2017/01/31 by Dimitri Van De Ville, Robin Demesmaeker, Maria Giulia Preti · 3 citations
Computer Science · Neuroscience · #Advanced Graph Neural Networks #Functional Brain Connectivity Studies #Graph Theory and Algorithms #cs.CV #cs.LG
paper · pdf · doi:10.1109/lsp.2017.2704359
4 pages, 5 figures, submitted to IEEE Signal Processing Letters
openalex created_date 2017/02/10 · arxiv created 2017/03/21 · openalex publication_date 2017/05/15 · arxiv updated 2017/06/28 · openalex updated_date 2026/07/28
The study of complex systems benefits from graph models and their analysis. In particular, the eigendecomposition of the graph Laplacian lets emerge properties of global organization from local interactions; e.g., the Fiedler vector has the smallest non-zero eigenvalue and plays a key role for graph clustering. Graph signal processing focusses on the analysis of signals that are attributed to the graph nodes. The eigendecomposition of the graph Laplacian allows to define the graph Fourier transform and extend conventional signal-processing operations to graphs. Here, we introduce the design of Slepian graph signals, by maximizing energy concentration in a predefined subgraph for a graph spectral bandlimit. We establish a novel link with classical Laplacian embedding and graph clustering, which provides a meaning to localized graph frequencies.