Thesis available - Transformation-Invariant Topology Preserving Maps

[Stephen McGlinchey]

The following PhD thesis is available from
http://cis.paisley.ac.uk/mcgl-ci0/

"Transformation-Invariant Topology Preserving Maps"

Stephen J. McGlinchey (March 2000)

Abstract

This thesis investigates the use of unsupervised learning in the context of
artificial neural networks to determine filters of data sets that exhibit
invariances of one sort or another. The artificial neural networks in this
thesis are all of a general type known as topology-preserving mappings.
Topology-preserving maps have been of great interest in the computational
intelligence community since they were devised in the 1980s. These are
methods of mapping high dimensional data to a space of smaller
dimensionality, whilst preserving the topographic structure of the data, at
least to some degree.  Such models have been successfully used in
applications such as speech processing, robotics, data visualisation and
computer vision, to name but a few. Apart from the many engineering
applications of topology preservation, they have also been of biological
interest since ensembles of neurons in biological brains have similar
properties in that neurons that are close together in certain parts of the
brain respond similarly to input data.

 The specific contributions of this thesis are:

1.      An investigation of matrix constraints to preserve topological
relations in neural network algorithms, which have previously only used
orthonormality as a constraint. The previous algorithms are then seen as
special cases of our new algorithms.

2.      the development of a topology-preserving map network that ignores
the magnitude of input data and respond to its radial location. The
organised mappings are able to reliably classify data, where the magnitude
of the data has little or no bearing on which class they belongs to. For
example, voiced phonemes were classified with amplitude invariance, i.e.
regardless of the volume of the speech.

3.      a novel neural network method based on Kohonens self-organising map
(Kohonen, 1997) algorithm, but combining it with a principal component
analysis network to give a set of local principal components which globally
cover the data set with a smooth ordering. The resulting filters are
transformation invariant for some simple transformations.

Stephen McGlinchey
Dept. of Computing & Information Systems
University of Paisley
High Street
Paisley PA1 2BE
Scotland
email: stephen-m at uk2.net
fax: +44 141 848 3542
http://cis.paisley.ac.uk/mcgl-ci0/