{"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-data-under-structural-and","title":"Graph Learning from Data under Structural and Laplacian Constraints","arxiv_id":"1611.05181","date":"2016-11-16","proceeding":null,"authors":["Hilmi E. Egilmez","Eduardo Pavez","Antonio Ortega"],"abstract":"Graphs are fundamental mathematical structures used in various fields to\nrepresent data, signals and processes. In this paper, we propose a novel\nframework for learning/estimating graphs from data. The proposed framework\nincludes (i) formulation of various graph learning problems, (ii) their\nprobabilistic interpretations and (iii) associated algorithms. Specifically,\ngraph learning problems are posed as estimation of graph Laplacian matrices\nfrom some observed data under given structural constraints (e.g., graph\nconnectivity and sparsity level). From a probabilistic perspective, the\nproblems of interest correspond to maximum a posteriori (MAP) parameter\nestimation of Gaussian-Markov random field (GMRF) models, whose precision\n(inverse covariance) is a graph Laplacian matrix. For the proposed graph\nlearning problems, specialized algorithms are developed by incorporating the\ngraph Laplacian and structural constraints. The experimental results\ndemonstrate that the proposed algorithms outperform the current\nstate-of-the-art methods in terms of accuracy and computational efficiency.","url_abs":"http://arxiv.org/abs/1611.05181v3","url_pdf":"http://arxiv.org/pdf/1611.05181v3.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-data-under-structural-and","repo_url":"https://github.com/STAC-USC/Graph_Learning","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null},{"paper_slug":"graph-learning-from-data-under-structural-and","repo_url":"https://github.com/STAC-USC/graph_learning_properties","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"graph-learning","task_name":"Graph Learning"},{"task_slug":"parameter-estimation","task_name":"parameter estimation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1611.05181","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}