A model and an algebra for semi-structured and full-text queries

The need for a convergence between semi-structured data management and Information Retrieval techniques is manifest to the scientific community. In order to fulfil this growing request, W3C has recently proposed XQuery Full Text, an IR-oriented extension of XQuery. However, the issue of query optimization requires the study of important properties like query equivalence and containment; to this aim, a formal representation of document and queries is needed. The goal of this thesis is to establish such formal background. We define a data model for XML documents and propose an algebra able to represent most of XQuery Full-Text expressions. We show how an XQuery Full-Text expression can be translated into an algebraic expression and how an algebraic expression can be optimized.

Kernel Methods for Tree Structured Data

Machine learning comprises a series of techniques for automatic extraction of meaningful information from large collections of noisy data. In many real world applications, data is naturally represented in structured form. Since traditional methods in machine learning deal with vectorial information, they require an a priori form of preprocessing. Among all the learning techniques for dealing with structured data, kernel methods are recognized to have a strong theoretical background and to be effective approaches. They do not require an explicit vectorial representation of the data in terms of features, but rely on a measure of similarity between any pair of objects of a domain, the kernel function. Designing fast and good kernel functions is a challenging problem. In the case of tree structured data two issues become relevant: kernel for trees should not be sparse and should be fast to compute. The sparsity problem arises when, given a dataset and a kernel function, most structures of the dataset are completely dissimilar to one another. In those cases the classifier has too few information for making correct predictions on unseen data. In fact, it tends to produce a discriminating function behaving as the nearest neighbour rule. Sparsity is likely to arise for some standard tree kernel functions, such as the subtree and subset tree kernel, when they are applied to datasets with node labels belonging to a large domain. A second drawback of using tree kernels is the time complexity required both in learning and classification phases. Such a complexity can sometimes prevents the kernel application in scenarios involving large amount of data. This thesis proposes three contributions for resolving the above issues of kernel for trees. A first contribution aims at creating kernel functions which adapt to the statistical properties of the dataset, thus reducing its sparsity with respect to traditional tree kernel functions. Specifically, we propose to encode the input trees by an algorithm able to project the data onto a lower dimensional space with the property that similar structures are mapped similarly. By building kernel functions on the lower dimensional representation, we are able to perform inexact matchings between different inputs in the original space. A second contribution is the proposal of a novel kernel function based on the convolution kernel framework. Convolution kernel measures the similarity of two objects in terms of the similarities of their subparts. Most convolution kernels are based on counting the number of shared substructures, partially discarding information about their position in the original structure. The kernel function we propose is, instead, especially focused on this aspect. A third contribution is devoted at reducing the computational burden related to the calculation of a kernel function between a tree and a forest of trees, which is a typical operation in the classification phase and, for some algorithms, also in the learning phase. We propose a general methodology applicable to convolution kernels. Moreover, we show an instantiation of our technique when kernels such as the subtree and subset tree kernels are employed. In those cases, Direct Acyclic Graphs can be used to compactly represent shared substructures in different trees, thus reducing the computational burden and storage requirements.

Connecting works of art within the semantic web of symbolic meanings

My doctoral research is about the modelling of symbolism in the cultural heritage domain, and on connecting artworks based on their symbolism through knowledge extraction and representation techniques. In particular, I participated in the design of two ontologies: one models the relationships between a symbol, its symbolic meaning, and the cultural context in which the symbol symbolizes the symbolic meaning; the second models artistic interpretations of a cultural heritage object from an iconographic and iconological (thus also symbolic) perspective. I also converted several sources of unstructured data, a dictionary of symbols and an encyclopaedia of symbolism, and semi-structured data, DBpedia and WordNet, to create HyperReal, the first knowledge graph dedicated to conventional cultural symbolism. By making use of HyperReal's content, I showed how linked open data about cultural symbolism could be utilized to initiate a series of quantitative studies that analyse (i) similarities between cultural contexts based on their symbologies, (ii) broad symbolic associations, (iii) specific case studies of symbolism such as the relationship between symbols, their colours, and their symbolic meanings. Moreover, I developed a system that can infer symbolic, cultural context-dependent interpretations from artworks according to what they depict, envisioning potential use cases for museum curation. I have then re-engineered the iconographic and iconological statements of Wikidata, a widely used general-domain knowledge base, creating ICONdata: an iconographic and iconological knowledge graph. ICONdata was then enriched with automatic symbolic interpretations. Subsequently, I demonstrated the significance of enhancing artwork information through alignment with linked open data related to symbolism, resulting in the discovery of novel connections between artworks. Finally, I contributed to the creation of a software application. This application leverages established connections, allowing users to investigate the symbolic expression of a concept across different cultural contexts through the generation of a three-dimensional exhibition of artefacts symbolising the chosen concept.