Vertex-frequency analysis on graphs

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• 作者：David I Shuman^a ; ^{dshuman1@macalester.edu" class="auth_mail" title="E-mail the corresponding author} ; Benjamin Ricaud^b ; ^{benjamin.ricaud@epfl.ch" class="auth_mail" title="E-mail the corresponding author} ; Pierre Vandergheynst^b ; ¹ ; ^{pierre.vandergheynst@epfl.ch" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Signal processing on graphs ; Time-frequency analysis ; Generalized translation and modulation ; Spectral graph theory ; Localization ; Clustering
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：40
• 期：2
• 页码：260-291
• 全文大小：2531 K

文摘

One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric structure of the underlying graph data domain. In this paper, we generalize one of the most important signal processing tools – windowed Fourier analysis – to the graph setting. Our approach is to first define generalized convolution, translation, and modulation operators for signals on graphs, and explore related properties such as the localization of translated and modulated graph kernels. We then use these operators to define a windowed graph Fourier transform, enabling vertex-frequency analysis. When we apply this transform to a signal with frequency components that vary along a path graph, the resulting spectrogram matches our intuition from classical discrete-time signal processing. Yet, our construction is fully generalized and can be applied to analyze signals on any undirected, connected, weighted graph.