{"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/complete-dictionary-learning-via-ell_p-norm","title":"Complete Dictionary Learning via $\\ell_p$-norm Maximization","arxiv_id":"2002.10043","date":"2020-02-24","proceeding":null,"authors":["Yifei Shen","Ye Xue","Jun Zhang","Khaled B. Letaief","Vincent Lau"],"abstract":"Dictionary learning is a classic representation learning method that has been widely applied in signal processing and data analytics. In this paper, we investigate a family of $\\ell_p$-norm ($p>2,p \\in \\mathbb{N}$) maximization approaches for the complete dictionary learning problem from theoretical and algorithmic aspects. Specifically, we prove that the global maximizers of these formulations are very close to the true dictionary with high probability, even when Gaussian noise is present. Based on the generalized power method (GPM), an efficient algorithm is then developed for the $\\ell_p$-based formulations. We further show the efficacy of the developed algorithm: for the population GPM algorithm over the sphere constraint, it first quickly enters the neighborhood of a global maximizer, and then converges linearly in this region. Extensive experiments will demonstrate that the $\\ell_p$-based approaches enjoy a higher computational efficiency and better robustness than conventional approaches and $p=3$ performs the best.","url_abs":"https://arxiv.org/abs/2002.10043v3","url_pdf":"https://arxiv.org/pdf/2002.10043v3.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":"complete-dictionary-learning-via-ell_p-norm","repo_url":"https://github.com/yokoxue/LpDL","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"computational-efficiency","task_name":"Computational Efficiency"},{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":"representation-learning","task_name":"Representation 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}