data model and design issues that are specifically oriented to GIS-T, the application of GISystems to research, planning and management in transportation, and identifies several improvements of the traditional network data model that are required to support advanced network analysis in a ground transportation context. These improvements include turn-tables, dynamic segmentation, linear referencing, traffic lines and nonplanar networks. The chapter shifts attention also to network routing problems that have become prominent in GIS-T: the traveling-salesman problem, the vehicle-routing problem and the shortest-path problem with time windows, a problem that occurs as a subproblem in many time-constrained routing and scheduling issues of practical importance.

The chapter outlines the general architecture of a knowledge based GISystem that has the potential to intelligently support decision making in a GIS environment. The efficient and effective integration of spatial data, spatial analytic procedures and models, procedural and declarative knowledge is through fuzzy logic, expert systems and neural network technologies. A specific focus of the discussion is on the expert system and neural network components of the system, technologies which had been relatively unknown in the GIS community at the time this chapter was written.

This chapter is a tutorial text that gives an introductory exposure to computational neural networks for students and professional researchers in spatial data analysis. The text covers a wide range of topics important for developing neural networks into an advanced spatial analytic tool for non-parametric modelling. The topics covered include a definition of computational neural networks in mathematical terms and a careful and detailed description of neural networks in terms of the properties of the processing elements, the network topology and learning in the network. The chapter presents four important families of neural networks that are especially attractive for solving real world spatial analysis problems: backpropagation networks, radial basis function networks, supervised and unsupervised ART models, and self-organising feature map networks.

This paper suggests a new modelling approach, based upon a general nested sigmoid neural network model. Its feasibility is illustrated in the context of modelling interregional telecommunication traffic in Austria and its performance is evaluated in comparison with the classical regression approach of the gravity type. The application of this neural network approach may be viewed as a three-stage process. The first stage refers to the identification of an appropriate network from the family of two-layered feedforward networks with three input nodes, one layer of (sigmoidal) intermediate nodes and one (sigmoidal) output node. There is no general procedure to address this problem. We solved this issue experimentally. The input-output dimensions have been chosen in order to make the comparison with the gravity model as close as possible. The second stage involves the estimation of the network parameters of the selected neural network model. This is performed via the adaptive setting of the network parameters (training, estimation) by means of the application of a least mean squared error goal and the error back-propagating technique, a recursive learning procedure using a gradient search to minimise the error goal. Particular emphasis is laid on the sensitivity of the network performance to the choice of the initial network parameters as well as on the problem of overfitting. The final stage of applying the neural network approach refers to the testing of the interregional teletraffic flows predicted. Prediction quality is analysed by means of two performance measures, average relative variance and the coefficient of determination, as well as by the use of residual analysis. The analysis shows that the neural network model approach outperforms the classical regression approach to modelling telecommunication traffic in Austria.

Building a feedforward computational neural network model (CNN) involves two distinct tasks: determination of the network topology and weight estimation. The specification of a problem adequate network topology is a key issue and the primary focus of this contribution. Up to now, this issue has been either completely neglected in spatial application domains, or tackled by search heuristics (see Fischer and Gopal 1994). With the view of modelling interactions over geographic space, the current chapter considers this problem as a global optimisation problem and proposes a novel approach that embeds backpropagation learning into the evolutionary paradigm of genetic algorithms. This is accomplished by interweaving a genetic search for finding an optimal CNN topology with gradient-based backpropagation learning for determining the network parameters. Thus, the model builder will be relieved of the burden of identifying appropriate CNN-topologies that will allow a problem to be solved with simple, but powerful learning mechanisms, such as backpropagation of gradient descent errors. The approach has been applied to the family of three inputs, single hidden layer, single output feedforward CNN models using interregional telecommunication traffic data for Austria, to illustrate its performance and to evaluate its robustness.

This paper evaluates the classification accuracy of three neural network classifiers on a satellite image-based pattern classification problem. The multispectral pattern classification task is to assign pixels to one of eight prespecified urban land use categories on a pixel-bypixel basis. The neural network classifiers used include two types of the Multi-Layer-Perceptron (MLP) and the Radial Basis Function Network. A normal (conventional) classifier is used as a benchmark to evaluate the performance of neural network classifiers. The satellite image consists of 2,460 pixels selected from a section (270 × 360) of a Landsat-5 TM scene from the city of Vienna and its northern surroundings. In addition to evaluation of classification accuracy, the neural classifiers are analysed for generalisation capability and stability of results. The best result in terms of classification accuracy is provided by the MLP-1 classifier with weight elimination. It has a small number of parameters and requires no problem-specific system of initial weight values. Its in-sample classification error is 7.87% and its out-of-sample classification error is 10.24% for the problem at hand. Four classes of simulations have been undertaken to illustrate the properties of the classifier in general and the stability of the result with respect to control parameters, such as the gradient descent control term, initial parameter conditions, and different training and testing sets.

This paper attempts to develop a mathematically rigid framework for minimising the cross-entropy function in an error backpropagating framework. In doing so, we derive the backpropagation formulae for evaluating the partial derivatives in a computationally efficient way. Various techniques of optimising the multiple-class cross-entropy error function to train single hidden layer neural network classifiers with softmax output transfer functions are investigated on a real world multispectral pixel-by-pixel classification problem that is of fundamental importance in remote sensing. These techniques include epoch-based and batch versions of backpropagation of gradient descent, PR-conjugate gradient, and BFGS quasi-Newton errors. The method of choice depends upon the nature of the learning task and whether one wants to optimise learning for speed or classification performance. It was found that, comparatively considered, gradient descent error backpropagation provided the best and most stable out-of-sample performance results across batch and epoch-based modes of operation. If the goal is to maximise learning speed and a sacrifice in classification accuracy is acceptable, then PR-conjugate gradient error backpropagation tends to be superior. If the training set is very large, stochastic epoch-based versions of local optimisers should be chosen utilising a larger rather than a smaller epoch size to avoid unacceptable instabilities in the classification results.