Advertisement

Using Nested Surfaces for Visual Detection of Structures in Databases

  • Arturas Mazeika
  • Michael H. Böhlen
  • Peer Mylov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4404)

Abstract

We define, compute, and evaluate nested surfaces for the purpose of visual data mining. Nested surfaces enclose the data at various density levels, and make it possible to equalize the more and less pronounced structures in the data. This facilitates the detection of multiple structures, which is important for data mining where the less obvious relationships are often the most interesting ones. The experimental results illustrate that surfaces are fairly robust with respect to the number of observations, easy to perceive, and intuitive to interpret. We give a topology-based definition of nested surfaces and establish a relationship to the density of the data. Several algorithms are given that compute surface grids and surface contours, respectively.

Keywords

Probability Density Function Density Level Visual Detection Grid Line Data Cube 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Silverman, B.W.: Density Estimation for Statistics and Data Analysis. Chapman & Hall, London (1986)zbMATHGoogle Scholar
  2. 2.
    Keim, D.A., Kriegel, H.-P.: Visualization Techniques for Mining Large Databases: A Comparison. Transactions on Knowledge and Data Engineering, Special Issue on Data Mining 8(6), 923–938 (1996)CrossRefGoogle Scholar
  3. 3.
    Scot, D.W.: Multivariate Density Estimation. Wiley & Sons, New York (1992)Google Scholar
  4. 4.
    Wegman, E.J., Luo, Q.: Visualizing Densities. Technical Report Report No. 100, Center for Computational Statistics, George Mason University (1994)Google Scholar
  5. 5.
    van den Eijkel, G.C., Van der Lubbe, J.C.A., Backer, E.: A Modulated Parzen-Windows Approach for Probability Density Estimation. IDA (1997)Google Scholar
  6. 6.
    Bredon, G.E.: Topology and Geometry. Springer, Heidelberg (1995)Google Scholar
  7. 7.
    Shen, H., Johnson, C.: Sweeping Simplicies: A Fast Isosurface Extraction Algorithm for Unstructured Grids (1995)Google Scholar
  8. 8.
    Wilhelms, J., Van Gelder, A.: Octrees for Faster Isosurface Generation. ACM Transactions on Graphics 11(3), 201–227 (1992)zbMATHCrossRefGoogle Scholar
  9. 9.
    Devroy, L., Gyorfi, L.: Nonparametric Density Estimation. Jhon Wiley & Sons, Chichester (1984)Google Scholar
  10. 10.
    Farmen, M., Marron, J.S.: An Assesment of Finite Sample Performace of Adaptive Methods inDensity Estimation. Computational Statistics and Data Analysis (1998)Google Scholar
  11. 11.
    Jones, M.C., Wand, M.P.: Kernel Smoothing. Chapman & Hall, London (1985)Google Scholar
  12. 12.
    Lorensen, W., Cline, H.: Marchine cubes: A high resolution 3d surface construction algorithm (1987)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Arturas Mazeika
    • 1
    • 2
  • Michael H. Böhlen
    • 1
  • Peer Mylov
    • 2
  1. 1.Faculty of Computer ScienceFree University of Bozen-BolzanoBozenItaly
  2. 2.Institute of CommunicationAalborg UniversityAalborgDenmark

Personalised recommendations