{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,8]],"date-time":"2026-02-08T07:14:12Z","timestamp":1770534852872,"version":"3.49.0"},"reference-count":79,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2017,8,20]],"date-time":"2017-08-20T00:00:00Z","timestamp":1503187200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Informatics"],"abstract":"<jats:p>Understanding large multidimensional datasets is one of the most challenging problems in visual data exploration. One key challenge that increases the size of the exploration space is the number of views that one can generate from a single dataset, based on the use of multiple parameter values and exploration paths. Often, no such single view contains all needed insights. The question thus arises of how we can efficiently combine insights from multiple views of a dataset. We propose a set of techniques that considerably reduce the exploration effort for such situations, based on the explicit depiction of the view space, using a small multiple metaphor. We leverage this view space by offering interactive techniques that enable users to explicitly create, visualize, and follow their exploration path. This way, partial insights obtained from each view can be efficiently and effectively combined. We demonstrate our approach by applications using real-world datasets from air traffic control, software maintenance, and machine learning.<\/jats:p>","DOI":"10.3390\/informatics4030026","type":"journal-article","created":{"date-parts":[[2017,8,21]],"date-time":"2017-08-21T11:10:51Z","timestamp":1503313851000},"page":"26","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Multidimensional Data Exploration by Explicitly Controlled Animation"],"prefix":"10.3390","volume":"4","author":[{"given":"Johannes","family":"Kruiger","sequence":"first","affiliation":[{"name":"Institute Johann Bernoulli, University of Groningen, 9727 Groningen, The Netherlands"}]},{"given":"Almoctar","family":"Hassoumi","sequence":"additional","affiliation":[{"name":"ENAC\/DEVI, University of Toulouse, 31055 Toulouse, France"}]},{"given":"Hans-J\u00f6rg","family":"Schulz","sequence":"additional","affiliation":[{"name":"Institute for Computer Science, University of Rostock, 18051 Rostock, Germany"}]},{"given":"AlexandruC","family":"Telea","sequence":"additional","affiliation":[{"name":"Institute Johann Bernoulli, University of Groningen, 9727 Groningen, The Netherlands"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4318-6717","authenticated-orcid":false,"given":"Christophe","family":"Hurter","sequence":"additional","affiliation":[{"name":"ENAC\/DEVI, University of Toulouse, 31055 Toulouse, France"}]}],"member":"1968","published-online":{"date-parts":[[2017,8,20]]},"reference":[{"key":"ref_1","unstructured":"Card, S.K., Mackinlay, J.D., and Shneiderman, B. (1999). Readings in Information Visualization: Using Vision to Think, Morgan Kaufmann Publishers Inc."},{"key":"ref_2","first-page":"2600","article-title":"MoleView: An attribute and structure-based semantic lens for large element-based plots","volume":"17","author":"Hurter","year":"2011","journal-title":"IEEE TVCG"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Rao, R., and Card, S.K. (1994, January 24\u201328). The Table Lens: Merging Graphical and Symbolic Representations in an Interactive Focus+Context Visualization for Tabular Information. Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, Boston, MA, USA.","DOI":"10.1145\/191666.191776"},{"key":"ref_4","unstructured":"Telea, A. (2006, January 8\u201310). Combining Extended Table Lens and Treemap Techniques for Visualizing Tabular Data. Proceedings of the Eighth Joint Eurographics\/IEEE VGTC conference on Visualization, Lisbon, Portugal."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Brosz, J., Nacenta, M.A., Pusch, R., Carpendale, S., and Hurter, C. (2013, January 8\u201311). Transmogrification: Causal manipulation of visualizations. Proceedings of the 26th Annual ACM Symposium on User Interface Software and Technology, St. Andrews, UK.","DOI":"10.1145\/2501988.2502046"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Hurter, C., Taylor, R., Carpendale, S., and Telea, A. (2014, January 4\u20137). Color tunneling: Interactive exploration and selection in volumetric datasets. Proceedings of the 2014 IEEE Pacific Visualization Symposium, Yokohama, Japan.","DOI":"10.1109\/PacificVis.2014.61"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Lhuillier, A., Hurter, C., and Telea, A. (2017). State of the Art in Edge and Trail Bundling Techniques. Comput. Graph. Forum.","DOI":"10.1111\/cgf.13213"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1007\/BF01898350","article-title":"The plane with parallel coordinates","volume":"1","author":"Inselberg","year":"1985","journal-title":"Vis. Comput."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Inselberg, A. (2009). Parallel Coordinates, Springer.","DOI":"10.1007\/978-0-387-68628-8"},{"key":"ref_10","unstructured":"Cleveland, W.S. (1993). Visualizing Data, Hobart Press."},{"key":"ref_11","unstructured":"Borg, I., and Groenen, P. (2005). Modern Multidimensional Scaling: Theory and Applications, Springer. [2nd ed.]."},{"key":"ref_12","first-page":"2579","article-title":"Visualizing High-dimensional Data using t-SNE","volume":"9","author":"Hinton","year":"2008","journal-title":"JMLR"},{"key":"ref_13","unstructured":"Jolliffe, I.T. (2002). Principal Component Analysis, Springer. [2nd ed.]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","article-title":"A global geometric framework for nonlinear dimensionality reduction","volume":"290","author":"Tenenbaum","year":"2000","journal-title":"Science"},{"key":"ref_15","first-page":"2563","article-title":"Local Affine Multidimensional Projection","volume":"17","author":"Joia","year":"2011","journal-title":"IEEE TVCG"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kandogan, E. (2001, January 26\u201329). Visualizing Multi-Dimensional Clusters, Trends, and Outliers Using Star Coordinates. Proceedings of the Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA.","DOI":"10.1145\/502512.502530"},{"key":"ref_17","unstructured":"Kandogan, E. (2000, January 9\u201310). Star Coordinates: A Multi-Dimensional Visualization Technique with Uniform Treatment of Dimensions. Proceedings of the IEEE InfoVis 2000, Salt Lake City, UT, USA."},{"key":"ref_18","first-page":"2615","article-title":"Orthographic Star Coordinates","volume":"19","author":"Lehmann","year":"2013","journal-title":"IEEE TVCG"},{"key":"ref_19","first-page":"389","article-title":"Adaptable Radial Axes Plots for Improved Multivariate Data Visualization","volume":"36","author":"Sanchez","year":"2017","journal-title":"CGF"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1093\/biomet\/58.3.453","article-title":"The biplot graphic display of matrices with application to principal component analysis","volume":"58","author":"Gabriel","year":"1971","journal-title":"Biometrika"},{"key":"ref_21","first-page":"619","article-title":"A comparative study between RadViz and Star Coordinates","volume":"22","author":"Raya","year":"2016","journal-title":"IEEE TVCG"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1177\/1473871612439357","article-title":"Properties of normalized radial visualizations","volume":"11","author":"Daniels","year":"2012","journal-title":"Inf. Visual."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","article-title":"Nonlinear Dimensionality Reduction by Locally Linear Embedding","volume":"290","author":"Roweis","year":"2000","journal-title":"Science"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"26","DOI":"10.1016\/j.cag.2014.01.006","article-title":"Visual analysis of dimensionality reduction quality for parameterized projections","volume":"41","author":"Martins","year":"2014","journal-title":"Comput. Graph."},{"key":"ref_25","unstructured":"Tollis, I., Battista, G.D., Eades, P., and Tamassia, R. (1999). Graph Drawing: Algorithms for the Visualization of Graphs, Prentice Hall."},{"key":"ref_26","first-page":"1745","article-title":"Graph Layouts by t-SNE","volume":"36","author":"Kruiger","year":"2017","journal-title":"CGF"},{"key":"ref_27","first-page":"741","article-title":"Hierarchical edge bundles: Visualization of adjacency relations in hierarchical data","volume":"12","author":"Holten","year":"2006","journal-title":"IEEE TVCG"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2364","DOI":"10.1109\/TVCG.2011.233","article-title":"Skeleton-based edge bundling for graph visualization","volume":"17","author":"Ersoy","year":"2011","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1111\/j.1467-8659.2012.03079.x","article-title":"Graph bundling by kernel density estimation","volume":"31","author":"Hurter","year":"2012","journal-title":"Comput. Graph. Forum"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Peysakhovich, V., Hurter, C., and Telea, A. (2015, January 14\u201317). Attribute-Driven Edge Bundling for General Graphs with Applications in Trail Analysis. Proceedings of the 2015 IEEE Pacific Visualization Symposium (PacificVis), Hangzhou, China.","DOI":"10.1109\/PACIFICVIS.2015.7156354"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Lhuillier, A., Hurter, C., and Telea, A. (2017, January 18\u201321). FFTEB: Edge Bundling of Huge Graphs by the Fast Fourier Transform. Proceedings of the 10th IEEE Pacific Visualization Symposium, PacificVis 2017, Seoul, Korea.","DOI":"10.1109\/PACIFICVIS.2017.8031594"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1545","DOI":"10.1111\/cgf.13186","article-title":"Visual Exploration of Global Trade Networks with Time-Dependent and Weighted Hierarchical Edge Bundles on GPU","volume":"36","author":"Hofmann","year":"2017","journal-title":"Comput. Graph. Forum"},{"key":"ref_33","first-page":"2550","article-title":"CUBu: Universal real-time bundling for large graphs","volume":"22","author":"Codreanu","year":"2016","journal-title":"IEEE TVCG"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1006\/ijhc.2002.1017","article-title":"Animation: Can It Facilitate?","volume":"57","author":"Tversky","year":"2002","journal-title":"Int. J. Hum.-Comput. Stud."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Chevalier, F., Riche, N.H., Plaisant, C., Chalbi, A., and Hurter, C. (2016, January 7\u201310). Animations 25 Years Later: New Roles and Opportunities. Proceedings of the International Working Conference on Advanced Visual Interfaces (AVI \u201916), Bari, Italy.","DOI":"10.1145\/2909132.2909255"},{"key":"ref_36","unstructured":"Bertin, J. (1983). Semiology of Graphics, University of Wisconsin Press."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1057\/palgrave.ivs.9500170","article-title":"DataMeadow: A visual canvas for analysis of large-scale multivariate data","volume":"7","author":"Elmqvist","year":"2008","journal-title":"Inf. Vis."},{"key":"ref_38","first-page":"539","article-title":"Animation, Small Multiples, and the Effect of Mental Map Preservation in Dynamic Graphs","volume":"17","author":"Archambault","year":"2011","journal-title":"IEEE TVCG"},{"key":"ref_39","first-page":"1141","article-title":"Rolling the dice: Multidimensional visual exploration using scatterplot matrix navigation","volume":"14","author":"Elmqvist","year":"2008","journal-title":"IEEE TVCG"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"128","DOI":"10.1137\/0906011","article-title":"The grand tour: A tool for viewing multidimensional data","volume":"6","author":"Asimov","year":"1985","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0167-9473(02)00144-5","article-title":"Class visualization of high-dimensional data with applications","volume":"41","author":"Dhillon","year":"2002","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_42","first-page":"435","article-title":"Projection pursuit","volume":"13","author":"Huber","year":"1985","journal-title":"Ann. Stat."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"721","DOI":"10.1080\/02664760120098784","article-title":"Visualization of Multidimensional Data Using Modifications of the Grand Tour","volume":"29","author":"Huh","year":"2002","journal-title":"J. Appl. Stat."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"599","DOI":"10.1016\/j.neucom.2014.07.072","article-title":"Projection inspector: Assessment and synthesis of multidimensional projections","volume":"150","author":"Pagliosa","year":"2015","journal-title":"Neurocomputing"},{"key":"ref_45","unstructured":"Ebert, D., Gross, M., and Hamann, B. (1999). Image graphs\u2014A novel approach to visual data exploration. Visualization\u201999: Proceedings of the IEEE Conference on Visualization, IEEE Computer Society."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1109\/T-C.1974.224051","article-title":"A projection pursuit algorithm for exploratory data analysis","volume":"100","author":"Friedman","year":"1974","journal-title":"IEE Trans. Comput."},{"key":"ref_47","first-page":"609","article-title":"Optimal Sets of Projections of High-Dimensional Data","volume":"22","author":"Lehmann","year":"2015","journal-title":"IEEE TVCG"},{"key":"ref_48","unstructured":"Seo, J., and Shneiderman, B. (2004, January 10\u201312). A rank-by-feature framework for unsupervised multidimensional dataexploration using low dimensional projections. Proceedings of the IEEE Symposium on Information Visualization, Austin, TX, USA."},{"key":"ref_49","first-page":"831","article-title":"Selecting good views of high-dimensional data using class consistency","volume":"28","author":"Sips","year":"2009","journal-title":"CGF"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1057\/ivs.2010.2","article-title":"Techniques for precision-based visual analysis of projected data","volume":"9","author":"Schreck","year":"2010","journal-title":"Inf. Vis."},{"key":"ref_51","first-page":"1895","article-title":"Selecting coherent and relevant plots in large scatterplot matrices","volume":"31","author":"Lehmann","year":"2012","journal-title":"CGF"},{"key":"ref_52","unstructured":"Whitted, T. (1997). Design Galleries: A General Approach to Setting Parameters for Computer Graphics and Animation. ACM SIGGRAPH\u201997: Proceedings of the International Conference on Computer Graphics and Interactive Techniques, ACM Press\/Addison-Wesley Publishing Co. ."},{"key":"ref_53","first-page":"347","article-title":"Graph Multidrawing: Finding Nice Drawings Without Defining Nice","volume":"Volume 1547","author":"Whitesides","year":"1998","journal-title":"GD\u201998: Proceedings of the International Symposium on Graph Drawing"},{"key":"ref_54","unstructured":"Wu, Y., Xu, A., Chan, M.Y., Qu, H., and Guo, P. (2007, January 3\u20134). Palette-Style Volume Visualization. Proceedings of the EG\/IEEE Conference on Volume Graphics, Prague, Czech Republic."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1109\/2945.942695","article-title":"Visualization exploration and encapsulation via a spreadsheet-like interface","volume":"7","author":"Ma","year":"2001","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1111\/j.1467-8659.2009.01403.x","article-title":"Image Appearance Exploration by Model-Based Navigation","volume":"28","author":"Shapira","year":"2009","journal-title":"Comput. Graph. Forum"},{"key":"ref_57","doi-asserted-by":"crossref","unstructured":"Van Wijk, J.J., and van Overveld, C.W. (2003). Preset based interaction with high dimensional parameter spaces. Data Visualization, Springer.","DOI":"10.1007\/978-1-4615-1177-9_27"},{"key":"ref_58","first-page":"1017","article-title":"FromDaDy: Spreading data across views to support iterative exploration of aircraft trajectories","volume":"15","author":"Hurter","year":"2009","journal-title":"IEEE TVCG"},{"key":"ref_59","first-page":"1","article-title":"Image-Based Visualization: Interactive Multidimensional Data Exploration","volume":"3","author":"Hurter","year":"2015","journal-title":"Synth. Lect. Vis."},{"key":"ref_60","first-page":"564","article-title":"Least square projection: A fast high-precision multidimensional projection technique and its application to document mapping","volume":"14","author":"Paulovich","year":"2008","journal-title":"IEEE TVCG"},{"key":"ref_61","first-page":"12811290","article-title":"Two-phase mapping for projecting massive data sets","volume":"16","author":"Paulovich","year":"2010","journal-title":"IEEE TVCG"},{"key":"ref_62","unstructured":"Pekalska, E., de Ridder, D., Duin, R., and Kraaijveld, M. (1999, January 15\u201317). A new method of generalizing Sammon mapping with application to algorithm speed-up. Proceedings of the Annual Conference Advanced School for Computer Image (ASCI), Heijen, The Netherlands."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1057\/palgrave.ivs.9500069","article-title":"A pivot-based routine for improved parent-finding in hybrid MDS","volume":"3","author":"Morrison","year":"2004","journal-title":"Inf. Vis."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Faith, J. (2007, January 4\u20136). Targeted Projection Pursuit for Interactive Exploration of High-Dimensional Data Sets. Proceedings of the 11th International Conference on Information Visualization, Zurich, Switzerland.","DOI":"10.1109\/IV.2007.107"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Roberts, J.C. (2004). Exploratory Visualization with Multiple Linked Views. Exploring Geovisualization, Elsevier.","DOI":"10.1016\/B978-008044531-1\/50426-7"},{"key":"ref_66","unstructured":"North, C., and Shneiderman, B. (1997). A Taxonomy of Multiple Window Coordination, School of Computing, Univercity of Maryland. Technical Report T.R. 97-90."},{"key":"ref_67","unstructured":"Baldonaldo, M., Woodruff, A., and Kuchinsky, A. (2000, January 24\u201326). Guidelines for using multiple views in information visualization. Proceedings of the Working Conference on Advanced Visual Interfaces (AVI), Palermo, Italy."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/00401706.1987.10488204","article-title":"Brushing scatterplots","volume":"29","author":"Becker","year":"1987","journal-title":"Technometrics"},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.jvlc.2015.09.004","article-title":"Preset-based Generation and Exploration of Visualization Designs","volume":"31","author":"Schulz","year":"2015","journal-title":"J. Vis. Lang. Comput."},{"key":"ref_70","unstructured":"Liu, B., W\u00fcnsche, B., and Ropinski, T. (2010, January 17\u201321). Visualization by Example\u2014A Constructive Visual Component-based Interface for Direct Volume Rendering. Proceedings of the International Conference on Computer Graphics Theory and Applications, Angers, France."},{"key":"ref_71","doi-asserted-by":"crossref","unstructured":"Chevalier, F., Dragicevic, P., and Hurter, C. (2012, January 7\u201310). Histomages: Fully Synchronized Views for Image Editing. Proceedings of the 25th Annual ACM Symposium on User Interface Software and Technology, Cambridge, MA, USA.","DOI":"10.1145\/2380116.2380152"},{"key":"ref_72","doi-asserted-by":"crossref","unstructured":"Shepard, D. (1968, January 27\u201329). A Two-dimensional Interpolation Function for Irregularly-Spaced Data. Proceedings of the 23rd ACM National Conference, Las Vegas, NV, USA.","DOI":"10.1145\/800186.810616"},{"key":"ref_73","first-page":"2366","article-title":"A Design Space of Visualization Tasks","volume":"19","author":"Schulz","year":"2013","journal-title":"IEEE TVCG"},{"key":"ref_74","unstructured":"Shneiderman, B. (1996, January 3\u20136). The Eyes Have It: A Task by Data Type Taxonomy for Information Visualizations. Proceedings of the 1996 IEEE Symposium on Visual Languages, Boulder, CO, USA."},{"key":"ref_75","unstructured":"Kruiger, H., Hassoumi, A., Schulz, H.-J., Telea, A., and Hurter, C. (2017, August 17). Video Material for the Animation-Based Exploration. Available online: http:\/\/recherche.enac.fr\/~hurter\/SmallMultiple\/."},{"key":"ref_76","doi-asserted-by":"crossref","unstructured":"Meirelles, P., Santos, C., Miranda, J., Kon, F., Terceiro, A., and Chavez, C. (October, January 27). A study of the relationships between source code metrics and attractiveness in free software projects. Proceedings of the 2010 Brazilian Symposium on Software Engineering, Bahia, Brazil.","DOI":"10.1109\/SBES.2010.27"},{"key":"ref_77","doi-asserted-by":"crossref","first-page":"154","DOI":"10.1177\/1473871615600010","article-title":"Explaining three-dimensional dimensionality reduction plots","volume":"15","author":"Coimbra","year":"2016","journal-title":"Inf. Vis."},{"key":"ref_78","unstructured":"Lichman, M. (2017, August 17). UCI Machine Learning Repository. Available online: http:\/\/archive.ics.uci.edu\/ml."},{"key":"ref_79","doi-asserted-by":"crossref","unstructured":"Rauber, P.E., Falcao, A.X., and Telea, A.C. (2017). Projections as Visual Aids for Classification System Design. Inf. Vis.","DOI":"10.1177\/1473871617713337"}],"container-title":["Informatics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-9709\/4\/3\/26\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:42:50Z","timestamp":1760208170000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-9709\/4\/3\/26"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8,20]]},"references-count":79,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2017,9]]}},"alternative-id":["informatics4030026"],"URL":"https:\/\/doi.org\/10.3390\/informatics4030026","relation":{},"ISSN":["2227-9709"],"issn-type":[{"value":"2227-9709","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8,20]]}}}