{"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/learning-laplacian-matrix-in-smooth-graph","title":"Learning Laplacian Matrix in Smooth Graph Signal Representations","arxiv_id":"1406.7842","date":"2014-06-30","proceeding":null,"authors":["Xiaowen Dong","Dorina Thanou","Pascal Frossard","Pierre Vandergheynst"],"abstract":"The construction of a meaningful graph plays a crucial role in the success of\nmany graph-based representations and algorithms for handling structured data,\nespecially in the emerging field of graph signal processing. However, a\nmeaningful graph is not always readily available from the data, nor easy to\ndefine depending on the application domain. In particular, it is often\ndesirable in graph signal processing applications that a graph is chosen such\nthat the data admit certain regularity or smoothness on the graph. In this\npaper, we address the problem of learning graph Laplacians, which is equivalent\nto learning graph topologies, such that the input data form graph signals with\nsmooth variations on the resulting topology. To this end, we adopt a factor\nanalysis model for the graph signals and impose a Gaussian probabilistic prior\non the latent variables that control these signals. We show that the Gaussian\nprior leads to an efficient representation that favors the smoothness property\nof the graph signals. We then propose an algorithm for learning graphs that\nenforces such property and is based on minimizing the variations of the signals\non the learned graph. Experiments on both synthetic and real world data\ndemonstrate that the proposed graph learning framework can efficiently infer\nmeaningful graph topologies from signal observations under the smoothness\nprior.","url_abs":"http://arxiv.org/abs/1406.7842v3","url_pdf":"http://arxiv.org/pdf/1406.7842v3.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":"learning-laplacian-matrix-in-smooth-graph","repo_url":"https://github.com/Anou9531/Laplacian","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"learning-laplacian-matrix-in-smooth-graph","repo_url":"https://github.com/ktran1/Leant_Laplacian","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"graph-learning","task_name":"Graph Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}