Signal Processing on Graphs - Contributions to an Emerging Field. (Traitement du signal sur graphes - Contributions à un domaine émergent)
Signal Processing on Graphs - Contributions to an Emerging Field. (Traitement du signal sur graphes - Contributions à un domaine émergent)
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图信号处理 - 对新兴领域的贡献。
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Benjamin Girault
中科院分区：
文献类型：
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作者：
Benjamin Girault
This dissertation introduces in its first part the field of signal processing on graphs. We start by reminding the required elements from linear algebra and spectral graph theory. Then, we define signal processing on graphs and give intuitions on its strengths and weaknesses compared to classical signal processing. In the second part, we introduce our contributions to the field. Chapter 4 aims at the study of structural properties of graphs using classical signal processing through a transformation from graphs to time series. Doing so, we take advantage of a unified method of semi-supervised learning on graphs dedicated to classification to obtain a smooth time series. Finally, we show that we can recognize in our method a smoothing operator on graph signals. Chapter 5 introduces a new translation operator on graphs defined by analogy to the classical time shift operator and verifying the key property of isometry. Our operator is compared to the two operators of the literature and its action is empirically described on several graphs. Chapter 6 describes the use of the operator above to define stationary graph signals. After giving a spectral characterization of these graph signals, we give a method to study and test stationarity on real graph signals. The closing chapter shows the strength of the matlab toolbox developed and used during the course of this PhD.
