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.

The Romanian Orthodox Church

At first glance, the nationalist ideology of the French Revolution seems to have had little impact on the Orthodox Church in Romanian-speaking territories. Romanians were the predominant inhabitants of the principalities of Wallachia and Moldavia and the neighboring territories of Transylvania (including Crişana, Maramureş and Banat), Bukovina, Bessarabia, and Dobrudja. The majority of ethnic Romanians belonged to the Orthodox faith while their communities were at the intersection of geopo liti cal interests of the Rus sian, Ottoman, and Habsburg empires. In 1859 the Principalities of Wallachia and Moldavia (known as the Old Kingdom between 1866 and 1918) united into a single state under the rule of a local prince. The term "Romania" began to be used by the new state in its of cial documents in 1862. Two years later, the state supported the declaration of a Romanian autocephalous (in de pen dent) church that was recognized by the Ecumenical Patriarchate in 1885. As an integrative part of the Orthodox commonwealth, the church was situated between the competing jurisdictions of the Ecumenical Patriarchate and the Rus sian Orthodox Church, while its declaration of autocephaly followed a pattern in the spread of national churches in Southeastern Europe. From the Treaty of Kuchuk Kainardji of 1774 to the beginning of the Greek War for In de pen dence in 1821, the Romanian principalities were under the suzerainty of the Ottoman Empire, which had full control of their po liti cal and economic affairs. The sultan appointed princes, and the Porte determined their po liti cal and judicial status. The princes were drawn from the "Phanariots," and were directly appointed by the Porte from preponderantly Greek elite rather than the Romanian local elite, the boyars (boieri).1 In each principality, the church was headed by a metropolitan who was under the direct jurisdiction of the Ecumenical Patriarchate. That religion mattered to local population as a means of social cohesion was suggestively depicted by Anatole de Demidoff, an En glish traveler in the region in 1837. Arriving in Bucharest, the capital of Wallachia, he claimed that: I know of no city in Europe in which it is possible to find more agreeable society, or in which there is a better tone, united with the most charming gaiety⋯. Religion, which is here of the schismatic Greek creed, does not, properly speaking, hold any great empire over the minds of the Wallachian people, but they observe its outward forms, and particularly the austerities of fasting, with scrupulous exactitude. The people are seen to attend divine ser vice with every sign of respect, and the great number of churches existing in Wallachia, bear witness to the ardent zeal with which outward worship is honored.2 The Romanian Orthodox Church was a national institution, closely linked to social, economic, and po liti cal structures. In most cases, Orthodox hierarchs were appointed from the families of boyars, thus ensuring a close relationship with the state authorities and its policies. As one of the largest landowners in the principalities, the church had a prime role in administrating healthcare and education. Although the majority of the clergy was uneducated, it dispensed both ecclesiastical and civil justice and in many cases worked closely with boyars in local administration.3 The lower clergy not only contributed directly to the economy but also benefited from tax privileges. Some small villages had an unusually high proportion of clergy in comparison to the overall population. For example, in 1810, Stənisləveşti, a village in the south of Wallachia, was composed of eleven houses and had two priests, five deacons, and three cantors; similarly, the Frəsinet village of nineteen houses had two priests and five deacons.4 Although these cases were exceptional, they indicate both the economic value of being a member of the clergy and the wider canonical dimension of church jurisdiction. The special status of the clergy was reflected not only at lower but also at higher levels. Bishops and metropolitans engaged with state policy and in many cases opposition to the authorities led to the loss of a spiritual seat. The metropolitan of each principality worked with the prince and was president of the divan, the gathering of all boyars. He held the right to be the first person to comment on state policy and to make recommendations when the prince was absent. The metropolitan replaced the prince when the principality had no political ruler, such as in the cases of Metropolitan Veniamin Costachi of Moldavia in 1806 and Metropolitan Dositei Filitti of Wallachia, while the bishops of Buzəu and Argeş were members of the provisional government during the Rus sian occupation of the principalities in 1808. The higher clergy had both religious and political prerogatives in relation to foreign powers as evident in their heading of the boyars' delegation to peace negotiation between the Rus sian and Ottoman empires at Focşani in 1772 and addressing memoranda to the Austrian and Rus sian governments in 1802.5 The primary role of the church in the principalities of Moldavia and Wallachia was paralleled by the national mobilization of Orthodox communities in the neighboring territories that had Romanian inhabitants. Although throughout the region Orthodox communities were incorporated into church structures as part of the Habsburg, Austrian or Rus sian empires, the nineteenth century was characterized by the leadership's search for political autonomy and the building of a Romanian national identity. The Orthodox communities outside the Old Kingdom maintained relations with the faithful in principalities across the Carpathian Mountains and the Dniester River and sought support in their struggle for political and religious rights.