Data analysis through graph decomposition
This work is developed within the field of data mining and data visualization. Under the premise that many of the algorithms give as result huge amounts of data impossible to handle for the users, we work with the decomposition of Gaifman graphs and its variations as an option for data visualization...
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/669758 |
| Acceso en línea: | http://hdl.handle.net/10803/669758 https://dx.doi.org/10.5821/dissertation-2117-330388 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Informàtica 004 |
| Sumario: | This work is developed within the field of data mining and data visualization. Under the premise that many of the algorithms give as result huge amounts of data impossible to handle for the users, we work with the decomposition of Gaifman graphs and its variations as an option for data visualization. In fact, we apply the decomposition method based on the so-called 2-structures. This decomposition method has been theoretical developed but has not any practical application yet in this field, being this part of our contribution. Thus, from a dataset we construct the Gaifman graph (and possible variations of it) that represents information about co-occurrence patterns. More precisely, the construction of the Gaifman graphs from the dataset is based on co-occurrence, or lack of it, of items in the dataset. That is, those pair of items that appear together in any transaction are connected and those items that never appear together are disconnected. We may do the natural completion of the graph adding the absent edges with a different kind of edges, in this way we get a complete graph with two equivalence classes on its edges. Now, think of the graph where the kind of edges are determined by the multiplicity of the items that they connect, that is, by the number of transactions that contains the pair of items that the edge connects. In this case we have as many equivalence relations as different multiplicities, and we may apply some discretization methods on them to get different variations of the graphs. All these variations can be seen as 2-structures. The application of the 2-structure decomposition method produces as result a hierarchical visualization of the co-occurrences on data. In fact, the decomposition method is based on clan decomposition. Given a 2-structure defined on U, a set of vertices C, C subset of U, is a clan if, for each z not in C, z may not distinguish among the elements of C. We connect this decomposition with an associated closure space, developing this intuition by introducing a construction of implication sets, named clan implications. Based on the definition of a clan, let x, y be elements of any clan C, if there is z such that sees in a different way x and y, that is the edges (x,z) and (x,y) are in different equivalence classes, so z in C; this is equivalent to C logically entails the implication xy then z. Throughout the thesis, in order to explain our work in a constructive way, we first work with the case of having only two equivalence classes and its corresponding nomenclature (modules), and then we extend the theory to work with more equivalence classes. Our main contributions are: an algorithm (with its full implementation) for the clan decomposition method; the theorems that support our approach, and examples of its application to demonstrate its usability. |
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