Quantitative data visualization with interactive KDE surfaces

ABSTRACT

Kernel density estimation (KDE) is an established statistical concept for assessing the distributional characteristics of data that also has proven its usefulness for data visualization. In this work, we present several enhancements to such a KDE-based visualization that aim (a) at an improved specificity of the visualization with respect to the communication of quantitative information about the data and its distribution and (b) at an improved integration of such a KDE-based visualization in an interactive visualization setting, where, for example, linking and brushing is easily possible both from and to such a visualization. With our enhancements to KDE-based visualization, we can extend the utilization of this great statistical concept in the context of interactive visualization.

References

1. Artero, A. O., de Oliveira, M. C. F., and Levkowitz, H. 2004. Uncovering clusters in crowded parallel coordinates visualizations. In INFOVIS '04: Proceedings of the IEEE Symposium on Information Visualization, IEEE Computer Society, Washington, DC, USA, 81--88.
2. Bachthaler, S., and Weiskopf, D. 2008. Continuous scatterplots. IEEE Transactions on Visualization and Computer Graphics 14, 6, 1428--1435.
3. Bissantz, N., and Holzmann, H. 2007. Estimation of a quadratic regression functional using the sinc kernel. Journal of Statistical Planning and Inference 137, 3, 712--719. Special Issue on Nonparametric Statistics and Related Topics: In honor of M. L. Puri, Special Issue on Nonparametric Statistics and Related Topics: In honor of M. L. Puri.
4. Borland, D., and Taylor II, R. M. 2007. Rainbow color map (still) considered harmful. IEEE Computer Graphics and Applications 27, 2, 14--17.
5. Brandes, U., and Willhalm, T. 2002. Visualization of bibliographic networks with a reshaped landscape metaphor. In VISSYM '02: Proceedings of the symposium on Data Visualisation 2002, Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 159--164.
6. Cockburn, A., and McKenzie, B. 2002. Evaluating the effectiveness of spatial memory in 2d and 3d physical and virtual environments. In CHI '02: Proceedings of the SIGCHI conference on Human factors in computing systems, ACM, New York, NY, USA, 203--210.
7. Comaniciu, D., and Meer, P. 2002. Mean shift: a robust approach toward feature space analysis. Pattern Analysis and Machine Intelligence, IEEE Transactions on 24, 5 (August), 603--619.
8. Comaniciu, D., Ramesh, V., and Bue, A. D. 2002. Multivariate saddle point detection for statistical clustering. In ECCV '02: Proceedings of the 7th European Conference on Computer Vision-Part III, Springer-Verlag, London, UK, 561--576.
9. Dijkstra, E. W. 1959. A note on two problems in connexion with graphs. Numerische Mathematik 1, 269--271.
10. Eilers, P. H. C., and Goeman, J. J. 2004. Enhancing scatterplots with smoothed densities. Bioinformatics 20, 5, 623--628.
11. Ertl, T. 2009. The future of scientific visualization. In VRVis-Symposium -- Visual Computing Trends 2009, vol. http://www.vrvis.at/presse/pressemitteilungen-pdf/vct-2009-talk-ertl.
12. Göddeke, D. 2006. http://www.mathematik.unidortmund.de/goeddeke/gpgpu/tutorial2.html.
13. Godtliebsen, F., Marron, J. S., and Chaudhuri, P. 2002. Significance in scale space for bivariate density estimation. Journal of Computational and Graphical Statistics 11, 1, 1--21.
14. Hahne, F., Arlt, D., Sauermann, M., Majety, M., Poustka, A., Wiemann, S., and Huber, W. 2006. Statistical methods and software for the analysis of high throughput reverse genetic assays using flow cytometry readouts. Genome Biology 7 (August), R77+.
15. Inselberg, A. 1985. The plane with parallel coordinates. The Visual Computer 1, 4 (Dec), 69--91.
16. Johansson, J., Ljung, P., Jern, M., and Cooper, M. 2005. Revealing structure within clustered parallel coordinates displays. In INFOVIS '05: Proceedings of the Proceedings of the 2005 IEEE Symposium on Information Visualization, IEEE Computer Society, Washington, DC, USA, 125--132.
17. Keim, D. A. 2002. Information visualization and visual data mining. IEEE Transactions on Visualization and Computer Graphics 8, 1, 1--8.
18. Kidwell, P., Lebanon, G., and Cleveland, W. S. 2008. Visualizing incomplete and partially ranked data. IEEE Trans. Vis. Comput. Graph. 14, 6, 1356--1363.
19. Macaulay, F. R. 1931. The Whittaker-Henderson method of graduation. In The Smoothing of Time Series, NBER Chapters. National Bureau of Economic Research, Inc, December, 89--99.
20. Maciejewski, R., Rudolph, S., Hafen, R., Abusalah, A. M., Yakout, M., Ouzzani, M., Cleveland, W. S., Grannis, S. J., and Ebert, D. S. 2009. A visual analytics approach to understanding spatiotemporal hotspots. IEEE Transactions on Visualization and Computer Graphics 99, 2.
21. Maciejewski, R., Woo, I., Chen, W., and Ebert, D. 2009. Structuring feature space: A non-parametric method for volumetric transfer function generation. IEEE Transactions on Visualization and Computer Graphics 15, 6, 1473--1480.
22. Minnotte, M. C., and Scott, D. W. 1993. The mode tree: A tool for visualization of nonparametric density features. Journal of Computational and Graphical Statistics 2, 51--68.
23. Novotny, M., and Hauser, H. 2006. Outlier-preserving focus+context visualization in parallel coordinates. IEEE Transactions on Visualization and Computer Graphics 12, 5, 893--900.
24. Parzen, E. 1962. On estimation of a probability density function and mode. The Annals of Mathematical Statistics 33, 3, 1065--1076.
25. Phong, B. T. 1975. Illumination for computer generated pictures. Commun. ACM 18, 6 (June), 311--317.
26. Rosenblatt, M. 1956. Remarks on some non-parametric estimates of a density function. The Annals of Mathematical Statistics 27, 832--837.
27. Scott, D. W., and Sain, S. R. 2004. "Multi-Dimensional Density Estimation". Elsevier, 229--263.
28. Scott, D. W. 1985. Average shifted histograms: effective non-parametric estimators in several dimensions. Ann. Statist, 13, 1024--1040.
29. Silverman, B. W. 1986. Density Estimation for Statistics and Data Analysis. Chapman & Hall/CRC, April.
30. Spence, R. 2001. Information visualization. ACM Press books. Addison-Wesley, Harlow, England.
31. Statlib. Statlib. http://lib.stat.cmu.edu/.
32. Tory, M., Sprague, D., Wu, F., So, W. Y., and Munzner, T. 2007. Spatialization design: Comparing points and landscapes. IEEE Transactions on Visualization and Computer Graphics 13, 6, 1262--1269.
33. Tory, M., Swindells, C., and Dreezer, R. 2009. Comparing dot and landscape spatializations for visual memory differences. IEEE Transactions on Visualization and Computer Graphics 15, 1033--1040.
34. Turlach, B. A. 1993. Bandwidth selection in kernel density estimation: A review. In CORE and Institut de Statistique, 23--493.
35. Ward, M. O., Rundensteiner, E. A., Cui, Q., Xie, Z., Yang, D., Wad, C., and Nguyen, D. Q., 2009. XmdvTool.
36. Ware, C. 2004. Information Visualization: Perception for Design. Morgan Kaufmann Publishers Inc., San Francisco, CA, USA.
37. Wegman, E. J. 1990. Hyperdimensional data analysis using parallel coordinates. Journal of the American Statistical Association 85, 411, 664--675.
38. Whittaker, E. T. 1923. On a new method of graduation. Proc. Edinburgh Math. Soc, 41, 63--75.
39. Wyszecki, G., and Stiles, W. S. 1982. Color Science: Concepts and Methods, Quantitative Data and Formulae, 2 ed. Wiley-Interscience, September.

Index Terms

• Computing methodologies

  • Computer graphics

    • Image manipulation

    • Rendering