{"scopus_import":"1","date_published":"2006-03-01T00:00:00Z","publication":"Numerical Linear Algebra with Applications","publisher":"Wiley","language":[{"iso":"eng"}],"quality_controlled":"1","title":"Multigrid multidimensional scaling","issue":"2-3","publication_status":"published","author":[{"last_name":"Bronstein","first_name":"M. M.","full_name":"Bronstein, M. M."},{"first_name":"Alexander","orcid":"0000-0001-9699-8730","last_name":"Bronstein","full_name":"Bronstein, Alexander","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6"},{"full_name":"Kimmel, R.","first_name":"R.","last_name":"Kimmel"},{"full_name":"Yavneh, I.","first_name":"I.","last_name":"Yavneh"}],"_id":"18318","page":"149-171","extern":"1","year":"2006","month":"03","date_created":"2024-10-15T11:12:06Z","type":"journal_article","oa_version":"None","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"        13","status":"public","abstract":[{"lang":"eng","text":"Multidimensional scaling (MDS) is a generic name for a family of algorithms that construct a configuration of points in a target metric space from information about inter-point distances measured in some other metric space. Large-scale MDS problems often occur in data analysis, representation and visualization. Solving such problems efficiently is of key importance in many applications.\r\nIn this paper we present a multigrid framework for MDS problems. We demonstrate the performance of our algorithm on dimensionality reduction and isometric embedding problems, two classical problems requiring efficient large-scale MDS. Simulation results show that the proposed approach significantly outperforms conventional MDS algorithms."}],"date_updated":"2024-11-12T08:45:09Z","publication_identifier":{"issn":["1070-5325"],"eissn":["1099-1506"]},"day":"01","volume":13,"doi":"10.1002/nla.475","article_processing_charge":"No","citation":{"apa":"Bronstein, M. M., Bronstein, A. M., Kimmel, R., &#38; Yavneh, I. (2006). Multigrid multidimensional scaling. <i>Numerical Linear Algebra with Applications</i>. Wiley. <a href=\"https://doi.org/10.1002/nla.475\">https://doi.org/10.1002/nla.475</a>","ama":"Bronstein MM, Bronstein AM, Kimmel R, Yavneh I. Multigrid multidimensional scaling. <i>Numerical Linear Algebra with Applications</i>. 2006;13(2-3):149-171. doi:<a href=\"https://doi.org/10.1002/nla.475\">10.1002/nla.475</a>","short":"M.M. Bronstein, A.M. Bronstein, R. Kimmel, I. Yavneh, Numerical Linear Algebra with Applications 13 (2006) 149–171.","ieee":"M. M. Bronstein, A. M. Bronstein, R. Kimmel, and I. Yavneh, “Multigrid multidimensional scaling,” <i>Numerical Linear Algebra with Applications</i>, vol. 13, no. 2–3. Wiley, pp. 149–171, 2006.","mla":"Bronstein, M. M., et al. “Multigrid Multidimensional Scaling.” <i>Numerical Linear Algebra with Applications</i>, vol. 13, no. 2–3, Wiley, 2006, pp. 149–71, doi:<a href=\"https://doi.org/10.1002/nla.475\">10.1002/nla.475</a>.","ista":"Bronstein MM, Bronstein AM, Kimmel R, Yavneh I. 2006. Multigrid multidimensional scaling. Numerical Linear Algebra with Applications. 13(2–3), 149–171.","chicago":"Bronstein, M. M., Alex M. Bronstein, R. Kimmel, and I. Yavneh. “Multigrid Multidimensional Scaling.” <i>Numerical Linear Algebra with Applications</i>. Wiley, 2006. <a href=\"https://doi.org/10.1002/nla.475\">https://doi.org/10.1002/nla.475</a>."},"article_type":"original"}