{"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-parametric-dictionaries-for-graph","title":"Learning parametric dictionaries for graph signals","arxiv_id":"1401.0887","date":"2014-01-05","proceeding":null,"authors":["Dorina Thanou","David I Shuman","Pascal Frossard"],"abstract":"In sparse signal representation, the choice of a dictionary often involves a\ntradeoff between two desirable properties -- the ability to adapt to specific\nsignal data and a fast implementation of the dictionary. To sparsely represent\nsignals residing on weighted graphs, an additional design challenge is to\nincorporate the intrinsic geometric structure of the irregular data domain into\nthe atoms of the dictionary. In this work, we propose a parametric dictionary\nlearning algorithm to design data-adapted, structured dictionaries that\nsparsely represent graph signals. In particular, we model graph signals as\ncombinations of overlapping local patterns. We impose the constraint that each\ndictionary is a concatenation of subdictionaries, with each subdictionary being\na polynomial of the graph Laplacian matrix, representing a single pattern\ntranslated to different areas of the graph. The learning algorithm adapts the\npatterns to a training set of graph signals. Experimental results on both\nsynthetic and real datasets demonstrate that the dictionaries learned by the\nproposed algorithm are competitive with and often better than unstructured\ndictionaries learned by state-of-the-art numerical learning algorithms in terms\nof sparse approximation of graph signals. In contrast to the unstructured\ndictionaries, however, the dictionaries learned by the proposed algorithm\nfeature localized atoms and can be implemented in a computationally efficient\nmanner in signal processing tasks such as compression, denoising, and\nclassification.","url_abs":"http://arxiv.org/abs/1401.0887v1","url_pdf":"http://arxiv.org/pdf/1401.0887v1.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-parametric-dictionaries-for-graph","repo_url":"https://github.com/Xtina94/DictLearningCluster","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"denoising","task_name":"Denoising"},{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1401.0887","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}