A graph signal processing solution for defective directed graphs
Visualitza/Obre
Estadístiques de LA Referencia / Recolecta
Inclou dades d'ús des de 2022
Cita com:
hdl:2117/330654
Realitzat a/ambUSC Viterbi School of Engineering
Tipus de documentTreball Final de Grau
Data2020-06-29
Condicions d'accésAccés obert
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Abstract
The main purpose of this thesis is to nd a method that allows to systematically adapt GSP
techniques so they can be used on most non-diagonalizable graph operators.
In Chapter 1 we begin by presenting the framework in which GSP is developed, giving
some basic de nitions in the eld of graph theory and in relation with graph signals. We also
present the concept of a Graph Fourier Tranform (GFT), which will be of great importance
in the proposed solution.
Chapter 2 presents the actual motivation of the research: Why the computation of the
GFT is problematic for some directed graphs, and the speci c cases in which this happen. We
will see that the issue can not be assigned to a very speci c graph topography, and therefore
it is important to develop solutions that can be applied to any directed graph.
In Chapter 3 we introduce our proposed new method, which can be used to form, based on
the spectral decomposition of a matrix obtained through its Schur decomposition, a complete
basis of vectors that can be used as a replacement of the previously mentioned Graph Fourier
Transform. The proposed method, the Graph Schur Transform (GST), aims to o er a valid
operator to perform a spectral decomposition of a graph that can be used even in the case of
defective matrices.
Finally, in Chapter 4 we study the main properties of the proposed method and compare
them with the corresponding properties o ered by the Di usion Wavelets design. In the last
section we prove, for a large set of directed graphs, that the GST provides a valid solution for
the problem
MatèriesElectronic data processing -- Distributed processing, Graph theory, Signal theory (Telecomunication), Algebra, Processament distribuït de dades, Grafs, Teoria de, Senyal, Teoria del (Telecomunicació), Àlgebra
TitulacióGRAU EN ENGINYERIA FÍSICA (Pla 2011)
Fitxers | Descripció | Mida | Format | Visualitza |
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TFG_JuliaBarrufet.pdf | 1,524Mb | Visualitza/Obre |