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Interactive bivariate mode trees for visual structure analysis

Published:28 April 2011Publication History

ABSTRACT

The number of modes in a kernel density estimation of a certain data distribution is strongly dependent on the chosen scale parameter. In this paper, we present an interactive mode tree visualization that allows to visually analyze the modality structure of a data distribution. Due to the branched structure of the bivariate mode tree, composed of many curved arcs in 3D, we need to utilize advanced techniques, including clutter removal through transparency, on demand outlier suppression or preservation, and best views, to improve the legibility of the visualization mapping.

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. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. 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.Google ScholarGoogle ScholarCross RefCross Ref
  3. Cheng, Y. 1995. Mean shift, mode seeking, and clustering. Pattern Analysis and Machine Intelligence, IEEE Transactions on 17, 8 (Aug.), 790--799. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. 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. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Eilers, P. H. C., and Goeman, J. J. 2004. Enhancing scatter-plots with smoothed densities. Bioinformatics 20, 5, 623--628. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Florek, M., and Hauser, H. 2010. Quantitative data visualization with interactive kde aurfaces. In Conference Proceedings of Spring Conference on Computer Graphics, SCCG 2010, 39--47. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 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.Google ScholarGoogle ScholarCross RefCross Ref
  8. Inselberg, A. 1985. The plane with parallel coordinates. The Visual Computer 1, 4 (Dec), 69--91.Google ScholarGoogle ScholarCross RefCross Ref
  9. Jensen, H. W. 1996. Global illumination using photon maps. In Proceedings of the eurographics workshop on Rendering techniques '96, Springer-Verlag, 21--30. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Kidwell, P., Lebanon, G., and Cleveland, W. S. 2008. Visualizing incomplete and partially ranked data. IEEE Trans. Vis. Comput. Graph. 14, 6, 1356--1363. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Klemelä, J. 2008. Mode trees for multivariate data. Journal of Computational and Graphical Statistics 17, 4 (December), 860--869.Google ScholarGoogle ScholarCross RefCross Ref
  12. Leung, Y., Zhang, J.-S., and Xu, Z.-B. 2000. Clustering by scale-space filtering. Pattern Analysis and Machine Intelligence, IEEE Transactions on 22, 12 (December), 1396--1410. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. 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.Google ScholarGoogle Scholar
  14. 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. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Marchette, D. J., and Wegman, E. J. 1997. The filtered mode tree. Journal of Computational and Graphical Statistics 6, 2 (June), 143--159.Google ScholarGoogle Scholar
  16. 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.Google ScholarGoogle Scholar
  17. Minnotte, M. C., Marchette, D. J., and Wegman, E. J. 1998. The bumpy road to the mode forest. Journal of Computational and Graphical Statistics 7, 2 (June), 239--251.Google ScholarGoogle Scholar
  18. Parzen, E. 1962. On estimation of a probability density function and mode. The Annals of Mathematical Statistics 33, 3, 1065--1076.Google ScholarGoogle ScholarCross RefCross Ref
  19. Rosenblatt, M. 1956. Remarks on some non-parametric estimates of a density function. The Annals of Mathematical Statistics 27, 832--837.Google ScholarGoogle ScholarCross RefCross Ref
  20. Scott, D. W., and Sain, S. R. 2004. Multi-dimensional density estimation. Handbook of Statistics 24, 229--263.Google ScholarGoogle ScholarCross RefCross Ref
  21. Silverman, B. W. 1981. Using kernel density estimates to investigate multimodality. Journal of the Royal Statistical Society. Series B (Methodological) 43, 1, 97--99.Google ScholarGoogle ScholarCross RefCross Ref
  22. Statlib. http://lib.stat.cmu.edu/.Google ScholarGoogle Scholar
  23. Turlach, B. A. 1993. Bandwidth selection in kernel density estimation: A review. In CORE and Institut de Statistique, 23--493.Google ScholarGoogle Scholar
  24. Vázquez, P.-P., and Sbert, M. 2003. Fast adaptive selection of best views. In ICCSA'03: Proceedings of the 2003 international conference on Computational science and its applications, Springer-Verlag, Berlin, Heidelberg, 295--305. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Ward, M. O., Rundensteiner, E. A., Cui, Q., Xie, Z., Yang, D., Wad, C., and Nguyen, D. Q. XmdvTool. http://davis.wpi.edu/xmdv/.Google ScholarGoogle Scholar
  26. Wegman, E. J. 1990. Hyperdimensional data analysis using parallel coordinates. Journal of the American Statistical Association 85, 411, 664--675.Google ScholarGoogle ScholarCross RefCross Ref
  27. Whittaker, E. T. 1923. On a new method of graduation. Proc. Edinburgh Math. Soc, 41, 63--75.Google ScholarGoogle ScholarCross RefCross Ref
  28. Wyszecki, G., and Stiles, W. S. 1982. Color Science: Concepts and Methods, Quantitative Data and Formulae, 2 ed. Wiley-Interscience, September.Google ScholarGoogle Scholar

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      • Published in

        cover image ACM Other conferences
        SCCG '11: Proceedings of the 27th Spring Conference on Computer Graphics
        April 2011
        158 pages
        ISBN:9781450319782
        DOI:10.1145/2461217

        Copyright © 2011 ACM

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        Publication History

        • Published: 28 April 2011

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        SCCG '11 Paper Acceptance Rate20of42submissions,48%Overall Acceptance Rate42of81submissions,52%
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