Magnification factors for the GTM algorithm

The Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) has been introduced as a principled alternative to the Self-Organizing Map (SOM). As well as avoiding a number of deficiencies in the SOM, the GTM algorithm has the key property that the smoothness properties of the model are decoupled from the reference vectors, and are described by a continuous mapping from a lower-dimensional latent space into the data space. Magnification factors, which are approximated by the difference between code-book vectors in SOMs, can therefore be evaluated for the GTM model as continuous functions of the latent variables using the techniques of differential geometry. They play an important role in data visualization by highlighting the boundaries between data clusters, and are illustrated here for both a toy data set, and a problem involving the identification of crab species from morphological data.

Magnification factors for the SOM and GTM algorithms

Magnification factors specify the extent to which the area of a small patch of the latent (or `feature') space of a topographic mapping is magnified on projection to the data space, and are of considerable interest in both neuro-biological and data analysis contexts. Previous attempts to consider magnification factors for the self-organizing map (SOM) algorithm have been hindered because the mapping is only defined at discrete points (given by the reference vectors). In this paper we consider the batch version of SOM, for which a continuous mapping can be defined, as well as the Generative Topographic Mapping (GTM) algorithm of Bishop et al. (1997) which has been introduced as a probabilistic formulation of the SOM. We show how the techniques of differential geometry can be used to determine magnification factors as continuous functions of the latent space coordinates. The results are illustrated here using a problem involving the identification of crab species from morphological data.

Lexical database enrichment through semi-automated morphological analysis

Derivational morphology proposes meaningful connections between words and is largely unrepresented in lexical databases. This thesis presents a project to enrich a lexical database with morphological links and to evaluate their contribution to disambiguation. A lexical database with sense distinctions was required. WordNet was chosen because of its free availability and widespread use. Its suitability was assessed through critical evaluation with respect to specifications and criticisms, using a transparent, extensible model. The identification of serious shortcomings suggested a portable enrichment methodology, applicable to alternative resources. Although 40% of the most frequent words are prepositions, they have been largely ignored by computational linguists, so addition of prepositions was also required. The preferred approach to morphological enrichment was to infer relations from phenomena discovered algorithmically. Both existing databases and existing algorithms can capture regular morphological relations, but cannot capture exceptions correctly; neither of them provide any semantic information. Some morphological analysis algorithms are subject to the fallacy that morphological analysis can be performed simply by segmentation. Morphological rules, grounded in observation and etymology, govern associations between and attachment of suffixes and contribute to defining the meaning of morphological relationships. Specifying character substitutions circumvents the segmentation fallacy. Morphological rules are prone to undergeneration, minimised through a variable lexical validity requirement, and overgeneration, minimised by rule reformulation and restricting monosyllabic output. Rules take into account the morphology of ancestor languages through co-occurrences of morphological patterns. Multiple rules applicable to an input suffix need their precedence established. The resistance of prefixations to segmentation has been addressed by identifying linking vowel exceptions and irregular prefixes. The automatic affix discovery algorithm applies heuristics to identify meaningful affixes and is combined with morphological rules into a hybrid model, fed only with empirical data, collected without supervision. Further algorithms apply the rules optimally to automatically pre-identified suffixes and break words into their component morphemes. To handle exceptions, stoplists were created in response to initial errors and fed back into the model through iterative development, leading to 100% precision, contestable only on lexicographic criteria. Stoplist length is minimised by special treatment of monosyllables and reformulation of rules. 96% of words and phrases are analysed. 218,802 directed derivational links have been encoded in the lexicon rather than the wordnet component of the model because the lexicon provides the optimal clustering of word senses. Both links and analyser are portable to an alternative lexicon. The evaluation uses the extended gloss overlaps disambiguation algorithm. The enriched model outperformed WordNet in terms of recall without loss of precision. Failure of all experiments to outperform disambiguation by frequency reflects on WordNet sense distinctions.

Relationships between morphological types of plaque in Alzheimer’s disease as revealed in silver and immunostained preparations

The objective of this study was to determine the possible relationships between the morphological types of plaque revealed in silver and immunostained sections of Alzheimer’s disease (AD) tissue. The density of cored and uncored senile plaques in Glees and Marsland preparations, and of diffuse, primitive, classic and compact beta/A4 deposits in immunostained preparations were estimated. A principal components analysis (PCA) of the data suggested that three uncorrelated principal components accounted for 80% of the variation in lesion density in the tissues. This suggested that thee processes lead independently to the formation of: (1) the uncored Glees plaques; (2) the primitive beta/A4 deposits and most of the classic beta/A4 deposits and (3) the compact beta/A4 deposits and the remaining classic deposits. Hence, the uncored plaques revealed by the Glees stain and the primitive beta/A4 deposits represented distinct plaque populations. In addition, the classic beta/A4 deposits did not appear to represent a uniform plaque population but to originate from at least two pathological processes. The uncored Glees plaques appeared to the only plaque population closely related to the diffuse beta/A4 deposits.

IN VIVO analysis of ocular morphological changes during phakic accommodation

The principal theme of this thesis is the in vivo examination of ocular morphological changes during phakic accommodation, with particular attention paid to the ciliary muscle and crystalline lens. The investigations detailed involved the application of high-resolution imaging techniques to facilitate the acquisition of new data to assist in the clarification of aspects of the accommodative system that were poorly understood. A clinical evaluation of the newly available Grand Seiko Auto Ref/ Keratometer WAM-5500 optometer was undertaken to assess its value in the field of accommodation research. The device was found to be accurate and repeatable compared to subjective refraction, and has the added advantage of allowing dynamic data collection at a frequency of around 5 Hz. All of the subsequent investigations applied the WAM-5500 for determination of refractive error and objective accommodative responses. Anterior segment optical coherence tomography (AS-OCT) based studies examined the morphology and contractile response of youthful and ageing ciliary muscle. Nasal versus temporal asymmetry was identified, with the temporal aspect being both thicker and demonstrating a greater contractile response. The ciliary muscle was longer in terms of both its anterior (r = 0.49, P <0.001) and overall length (r = 0.45, P = 0.02) characteristics, in myopes. The myopic ciliary muscle does not appear to be merely stretched during axial elongation, as no significant relationship between thickness and refractive error was identified. The main contractile responses observed were a thickening of the anterior region and a shortening of the muscle, particularly anteriorly. Similar patterns of response were observed in subjects aged up to 70 years, supporting a lensocentric theory of presbyopia development. Following the discovery of nasal/ temporal asymmetry in ciliary muscle morphology and response, an investigation was conducted to explore whether the regional variations in muscle contractility impacted on lens stability during accommodation. A bespoke programme was developed to analyse AS-OCT images and determine whether lens tilt and decentration varied between the relaxed and accommodated states. No significant accommodative difference in these parameters was identified, implying that any changes in lens stability with accommodation are very slight, as a possible consequence of vitreous support. Novel three-dimensional magnetic resonance imaging (MRI) and analysis techniques were used to investigate changes in lens morphology and ocular conformation during accommodation. An accommodative reduction in lens equatorial diameter provides further evidence to support the Helmholtzian mechanism of accommodation, whilst the observed increase in lens volume challenges the widespread assertion that this structure is incompressible due to its high water content. Wholeeye MRI indicated that the volume of the vitreous chamber remains constant during accommodation. No significant changes in ocular conformation were detected using MRI. The investigations detailed provide further insight into the mechanisms of accommodation and presbyopia, and represent a platform for future work in this field.