{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T05:29:35Z","timestamp":1770528575919,"version":"3.49.0"},"reference-count":50,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2016,5,27]],"date-time":"2016-05-27T00:00:00Z","timestamp":1464307200000},"content-version":"vor","delay-in-days":26,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"published-print":{"date-parts":[[2016,5]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>To project high\u2010dimensional data to a 2D domain, there are two well\u2010established classes of approaches: RadViz and Star Coordinates. Both are well\u2010explored in terms of accuracy, completeness, distortions, and interaction issues. We present a generalization of both RadViz and Star Coordinates such that it unifies both approaches. We do so by considering the space of all projective projections. This gives additional degrees of freedom, which we use for three things: Firstly, we define a smooth transition between RadViz and Star Coordinates allowing the user to exploit the advantages of both approaches. Secondly, we define a data\u2010dependent magic lens to explore the data. Thirdly, we optimize the new degrees of freedom to minimize distortion. We apply our approach to a number of high\u2010dimensional benchmark datasets.<\/jats:p>","DOI":"10.1111\/cgf.12845","type":"journal-article","created":{"date-parts":[[2016,5,27]],"date-time":"2016-05-27T15:11:01Z","timestamp":1464361861000},"page":"443-453","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["General Projective Maps for Multidimensional Data Projection"],"prefix":"10.1111","volume":"35","author":[{"given":"Dirk J.","family":"Lehmann","sequence":"first","affiliation":[]},{"given":"Holger","family":"Theisel","sequence":"additional","affiliation":[{"name":"Department of Simulation and Graphics University of Magdeburg Germany"}]}],"member":"311","published-online":{"date-parts":[[2016,5,27]]},"reference":[{"key":"e_1_2_9_2_2","doi-asserted-by":"crossref","unstructured":"AmorimE. BrazilE. DanielsJ. JoiaP. NonatoL. SousaM.:iLAMP: Exploring High\u2010Dimensional Spacing through Backward Multidimensional Projection.IEEE Conf. on Vis. Analytics Sci. Tech. (VAST)(2012) 53\u201362. 2","DOI":"10.1109\/VAST.2012.6400489"},{"key":"e_1_2_9_3_2","unstructured":"AsuncionA. NewmanD.:UCI Machine Learning Repository. 5"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1137\/0906011"},{"key":"e_1_2_9_5_2","unstructured":"ApperleyM. D. TzavarasI. SpenceR.:A Bifocal Display Technique For Data Presentation. InProc. of Eurographics(1982) pp.27\u201343. 3"},{"key":"e_1_2_9_6_2","doi-asserted-by":"crossref","unstructured":"BordignonA. CastroR. LopesH. LewinerT. TavaresG.:Exploratory Visualization based on Multidimensional Transfer Functions and Star Coordinates. InXIX Brazilian Symposium on Computer Graphics and Image Processing(2006) pp.273\u2013280. 9","DOI":"10.1109\/SIBGRAPI.2006.17"},{"issue":"3","key":"e_1_2_9_7_2","first-page":"155","article-title":"Grand tour and projection pursuit","volume":"4","author":"Cook D.","year":"1995","journal-title":"Journal of Computational and Statistical Computing"},{"key":"e_1_2_9_8_2","first-page":"1","volume-title":"Graphical Methods for Data Analysis","author":"Chambers J.","year":"1983"},{"key":"e_1_2_9_9_2","doi-asserted-by":"crossref","unstructured":"ChengS. MuellerK.:Improving the Fidelity of Contextual Data Layouts using a Generalized Barycentric Coordinates Framework. InIEEE Pacific Visualization(2015) pp.295\u2013302. 2","DOI":"10.1109\/PACIFICVIS.2015.7156390"},{"key":"e_1_2_9_10_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2015.2467552"},{"key":"e_1_2_9_11_2","doi-asserted-by":"crossref","unstructured":"Di CaroL. Frias\u2010MartinezV. Frias\u2010MartinezE.:Analyzing the Role of Dimension Arrangement for Data Visualization in RadViz. InProc. of the 14th Pacific\u2010Asia conference on Advances in Knowledge Discovery and Data Mining \u2013 Volume Part II(2010) pp.125\u2013132. 1 2","DOI":"10.1007\/978-3-642-13672-6_13"},{"key":"e_1_2_9_12_2","doi-asserted-by":"publisher","DOI":"10.1177\/1473871612439357"},{"key":"e_1_2_9_13_2","doi-asserted-by":"crossref","unstructured":"EndertA. HanC. MaitiD. HouseL. LemanS. NorthC.:Observation\u2010level Interaction with Statistical Models for Visual Analytics. InIEEE Conf. on Vis. Analytics Sci. and Tech. (VAST)(2011) pp.121\u2013130. 2","DOI":"10.1109\/VAST.2011.6102449"},{"key":"e_1_2_9_14_2","unstructured":"EtemadpourR. MottaR. de Souza PaivaJ. G. MinghimR. de OliveiraM. C. F. LinsenL.:Perception\u2010based Evaluation of Projection Methods for Multidimensional Data Visualization.Proc. IEEE Information Visualization(2015).2"},{"key":"e_1_2_9_15_2","first-page":"1","volume-title":"Curves and Surfaces for CAGD: A Practical Guide","author":"Farin G.","year":"2002"},{"key":"e_1_2_9_16_2","doi-asserted-by":"crossref","unstructured":"FurnasG. W. BedersonB. B.:Space\u2010Scale Diagrams: Understanding Multiscale Interfaces. InProc. of CHI\u201095(1995) pp.234\u2013241. 3","DOI":"10.1145\/223904.223934"},{"key":"e_1_2_9_17_2","doi-asserted-by":"crossref","unstructured":"FisherR. A.:The Use of Multiple Measurements in Taxonomic Problems.Annals of Eugenics(1936).5","DOI":"10.1111\/j.1469-1809.1936.tb02137.x"},{"issue":"397","key":"e_1_2_9_18_2","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1080\/01621459.1987.10478427","article-title":"Exploratory Projection Pursuit","volume":"82","author":"Friedman J. H.","year":"1987","journal-title":"Journal of the American Statistical Association"},{"key":"e_1_2_9_19_2","first-page":"1","volume-title":"SAS System for Statistical Graphics","author":"Friendly M.","year":"1991"},{"key":"e_1_2_9_20_2","doi-asserted-by":"publisher","DOI":"10.1109\/T-C.1974.224051"},{"key":"e_1_2_9_21_2","doi-asserted-by":"crossref","unstructured":"FurnasG. W.:Generalized Fisheye Views. InHuman Factors in Computing Systems CHI'86 Conference Proc. (1986) pp.16\u201323. 3","DOI":"10.1145\/22339.22342"},{"key":"e_1_2_9_22_2","unstructured":"HoffmanP. GrinsteinG. MarxK. GrosseI. StanleyE.:DNA Visual and Analytic Data Mining. InProc. of the 8th conference on Visualization(1997) pp.437\u2013ff.1"},{"key":"e_1_2_9_23_2","doi-asserted-by":"crossref","unstructured":"HoffmanP. GrinsteinG. PinkneyD.:Dimensional Anchors: a Graphic Primitive for Multidimensional Multivariate Information Visualizations. InWorkshop on New Paradigms in Information Visualization and Manipulation(1999) pp.9\u201316. 1","DOI":"10.1145\/331770.331775"},{"key":"e_1_2_9_24_2","doi-asserted-by":"crossref","unstructured":"IngramS. MunznerT. IrvineV. ToryM. BergnerS. M\u00f6llerT.:DimStiller: Workflows for Dimensional Analysis and Reduction.IEEE Conf. Vis. Analytics Sci. Tech. (2010) 3\u201310. 1","DOI":"10.1109\/VAST.2010.5652392"},{"key":"e_1_2_9_25_2","doi-asserted-by":"crossref","unstructured":"IngramS. MunznerT. OlanoM.:Glimmer: Multilevel MDS on the GPU.IEEE Trans. Vis. Comput. Graph. (2009) 249\u2013ff.2","DOI":"10.1109\/TVCG.2008.85"},{"key":"e_1_2_9_26_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2011.220"},{"key":"e_1_2_9_27_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2009.01475.x"},{"key":"e_1_2_9_28_2","unstructured":"KandoganE.:Star Coordinates: A Multi\u2010Dimensional Visualization Technique with Uniform Treatment of Dimensions.IEEE Information Visualization(2000) 9\u201312. 1 2"},{"key":"e_1_2_9_29_2","doi-asserted-by":"crossref","unstructured":"KandoganE.:Visualizing Multi\u2010Dimensional Clusters Trends and Outliers Using Star Coordinates.In Proc. of the seventh ACM SIGKDD international Conference on Knowledge Discovery and Data Mining(2001) 107\u2013116. 2","DOI":"10.1145\/502512.502530"},{"key":"e_1_2_9_30_2","doi-asserted-by":"publisher","DOI":"10.1179\/caj.1978.15.1.36"},{"issue":"2","key":"e_1_2_9_31_2","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1145\/180171.180173","article-title":"A Review and Taxonomy of Distortion\u2010oriented Presentation Techniques","volume":"1","author":"Leung Y. K.","year":"1994","journal-title":"ACM Trans. Comput.\u2010Hum. Interact."},{"issue":"12","key":"e_1_2_9_32_2","first-page":"2615","article-title":"Orthographic Star Coordinates","volume":"19","author":"Lehmann D. J.","year":"2013","journal-title":"IEEE Information Visualization"},{"key":"e_1_2_9_33_2","unstructured":"LehmannD. J. TheiselH.:Optimal Sets of Projections of High\u2010Dimensional Data.IEEE Information Visualization(2015).2"},{"key":"e_1_2_9_34_2","first-page":"301","article-title":"Continuous Representation of Projected Attribute Spaces of Multifields over Any Spatial Sampling","volume":"32","author":"Molchanov V.","year":"2013","journal-title":"Proc. Eurovis"},{"key":"e_1_2_9_35_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2013.65"},{"key":"e_1_2_9_36_2","doi-asserted-by":"crossref","unstructured":"MaK.\u2010L. TeohS. T.:StarClass: Interactive Visual Classification Using Star Coordinates. InProc. of the 3rd SIAM International Conference on Data Mining(2003) pp.178\u2013185. 9","DOI":"10.1137\/1.9781611972733.16"},{"key":"e_1_2_9_37_2","doi-asserted-by":"publisher","DOI":"10.1002\/prot.340110203"},{"key":"e_1_2_9_38_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2012.65"},{"key":"e_1_2_9_39_2","first-page":"2","volume-title":"Visualization Data for Data Mining","author":"Nov\u00e1kov\u00e1 L.","year":"2009"},{"key":"e_1_2_9_40_2","first-page":"470","volume-title":"Proc. of the 6th WSEAS International Conference on Simulation, Modelling and Optimization","author":"Nov\u00e1kov\u00e1 L.","year":"2006"},{"key":"e_1_2_9_41_2","doi-asserted-by":"publisher","DOI":"10.1007\/s10844-011-0157-4"},{"key":"e_1_2_9_42_2","doi-asserted-by":"publisher","DOI":"10.1109\/TVCG.2010.207"},{"key":"e_1_2_9_43_2","unstructured":"Rubio\u2010SanchezM. DiazF. RayaL. SanchezA.:A Comparative Study between RadViz and Star Coordinates.IEEE Trans. Vis. Comput. Graph. (2015).2"},{"key":"e_1_2_9_44_2","unstructured":"StahnkeJ. DoerkM. MullerB. ThomA.:Probing Projections: Interaction Techniques for Interpreting Arrangements and Errors of Dimensionality Reductions.IEEE Information Visualization(2015).2"},{"key":"e_1_2_9_45_2","doi-asserted-by":"crossref","unstructured":"SchneidewindJ. SipsM. KeimD.:Pixnostics: Towards Measuring the Value of Visualization.Symp. Vis. Analytics Sci. Tech. (2006) 199\u2013206. 10","DOI":"10.1109\/VAST.2006.261423"},{"key":"e_1_2_9_46_2","doi-asserted-by":"crossref","unstructured":"StreetW. WolbergW. MangasarianO.:Nuclear Feature Extraction for Breast Tumor Diagnosis.SPIE International Symposium on Electronic Imaging: Science and Technology(1993) 861\u2013870. 5","DOI":"10.1117\/12.148698"},{"key":"e_1_2_9_47_2","doi-asserted-by":"crossref","unstructured":"ShaikJ. YeasinM.:Visualization of High Dimensional Data Using an Automated 3D Star Coordinate System.IEEE International Joint Conference on Neural Networks(2006) 2318\u20132325. 9","DOI":"10.1109\/IJCNN.2006.246848"},{"key":"e_1_2_9_48_2","doi-asserted-by":"publisher","DOI":"10.1117\/12.19904"},{"key":"e_1_2_9_49_2","unstructured":"TominskiC. GladischS. KisterU. DachseltR. SchumannH.:A Survey on Interactive Lenses in Visualization. InEuroVis State\u2010of\u2010the\u2010Art Reports(2014).3"},{"key":"e_1_2_9_50_2","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00280"},{"key":"e_1_2_9_51_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02288916"}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fcgf.12845","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fcgf.12845","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.12845","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,3]],"date-time":"2025-06-03T19:49:33Z","timestamp":1748980173000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/cgf.12845"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5]]},"references-count":50,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2016,5]]}},"alternative-id":["10.1111\/cgf.12845"],"URL":"https:\/\/doi.org\/10.1111\/cgf.12845","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5]]},"assertion":[{"value":"2016-05-27","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}