Prediction methods for statistical inference in graph signal processing
This thesis studies the problem of inferring topology from signal graphs. For this reason, the Master's Thesis is part of the current of thought, growing in recent years, in which the structure of the network is not assumed to be known. The problem of inferring topology is approached from two a...
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| Tipo de recurso: | tesis de maestría |
| Fecha de publicación: | 2020 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/331529 |
| Acceso en línea: | https://hdl.handle.net/2117/331529 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Signal processing Statistics signal graph estimation spectral templates statistical methods señal grafo métodos estadísticos plantillas espectrales Grafs, Teoria de Tractament del senyal Estadística Àrees temàtiques de la UPC::Enginyeria de la telecomunicació |
| Sumario: | This thesis studies the problem of inferring topology from signal graphs. For this reason, the Master's Thesis is part of the current of thought, growing in recent years, in which the structure of the network is not assumed to be known. The problem of inferring topology is approached from two angles. The first one, studies how to find the structure of a graph from spectral templates which can be noisy. Thus, from observations of the network, the spectral template of the graph that makes up the network is inferred. In previous works, like my Degree's Thesis, the algorithms for the inference of incomplete spectral templates were studied. In this Master's thesis, we go one step further by demonstrating why the techniques studied do not always work and proposing an algorithm based on LASSO to infer the network topology when the spectral templates are noisy. The proposed algorithm is compared with those previously studied obtaining better results in terms of RMSE and reliability. The second point of view addressed in this thesis is the inference of the network from statistical techniques. It is common to find networks whose nodes have some relation. These techniques are based on, from some observations of the network, trying to find the existing relationships between the different nodes of the graph. These techniques can be used in a more generic way than those based on spectral templates. Statistical methods are studied in more depth in this Master's Thesis. Initially, the Pearson correlation coefficient is explained. After studying it, some limitations are found. Thus, a new approach is proposed based on the conditional covariance. Then, it is assumed that the signals follow a Gaussian distribution which brings us to study the Maximum Likelihood estimator while considering the graph's sparsity. Although, the previous approach was improved, we are interested in finding even a better one. Hence, we study an approach based on linear regression. In this last algorithm, we include a term to promote sparsity when finding the solution. To conclude, the statistical methods studied, are compared by performing some simulations. By performing these simulations, it is observed that the best technique to infer the graph's topology is the one based on linear regression. |
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