{"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/convergence-radius-and-sample-complexity-of","title":"Convergence radius and sample complexity of ITKM algorithms for dictionary learning","arxiv_id":"1503.07027","date":"2015-03-24","proceeding":null,"authors":["Karin Schnass"],"abstract":"In this work we show that iterative thresholding and K-means (ITKM)\nalgorithms can recover a generating dictionary with K atoms from noisy $S$\nsparse signals up to an error $\\tilde \\varepsilon$ as long as the\ninitialisation is within a convergence radius, that is up to a $\\log K$ factor\ninversely proportional to the dynamic range of the signals, and the sample size\nis proportional to $K \\log K \\tilde \\varepsilon^{-2}$. The results are valid\nfor arbitrary target errors if the sparsity level is of the order of the square\nroot of the signal dimension $d$ and for target errors down to $K^{-\\ell}$ if\n$S$ scales as $S \\leq d/(\\ell \\log K)$.","url_abs":"http://arxiv.org/abs/1503.07027v4","url_pdf":"http://arxiv.org/pdf/1503.07027v4.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":"convergence-radius-and-sample-complexity-of","repo_url":"https://github.com/cristian-rusu-research/ADL-TOOLBOX","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok"}}],"tasks":[{"task_slug":"dictionary-learning","task_name":"Dictionary Learning"},{"task_slug":null,"task_name":"valid"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1503.07027","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}