21 September 2017 Guiding network analysis using graph slepians: an illustration for the C. Elegans connectome
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Abstract
Spectral approaches of network analysis heavily rely upon the eigendecomposition of the graph Laplacian. For instance, in graph signal processing, the Laplacian eigendecomposition is used to define the graph Fourier trans- form and then transpose signal processing operations to graphs by implementing them in the spectral domain. Here, we build on recent work that generalized Slepian functions to the graph setting. In particular, graph Slepi- ans are band-limited graph signals with maximal energy concentration in a given subgraph. We show how this approach can be used to guide network analysis; i.e., we propose a visualization that reveals network organization of a subgraph, but while striking a balance with global network structure. These developments are illustrated for the structural connectome of the C. Elegans.
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Dimitri Van De Ville, Robin Demesmaeker, Maria Giulia Preti, "Guiding network analysis using graph slepians: an illustration for the C. Elegans connectome", Proc. SPIE 10394, Wavelets and Sparsity XVII, 103941Y (21 September 2017); doi: 10.1117/12.2274814; https://doi.org/10.1117/12.2274814
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