Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

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.