{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T03:17:38Z","timestamp":1777778258437,"version":"3.51.4"},"reference-count":23,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2003,3,1]],"date-time":"2003-03-01T00:00:00Z","timestamp":1046476800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information Visualization"],"published-print":{"date-parts":[[2003,3]]},"abstract":"<jats:p>\n                    The term \u2018proximity data\u2019 refers to data sets within which it is possible to assess the similarity of pairs of objects. Multidimensional scaling (MDS) is applied to such data and attempts to map high-dimensional objects onto low-dimensional space through the preservation of these similarity relations. Standard MDS techniques have in the past suffered from high computational complexity and, as such, could not feasibly be applied to data sets over a few thousand objects in size. Through a novel hybrid approach based upon stochastic sampling, interpolation and spring models, we have designed an algorithm running in O( N\u221aN). Using Chalmers\u2019 1996 O( N\n                    <jats:sup>2<\/jats:sup>\n                    ) spring model as a benchmark for the evaluation of our technique, we compare layout quality and run times using sets of synthetic and real data. Our algorithm executes significantly faster than Chalmers\u2019 1996 algorithm, while producing superior layouts. In reducing complexity and run time, we allow the visualisation of data sets of previously infeasible size. Our results indicate that our method is a solid foundation for interactive and visual exploration of data.\n                  <\/jats:p>","DOI":"10.1057\/palgrave.ivs.9500040","type":"journal-article","created":{"date-parts":[[2003,6,30]],"date-time":"2003-06-30T11:45:47Z","timestamp":1056973547000},"page":"68-77","source":"Crossref","is-referenced-by-count":80,"title":["Fast Multidimensional Scaling Through Sampling, Springs and Interpolation"],"prefix":"10.1177","volume":"2","author":[{"given":"Alistair","family":"Morrison","sequence":"first","affiliation":[{"name":"Department of Computing Science, University of Glasgow, Lilybank Gardens, Glasgow, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Greg","family":"Ross","sequence":"additional","affiliation":[{"name":"Department of Computing Science, University of Glasgow, Lilybank Gardens, Glasgow, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthew","family":"Chalmers","sequence":"additional","affiliation":[{"name":"Department of Computing Science, University of Glasgow, Lilybank Gardens, Glasgow, U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2003,3,1]]},"reference":[{"key":"bibr1-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4899-3184-9"},{"key":"bibr2-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1109\/VISUAL.1996.567787"},{"key":"bibr3-palgrave.ivs.9500040","unstructured":"Basalaj W. Proximity visualisation of abstract data. Ph.D. thesis, University of Cambridge Computer Laboratory, 2000."},{"key":"bibr4-palgrave.ivs.9500040","unstructured":"Buja A, Swayne DF, Littman M, Dean N, Hofmann H. XGvis: Interactive data visualization with multidimensional scaling, 2001 [WWW document] http:\/\/www.research.att.com\/areas\/stat\/xgobi\/papers\/xgvis.pdf (accessed 11th December 2002)."},{"key":"bibr5-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1109\/72.846729"},{"key":"bibr6-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1145\/122860.122887"},{"key":"bibr7-palgrave.ivs.9500040","unstructured":"Littman M, Swayne DF, Dean N, Buja A. Visualizing the embedding of objects in Euclidean space. In: Newton HJ (Ed). Computing Science and Statistics, Proceedings of the 24th Symposium on the Interface, Vol. 24. Interface Foundation of North America, 1992, 208\u2013217."},{"key":"bibr8-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1145\/365024.365097"},{"key":"bibr9-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1145\/238386.238587"},{"key":"bibr10-palgrave.ivs.9500040","doi-asserted-by":"crossref","unstructured":"Wise JA, Thomas JJ, Pennock K, Lantrip D, Pottier M, Schur A, Crow V. Visualizing the non-visual: spatial analysis and interaction with information from text documents. IEEE Symposium on Information Visualization (Atlanta, U.S.A., 1995), IEEE: New York, 1995; 51\u201358.","DOI":"10.1109\/INFVIS.1995.528686"},{"key":"bibr11-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1984.10477098"},{"key":"bibr12-palgrave.ivs.9500040","doi-asserted-by":"crossref","unstructured":"Feiner S, Beshers C. Worlds within worlds: metaphors for exploring n-dimensional virtual worlds. ACM UIST Symposium on User Interface Software and Technology 1990 (Snowbird, U.S.A. 1990), ACM Press; New York, 76\u201383.","DOI":"10.1145\/97924.97933"},{"key":"bibr13-palgrave.ivs.9500040","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1080\/10618600.1996.10474696","volume":"5","author":"Buja A","year":"1996","journal-title":"Journal of Computational and Graphical Statistics"},{"key":"bibr14-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1145\/331499.331504"},{"key":"bibr15-palgrave.ivs.9500040","first-page":"149","volume":"42","author":"Eades P.","year":"1984","journal-title":"Congressus Numerantium"},{"key":"bibr16-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1109\/72.846743"},{"key":"bibr17-palgrave.ivs.9500040","unstructured":"MacQueen J. Some methods for classification and analysis of multivariate observations. fifth Symposium on Mathematics and Probability (Berkeley, U.S.A. 1967), University of California Press: Berkeley; 281\u2013297."},{"key":"bibr18-palgrave.ivs.9500040","unstructured":"Bradley PS, Fayyad UM. Refining initial points for K-means clustering. Fifteenth International Conference on Machine Learning (Madison, U.S.A. 1998), Morgan Kaufman: San Francisco, 91\u201399."},{"key":"bibr19-palgrave.ivs.9500040","doi-asserted-by":"crossref","unstructured":"Indyk P, Motwani R. Approximate nearest neighbours \u2013 towards removing the curse of dimensionality. ACM SIGMOD 1998 (Seattle, U.S.A. 1998), ACM: New York; 604\u2013613.","DOI":"10.1145\/276698.276876"},{"key":"bibr20-palgrave.ivs.9500040","unstructured":"Gionis A, Indyk P, Motwani R. Similarity search in high dimensions via hashing. 25th International Conference on Very Large Data Bases 1999 (Edinburgh, Scotland, 1999), Morgan Kaufmann; Los Altos, CA; 518\u2013529."},{"key":"bibr21-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1023\/A:1011343115154"},{"key":"bibr22-palgrave.ivs.9500040","doi-asserted-by":"publisher","DOI":"10.1109\/INFVIS.2002.1173161"},{"key":"bibr23-palgrave.ivs.9500040","volume-title":"Combining and comparing clustering and layout algorithms","author":"Morrison A","year":"2002"}],"container-title":["Information Visualization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1057\/palgrave.ivs.9500040","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1057\/palgrave.ivs.9500040","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T19:19:04Z","timestamp":1777490344000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1057\/palgrave.ivs.9500040"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,3]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2003,3]]}},"alternative-id":["10.1057\/palgrave.ivs.9500040"],"URL":"https:\/\/doi.org\/10.1057\/palgrave.ivs.9500040","relation":{},"ISSN":["1473-8716","1473-8724"],"issn-type":[{"value":"1473-8716","type":"print"},{"value":"1473-8724","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,3]]}}}