{"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/a-unified-framework-for-structured-graph","title":"A Unified Framework for Structured Graph Learning via Spectral Constraints","arxiv_id":"1904.09792","date":"2019-04-22","proceeding":null,"authors":["Sandeep Kumar","Jiaxi Ying","José Vinícius de M. Cardoso","Daniel Palomar"],"abstract":"Graph learning from data represents a canonical problem that has received\nsubstantial attention in the literature. However, insufficient work has been\ndone in incorporating prior structural knowledge onto the learning of\nunderlying graphical models from data. Learning a graph with a specific\nstructure is essential for interpretability and identification of the\nrelationships among data. Useful structured graphs include the multi-component\ngraph, bipartite graph, connected graph, sparse graph, and regular graph. In\ngeneral, structured graph learning is an NP-hard combinatorial problem,\ntherefore, designing a general tractable optimization method is extremely\nchallenging. In this paper, we introduce a unified graph learning framework\nlying at the integration of Gaussian graphical models and spectral graph\ntheory. To impose a particular structure on a graph, we first show how to\nformulate the combinatorial constraints as an analytical property of the graph\nmatrix. Then we develop an optimization framework that leverages graph learning\nwith specific structures via spectral constraints on graph matrices. The\nproposed algorithms are provably convergent, computationally efficient, and\npractically amenable for numerous graph-based tasks. Extensive numerical\nexperiments with both synthetic and real data sets illustrate the effectiveness\nof the proposed algorithms. The code for all the simulations is made available\nas an open source repository.","url_abs":"http://arxiv.org/abs/1904.09792v1","url_pdf":"http://arxiv.org/pdf/1904.09792v1.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":"a-unified-framework-for-structured-graph","repo_url":"https://github.com/dppalomar/spectralGraphTopology","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"GPL-3.0"}},{"paper_slug":"a-unified-framework-for-structured-graph","repo_url":"https://github.com/anshul3899/Structured-Graph-Learning","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[{"task_slug":"graph-learning","task_name":"Graph Learning"}],"methods":[{"method_slug":"interpretability","method_name":"Interpretability"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":"https://app.syntology.ai/?focus=1904.09792","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}