This thesis presents some substantial theoretical analyses and optimal treatments
of Kohonen's self-organising map (SOM) algorithm, and explores the practical
application potential of the algorithm for vector quantisation, pattern classification,
and image processing. It consists of two major parts. In the first part, the SOM
algorithm is investigated and analysed from a statistical viewpoint. The proof of its
universal convergence for any dimensionality is obtained using a novel and
extended form of the Central Limit Theorem. Its feature space is shown to be an
approximate multivariate Gaussian process, which will eventually converge and
form a mapping, which minimises the mean-square distortion between the feature
and input spaces. The diminishing effect of the initial states and implicit effects of
the learning rate and neighbourhood function on its convergence and ordering are
analysed and discussed. Distinct and meaningful definitions, and associated
measures, of its ordering are presented in relation to map's fault-tolerance. The
SOM algorithm is further enhanced by incorporating a proposed constraint, or
Bayesian modification, in order to achieve optimal vector quantisation or pattern
classification. The second part of this thesis addresses the task of unsupervised
texture-image segmentation by means of SOM networks and model-based
descriptions. A brief review of texture analysis in terms of definitions, perceptions,
and approaches is given. Markov random field model-based approaches are
discussed in detail. Arising from this a hierarchical self-organised segmentation
structure, which consists of a local MRF parameter estimator, a SOM network, and
a simple voting layer, is proposed and is shown, by theoretical analysis and
practical experiment, to achieve a maximum likelihood or maximum a posteriori
segmentation. A fast, simple, but efficient boundary relaxation algorithm is
proposed as a post-processor to further refine the resulting segmentation. The class
number validation problem in a fully unsupervised segmentation is approached by
a classical, simple, and on-line minimum mean-square-error method. Experimental
results indicate that this method is very efficient for texture segmentation
problems. The thesis concludes with some suggestions for further work on SOM
neural networks.