{"date_published":"2006-03-01T00:00:00Z","abstract":[{"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.","lang":"eng"}],"page":"149-171","article_processing_charge":"No","scopus_import":"1","author":[{"last_name":"Bronstein","first_name":"M. M.","full_name":"Bronstein, M. M."},{"last_name":"Bronstein","id":"58f3726e-7cba-11ef-ad8b-e6e8cb3904e6","full_name":"Bronstein, Alexander","orcid":"0000-0001-9699-8730","first_name":"Alexander"},{"first_name":"R.","full_name":"Kimmel, R.","last_name":"Kimmel"},{"full_name":"Yavneh, I.","first_name":"I.","last_name":"Yavneh"}],"quality_controlled":"1","extern":"1","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_status":"published","volume":13,"publication_identifier":{"eissn":["1099-1506"],"issn":["1070-5325"]},"publisher":"Wiley","type":"journal_article","doi":"10.1002/nla.475","date_updated":"2024-11-12T08:45:09Z","article_type":"original","date_created":"2024-10-15T11:12:06Z","citation":{"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.","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>","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>.","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>.","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>","ista":"Bronstein MM, Bronstein AM, Kimmel R, Yavneh I. 2006. Multigrid multidimensional scaling. Numerical Linear Algebra with Applications. 13(2–3), 149–171.","short":"M.M. Bronstein, A.M. Bronstein, R. Kimmel, I. Yavneh, Numerical Linear Algebra with Applications 13 (2006) 149–171."},"month":"03","day":"01","title":"Multigrid multidimensional scaling","oa_version":"None","_id":"18318","year":"2006","language":[{"iso":"eng"}],"issue":"2-3","publication":"Numerical Linear Algebra with Applications","intvolume":"        13"}