{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/when-slepian-meets-fiedler-putting-a-focus-on","title":"When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum","arxiv_id":"1701.08401","date":"2017-01-29","proceeding":null,"authors":["Dimitri Van De Ville","Robin Demesmaeker","Maria Giulia Preti"],"abstract":"The study of complex systems benefits from graph models and their analysis.\nIn particular, the eigendecomposition of the graph Laplacian lets emerge\nproperties of global organization from local interactions; e.g., the Fiedler\nvector has the smallest non-zero eigenvalue and plays a key role for graph\nclustering. Graph signal processing focusses on the analysis of signals that\nare attributed to the graph nodes. The eigendecomposition of the graph\nLaplacian allows to define the graph Fourier transform and extend conventional\nsignal-processing operations to graphs. Here, we introduce the design of\nSlepian graph signals, by maximizing energy concentration in a predefined\nsubgraph for a graph spectral bandlimit. We establish a novel link with\nclassical Laplacian embedding and graph clustering, which provides a meaning to\nlocalized graph frequencies.","url_abs":"http://arxiv.org/abs/1701.08401v2","url_pdf":"http://arxiv.org/pdf/1701.08401v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"when-slepian-meets-fiedler-putting-a-focus-on","repo_url":"https://github.com/miki998/graph_slepians","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"clustering","task_name":"Clustering"},{"task_slug":"graph-clustering","task_name":"Graph Clustering"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}