{"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/graph-learning-from-filtered-signals-graph","title":"Graph Learning from Filtered Signals: Graph System and Diffusion Kernel Identification","arxiv_id":"1803.02553","date":"2018-03-07","proceeding":null,"authors":["Hilmi E. Egilmez","Eduardo Pavez","Antonio Ortega"],"abstract":"This paper introduces a novel graph signal processing framework for building\ngraph-based models from classes of filtered signals. In our framework,\ngraph-based modeling is formulated as a graph system identification problem,\nwhere the goal is to learn a weighted graph (a graph Laplacian matrix) and a\ngraph-based filter (a function of graph Laplacian matrices). In order to solve\nthe proposed problem, an algorithm is developed to jointly identify a graph and\na graph-based filter (GBF) from multiple signal/data observations. Our\nalgorithm is valid under the assumption that GBFs are one-to-one functions. The\nproposed approach can be applied to learn diffusion (heat) kernels, which are\npopular in various fields for modeling diffusion processes. In addition, for\nspecific choices of graph-based filters, the proposed problem reduces to a\ngraph Laplacian estimation problem. Our experimental results demonstrate that\nthe proposed algorithm outperforms the current state-of-the-art methods. We\nalso implement our framework on a real climate dataset for modeling of\ntemperature signals.","url_abs":"http://arxiv.org/abs/1803.02553v1","url_pdf":"http://arxiv.org/pdf/1803.02553v1.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":"graph-learning-from-filtered-signals-graph","repo_url":"https://github.com/STAC-USC/Graph_Learning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"graph-learning","task_name":"Graph Learning"},{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1803.02553","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}