Visualizing high-dimensional data on a 2D canvas is generally challenging. It becomes significantly more difficult when multiple time-steps are to be presented, as the visual clutter quickly increases. Moreover, the challenge to perceive the significant temporal evolution is even greater. In this paper, we present a method to plot temporal high-dimensional data in a static scatterplot; it uses the established PCA technique to project data from multiple time-steps. The key idea is to extend each individual displacement prior to applying PCA, so as to skew the projection process, and to set a projection plane that balances the directions of temporal change and spatial variance. We present numerous examples and various visual cues to highlight the data trajectories, and demonstrate the effectiveness of the method for visualizing temporal data.
Archambault, D.; Purchase, H.; Pinaud, B. Animation, small multiples, and the effect of mental map preservation in dynamic graphs. IEEE Transactions on Visualization and Computer Graphics Vol. 17, No. 4, 539–552, 2011.
Rauber, P. E.; Falcâo, A. X.; Telea, A. C. Visualizing time-dependent data using dynamic t-SNE. In: Proceedings of the Eurographics Conference on Visualization (Short Papers), 73–77, 2016.
Tufte, E. Envisioning Information. Graphics Press Cheshire, 1990.
Keim, D. A. Information visualization and visual data mining. IEEE Transactions on Visualization and Computer Graphics Vol. 8, No. 1, 1–8, 2002.
Liu, S. S.; Maljovec, D.; Wang, B.; Bremer, P. T.; Pascucci, V. Visualizing high-dimensional data: Advances in the past decade. IEEE Transactions on Visualization and Computer Graphics Vol. 23, No. 3, 1249–1268, 2017.
Inselberg, A. The plane with parallel coordinates. The Visual Computer Vol. 1, No. 2, 69–91, 1985.
Kandogan, E. Star coordinates: A multi-dimensional visualization technique with uniform treatment of dimensions. In: Proceedings of the IEEE Information Visualization Symposium, Vol. 650, 22, 2000.
Keim, D. A.; Kriegel, H. P. VisDB: Database exploration using multidimensional visualization. IEEE Computer Graphics and Applications Vol. 14, No. 5, 40–49, 1994.
Chernoff, H. The use of faces to represent points in k-dimensional space graphically. Journal of the American Statistical Association Vol. 68, No. 342, 361–368, 1973.
Wang, Y. H.; Chen, X.; Ge, T.; Bao, C.; Sedlmair, M.; Fu, C. W.; Deussen, O.; Chen, B. Optimizing color assignment for perception of class separability in multiclass scatterplots. IEEE Transactions on Visualization and Computer Graphics Vol. 25, No. 1, 820–829, 2019.
Mayorga, A.; Gleicher, M. Splatterplots: Overcoming overdraw in scatter plots. IEEE Transactions on Visualization and Computer Graphics Vol. 19, No. 9, 1526–1538, 2013.
Lu, M.; Wang, S. Q.; Lanir, J.; Fish, N.; Yue, Y.; Cohen-Or, D.; Huang, H. Winglets: Visualizing association with uncertainty in multi-class scatterplots. IEEE Transactions on Visualization and Computer Graphics Vol. 26, No. 1, 770–779, 2020.
Chan, Y. H.; Correa, C. D.; Ma, K. L. The generalized sensitivity scatterplot. IEEE Transactions on Visualization and Computer Graphics Vol. 19, No. 10, 1768–1781, 2013.
Wilkinson, L.; Anand, A.; Grossman, R. High-dimensional visual analytics: Interactive exploration guided by pairwise views of point distributions. IEEE Transactions on Visualization and Computer Graphics Vol. 12, No. 6, 1363–1372, 2006.
Elmqvist, N.; Dragicevic, P.; Fekete, J. D. Rolling the dice: Multidimensional visual exploration using scatterplot matrix navigation. IEEE Transactions on Visualization and Computer Graphics Vol. 14, No. 6, 1539–1148, 2008.
Im, J. F.; McGuffin, M. J.; Leung, R. GPLOM: The generalized plot matrix for visualizing multidimensional multivariate data. IEEE Transactions on Visualization and Computer Graphics Vol. 19, No. 12, 2606–2614, 2013.
Dang, T. N.; Wilkinson, L. ScagExplorer: Exploring scatterplots by their scagnostics. In: Proceedings of the IEEE Pacific Visualization Symposium, 73–80, 2014
Jolliffe, I. Principal Component Analysis. Springer Berlin Heidelberg, 1094–1096, 2011.
Van der Maaten, L.; Hinton, G. Visualizing data using t-SNE. Journal of Machine Learning Research Vol. 9, No. 86, 2579–2605, 2008.
De Leeuw, J. Multidimensional scaling. 2000.
McInnes, L.; Healy, J.; Melville, J. UMAP: Uniform manifold approximation and projection for dimension reduction. arXiv preprint arXiv:1802.03426, 2018.
Nonato, L. G.; Aupetit, M. Multidimensional projection for visual analytics: Linking techniques with distortions, tasks, and layout enrichment. IEEE Transactions on Visualization and Computer Graphics Vol. 25, No. 8, 2650–2673, 2019.
Beck, F.; Burch, M.; Diehl, S.; Weiskopf, D. A taxonomy and survey of dynamic graph visualization. Computer Graphics Forum Vol. 36, No. 1, 133–159, 2017.
Krstajić, M.; Keim, D. A. Visualization of streaming data: Observing change and context in information visualization techniques. In: Proceedings of the IEEE International Conference on Big Data, 41–47, 2013.
Bach, B.; Pietriga, E.; Fekete, J. D. GraphDiaries: Animated transitions and temporal navigation for dynamic networks. IEEE Transactions on Visualization and Computer Graphics Vol. 20, No. 5, 740–754, 2014.
Liu, S. X.; Yin, J. L.; Wang, X. T.; Cui, W. W.; Cao, K. L.; Pei, J. Online visual analytics of text streams. IEEE Transactions on Visualization and Computer Graphics Vol. 22, No. 11, 2451–2466, 2016.
Fisher, D. Animation for visualization: Opportunities and drawbacks. In: Beautiful Visualization. O’Reilly Media, 329–352, 2010.
Wang, Y.; Archambault, D.; Scheidegger, C. E.; Qu, H. M. A vector field design approach to animated transitions. IEEE Transactions on Visualization and Computer Graphics Vol. 24, No. 9, 2487–2500, 2018.
Fujiwara, T.; Chou, J. K.; Shilpika, S.; Xu, P. P.; Ren, L.; Ma, K. L. An incremental dimensionality reduction method for visualizing streaming multidimensional data. IEEE Transactions on Visualization and Computer Graphics Vol. 26, No. 1, 418–428, 2020.
Alvarez, G. A.; Franconeri, S. L. How many objects can you track: Evidence for a resource-limited attentive tracking mechanism. Journal of Vision Vol. 7, No. 13, 14, 2007.
Crnovrsanin, T.; Muelder, C.; Correa, C.; Ma, K. Proximity-based visualization of movement trace data. In: Proceedings of the IEEE Symposium on Visual Analytics Science and Technology, 11–18, 2009.
Jackle, D.; Fischer, F.; Schreck, T.; Keim, D. A. Temporal MDS plots for analysis of multivariate data. IEEE Transactions on Visualization and Computer Graphics Vol. 22, No. 1, 141–150, 2016.
Wulms, J.; Buchmüller, J.; Meulemans, W.; Verbeek, K.; Speckmann, B. Spatially and temporally coherent visual summaries. arXiv preprint arXiv:1912.00719, 2019.
Hong, D.; Fessler, J. A.; Balzano, L. Optimally weighted PCA for high-dimensional heteroscedastic data. arXiv preprint arXiv:1810.12862, 2018.
Robertson, G.; Fernandez, R.; Fisher, D.; Lee, B.; Stasko, J. Effectiveness of animation in trend visualization. IEEE Transactions on Visualization and Computer Graphics Vol. 14, No. 6, 1325–1332, 2008.
This work was supported in part by the Israel Science Foundation (Grant No. 2366/16 and 2472/17).
Or Patashnik is a computer science M.Sc. student in Tel-Aviv University. She received her B.Sc. cum laude in computer science and mathematics from Tel-Aviv University in 2015.
Min Lu is an assistant professor at Shenzhen University. She received her B.Sc. degree in computer engineering from Beijing Normal University, China, in 2011, and received her Ph.D. degree in computer science from EECS, Peking University in 2017. Her major research interests include visualization methodology and visual analytics. More information can be found at https://deardeer.github.io/.
Amit H. Bermano has been a senior lecturer (assistant professor) in the School of Computer Science in Tel-Aviv University since 2018. Previously, he was a postdoctoral researcher in the Princeton Graphics Group (2016-2018), and a postdoctoral researcher at Disney Research Zurich (2015). He conducted his Ph.D. studies at ETH Zurich in collaboration with Disney Research Zurich (2011-2015). His master and bachelor degrees were obtained at the Technion—Israel Institute of Technology.
Daniel Cohen-Or is a professor in the School of Computer Science. He received his B.Sc. cum laude in mathematics and computer science (1985), and his M.Sc. cum laude in computer science (1986) from Ben-Gurion University, and his Ph.D. degree from the Department of Computer Science (1991) of the State University of New York at Stony Brook. He is on the editorial boards of a number of international journals, and a member of many program committees of international conferences. He was the recipient of a Eurographics Outstanding Technical Contributions Award in 2005, and an ACM SIGGRAPH Computer Graphics Achievement Award in 2018. In 2013 he received the People’s Republic of China Friendship Award. In 2015 he was named a Thomson Reuters Highly Cited Researcher. In 2019 he won the Kadar Family Award for Outstanding Research. In 2020 he received the Eurographics Distinguished Career Award. His research interests are in computer graphics, in particular, synthesis, processing, and modeling techniques. His current main interests are in image synthesis, motion and transformations, shapes, surfaces, analysis and reconstruction, and information visualization.
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Patashnik, O., Lu, M., Bermano, A.H. et al. Temporal scatterplots. Comp. Visual Media 6, 385–400 (2020). https://doi.org/10.1007/s41095-020-0197-1
- temporal data
- visual clutter
- principle component analysis (PCA)