{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T03:15:11Z","timestamp":1777778111781,"version":"3.51.4"},"reference-count":71,"publisher":"SAGE Publications","issue":"2","license":[{"start":{"date-parts":[[2015,9,14]],"date-time":"2015-09-14T00:00:00Z","timestamp":1442188800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Information Visualization"],"published-print":{"date-parts":[[2016,4]]},"abstract":"<jats:p>Understanding three-dimensional projections created by dimensionality reduction from high-variate datasets is very challenging. In particular, classical three-dimensional scatterplots used to display such projections do not explicitly show the relations between the projected points, the viewpoint used to visualize the projection, and the original data variables. To explore and explain such relations, we propose a set of interactive visualization techniques. First, we adapt and enhance biplots to show the data variables in the projected three-dimensional space. Next, we use a set of interactive bar chart legends to show variables that are visible from a given viewpoint and also assist users to select an optimal viewpoint to examine a desired set of variables. Finally, we propose an interactive viewpoint legend that provides an overview of the information visible in a given three-dimensional projection from all possible viewpoints. Our techniques are simple to implement and can be applied to any dimensionality reduction technique. We demonstrate our techniques on the exploration of several real-world high-dimensional datasets.<\/jats:p>","DOI":"10.1177\/1473871615600010","type":"journal-article","created":{"date-parts":[[2015,9,14]],"date-time":"2015-09-14T20:48:54Z","timestamp":1442263734000},"page":"154-172","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":38,"title":["Explaining three-dimensional dimensionality reduction plots"],"prefix":"10.1177","volume":"15","author":[{"given":"Danilo B","family":"Coimbra","sequence":"first","affiliation":[{"name":"University of S\u00e3o Paulo, S\u00e3o Carlos, Brazil"},{"name":"University of Groningen, Groningen, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rafael M","family":"Martins","sequence":"additional","affiliation":[{"name":"University of S\u00e3o Paulo, S\u00e3o Carlos, Brazil"},{"name":"University of Groningen, Groningen, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T\u00e1cito TAT","family":"Neves","sequence":"additional","affiliation":[{"name":"University of S\u00e3o Paulo, S\u00e3o Carlos, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alexandru C","family":"Telea","sequence":"additional","affiliation":[{"name":"University of Groningen, Groningen, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fernando V","family":"Paulovich","sequence":"additional","affiliation":[{"name":"University of S\u00e3o Paulo, S\u00e3o Carlos, Brazil"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2015,9,14]]},"reference":[{"key":"bibr1-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2008.153"},{"key":"bibr2-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2009.131"},{"key":"bibr3-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/MCG.2010.102"},{"key":"bibr4-1473871615600010","first-page":"324","volume-title":"Proceedings of the ACM (CHI 12)","author":"Endert A"},{"key":"bibr5-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1016\/0306-4573(93)90024-8"},{"key":"bibr6-1473871615600010","first-page":"282","volume-title":"Proceedings of the IEEE information visualization","author":"Paulovich FV"},{"key":"bibr7-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1057\/palgrave.ivs.9500099"},{"key":"bibr8-1473871615600010","first-page":"163","volume-title":"Proceedings of the ACM SIGMOD international conference on management of data","author":"Faloutsos C"},{"key":"bibr9-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2011.220"},{"key":"bibr10-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2009.140"},{"key":"bibr11-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.70443"},{"key":"bibr12-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.170"},{"key":"bibr13-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.70569"},{"key":"bibr14-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.207"},{"key":"bibr15-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03100.x"},{"key":"bibr16-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1023\/A:1012968507789"},{"key":"bibr17-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2013.153"},{"key":"bibr18-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijhcs.2005.02.001"},{"key":"bibr19-1473871615600010","volume-title":"Principal component analysis","author":"Jolliffe IT","year":"2002"},{"key":"bibr20-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1016\/j.cag.2014.01.006"},{"key":"bibr21-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01960.x"},{"key":"bibr22-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1007\/BF02289530"},{"key":"bibr23-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1126\/science.290.5500.2323"},{"key":"bibr24-1473871615600010","first-page":"705","volume-title":"Advances in neural information processing systems","volume":"15","author":"Silva V","year":"2003"},{"key":"bibr25-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1126\/science.290.5500.2319"},{"key":"bibr26-1473871615600010","volume-title":"Sparse multidimensional scaling using landmark points","author":"Silva V","year":"2004"},{"key":"bibr27-1473871615600010","first-page":"42","volume-title":"Proceedings of the graph drawing","author":"Brandes U"},{"key":"bibr28-1473871615600010","first-page":"239","volume-title":"Proceedings of the 12th international symposium GD","author":"Gansner ER"},{"key":"bibr29-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1969.222678"},{"key":"bibr30-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1002\/nla.475"},{"key":"bibr31-1473871615600010","first-page":"221","volume-title":"In Fifth Annual Conference of the Advanced School for Computing and Imaging","author":"Pekalska E","year":"1999"},{"key":"bibr32-1473871615600010","first-page":"149","volume":"42","author":"Eades P","year":"1984","journal-title":"Congr Numer"},{"key":"bibr33-1473871615600010","first-page":"127","volume-title":"Proceedings of the IEEE visualization","author":"Chalmers M"},{"key":"bibr34-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2007.70580"},{"key":"bibr35-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2008.85"},{"key":"bibr36-1473871615600010","first-page":"388","volume-title":"Proceedings of the IEEE information visualization","author":"Jourdan F"},{"key":"bibr37-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1057\/palgrave.ivs.9500054"},{"key":"bibr38-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2014.07.071"},{"key":"bibr39-1473871615600010","unstructured":"Sorzano C, Vargas J, Pascual-Montano A. A survey of dimensionality reduction techniques, 2014, http:\/\/arxiv.org\/pdf\/1403.2877"},{"key":"bibr40-1473871615600010","unstructured":"Van der Maaten L, Postma E, van den Herik H. Dimensionality reduction: a comparative review. J Mach Learn Res 2009; 10(1): 66\u201371 (Extended version), http:\/\/www.iai.uni-bonn.de\/~jz\/dimensionality_reduction_a_comparative_review.pdf"},{"key":"bibr41-1473871615600010","volume-title":"Biplots","volume":"54","author":"Gower JC","year":"1995"},{"key":"bibr42-1473871615600010","volume-title":"Biplots in practice","author":"Greenacre M","year":"2010"},{"key":"bibr43-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1002\/9780470973196"},{"key":"bibr44-1473871615600010","first-page":"652","volume-title":"Encyclopedia of measurement and statistics","author":"Abdi H","year":"2007"},{"key":"bibr45-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1111\/cgf.12194"},{"key":"bibr46-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2005.850151"},{"key":"bibr47-1473871615600010","first-page":"43","volume-title":"Proceedings of the IEEE visual analytics science and technology (VAST)","author":"Anand A"},{"key":"bibr48-1473871615600010","first-page":"671","volume-title":"Proceedings of 34th Conf of the cognitive science society (CogSci)","author":"Lewis J","year":"2012"},{"key":"bibr49-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1057\/ivs.2010.2"},{"key":"bibr50-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2006.11.018"},{"key":"bibr51-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2011.229"},{"key":"bibr52-1473871615600010","first-page":"49","volume-title":"Proceedings of the second international conference on coordinated and multiple views in exploratory visualization (CMV IEEE)","author":"Piringer H"},{"key":"bibr53-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01477.x"},{"key":"bibr54-1473871615600010","first-page":"327","volume-title":"Proceedings of the IEEE Pacific visualization symposium","author":"Hurter C"},{"key":"bibr55-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2011.201"},{"key":"bibr56-1473871615600010","first-page":"139","volume-title":"Proceedings of the IEEE information visualization","author":"Tavanti M"},{"key":"bibr57-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1006\/ijhc.2000.0417"},{"key":"bibr58-1473871615600010","volume-title":"Spatial metaphors for browsing large data archives","author":"Fabricant S","year":"2000"},{"key":"bibr59-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.197"},{"key":"bibr60-1473871615600010","unstructured":"Sanftmann H. 3D visualization of multivariate data, 2014, http:\/\/elib.uni-stuttgart.de\/opus\/volltexte\/2012\/7807"},{"key":"bibr61-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1145\/2590349"},{"key":"bibr62-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2012.35"},{"key":"bibr63-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2012.03126.x"},{"key":"bibr64-1473871615600010","volume-title":"Introduction to modern information retrieval","author":"Salton G","year":"1986"},{"key":"bibr65-1473871615600010","unstructured":"Brewer C, Harrower M. ColorBrewer, 2014, http:\/\/www.colorbrewer.org"},{"key":"bibr66-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1016\/j.dss.2009.05.016"},{"key":"bibr67-1473871615600010","unstructured":"Norman M, Whalen D. IEEE visualization 2008 contest data, 2013, http:\/\/sciviscontest.ieeevis.org\/2008"},{"key":"bibr68-1473871615600010","unstructured":"Frank A, Asuncion A. UCI machine learning archive, 2013, http:\/\/archive.ics.uci.edu\/ml\/"},{"key":"bibr69-1473871615600010","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2011.01958.x"},{"key":"bibr70-1473871615600010","doi-asserted-by":"crossref","unstructured":"Meirelles P, Santos C, Miranda J, A study of the relationships between source code metrics and attractiveness in free software projects. In: Proceedings of the Brazilian symposium on software engineering (SBES), 2012, pp. 11\u201320, http:\/\/flossmole.org","DOI":"10.1109\/SBES.2010.27"},{"key":"bibr71-1473871615600010","volume-title":"Object-oriented metrics in practice","author":"Lanza M","year":"2006"}],"container-title":["Information Visualization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1473871615600010","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/1473871615600010","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/1473871615600010","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T19:18:42Z","timestamp":1777490322000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/1473871615600010"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,9,14]]},"references-count":71,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,4]]}},"alternative-id":["10.1177\/1473871615600010"],"URL":"https:\/\/doi.org\/10.1177\/1473871615600010","relation":{},"ISSN":["1473-8716","1473-8724"],"issn-type":[{"value":"1473-8716","type":"print"},{"value":"1473-8724","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,9,14]]}}}