Dynamic reconstruction of sea clutter

Abstract

This thesis explores issues related to the modelling of sea clutter data using Radial Basis Function (RBF) networks and variants. Previous work had shown that sea clutter may be chaotic, and thus amenable to nonlinear time series analysis. Because RBF networks possess the property of universal approximation, it is possible to use them to model sea clutter data. This is a noisy, nonlinear problem; a large RBF network is usually required. The prescriptions for choosing embedding delay are put on a sound theoretical basis. The standard procedure for estimating embedding dimension is improved. Clipping is introduced, as a simple, yet effective way to stabilize iterated predictions. A method is devised to speed up cross validation, which applies to variants of the Radial Basis Function (RBF) utilizing clustering techniques. Error variance is used for selecting models, rather than mean squared error. The RBF architecture is revised to account for empty clusters. A possible explanation is found for the puzzling phenomenon of empty clusters. It is suggested that non-deterministic behaviour of the clustering stage could affect RBF performance. Several types of data driven, non-radial basis functions are introduced, which may require less centers, thereby alleviating the curse of dimensionality. This stemmed from a desire to find a compromise between coping with high dimensionality, and yet using all available information as effectively as possible. Regularization is extended to non-radial basis functions. The improved understanding and procedures were applied to model sea clutter using iterated prediction. One spin-off is that the significant computational savings from speeding up cross validation may tip the balance and encourage more applications to employ the RBF, rather than the Multilayer Perceptron (MLP). It may also discourage certain regularization techniques which cannot be accelerated.