{"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/the-effective-rank-a-measure-of-effective","title":"THE EFFECTIVE RANK: A MEASURE OF EFFECTIVE DIMENSIONALITY","arxiv_id":null,"date":"2007-01-01","proceeding":"EURASIP, EUPSICO 2007 1","authors":["Olivier Roy","Martin Vetterli"],"abstract":"Many signal processing algorithms include numerical problems where the solution is obtained by adjusting the value of parameters such that a specific matrix exhibits rank deficiency. Since rank minimization is generally not practicable owing to its integer nature, we propose a real-valued extension that we term effective rank. After proving some of its properties, the effective rank is provided with an operational meaning using a result on the coefficient rate of a stationary random process. Finally, the proposed measure is assessed in a practical scenario and other potential applications are suggested.","url_abs":"https://infoscience.epfl.ch/record/110188/files/RoyV07.pdf","url_pdf":"https://infoscience.epfl.ch/record/110188/files/RoyV07.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":"the-effective-rank-a-measure-of-effective","repo_url":"https://github.com/oznta/effective-rank","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}