• Save
High dimensional Data Visualization using Star Coordinates on Three Dimensions
Upcoming SlideShare
Loading in...5
×
 

Like this? Share it with your network

Share

High dimensional Data Visualization using Star Coordinates on Three Dimensions

on

  • 6,129 views

Elio Lozano and Edgar Acuña

Elio Lozano and Edgar Acuña
University of Puerto Rico at Mayaguez, Department of Mathematics.

Statistics

Views

Total Views
6,129
Views on SlideShare
6,122
Embed Views
7

Actions

Likes
0
Downloads
0
Comments
0

3 Embeds 7

http://www.slideshare.net 4
http://www.instac.es 2
http://64.233.183.104 1

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

High dimensional Data Visualization using Star Coordinates on Three Dimensions Presentation Transcript

  • 1. High dimensional Data Visualization using Star Coordinates on Three Dimensions Elio Lozano and Edgar Acuna Department of Mathematics University of Puerto Rico at Mayaguez
  • 2. Summary
      • In this work, we have enhanced the Kandogan’s two dimensional start coordinates visualization technique, and extended it to three dimensions.
      • We introduced new parameters to improve the star coordinate visualization, making this transformation one to one. These parameters were visualized with polygons or polyhedrons, using their original data values. Overlapping points were visualized on wire frame view or with different opacity.
  • 3. Related work
    • Hoffman et al. (1997) introduced RadViz in which spring constants were used to represent relational values between points.
    • Theisel and Kreusel (1999) introduced enhanced spring model visualization using spheres around the transformed point in three dimensions.
    • Kandogan (2001) introduced the 2D star coordinate plots, where the data is arranged in a circle with axis corresponding to each feature.
    • Tee and Ma (2003) developed starclass, a visual classification, using star coordinates.
    • High dimensional data visualization techniques are very useful in supervised classification and clustering.
  • 4. Star Coordinates
    • Each dimension is shown as an axis. Assume equal angles between the axes.
    • Data value in each dimension is represented as a vector.
    • Data points are scaled to the length of the axis with
    • the minimum mapping to origin and the maximum mapping to the end
    Figure taken from Kandogan[1]
  • 5. The Iris data set
    • It contains 150 instances gropued into three classes. Each class has 50 instances.
    • Four features are used to classify the data
    • It is a benchmark for supervised classification procedures.
  • 6. 2D Star Coordinates plot of Iris data set
  • 7. Enhanced 2D Star Coordinates of Iris data set with polygons and labels
  • 8. Here the three dimensional vectors a 1 ,…a n represent the axes. Collinear points are mapped to the same point using star coordinates in three dimensions. To avoid this overlapping we introduce new parameters to represent uniquely transformed points Three dimensional Star Coordinate Transformation where: A data point D j =(d j1 ,….d jn ) is mapped on the 3 dimensional point P j given by
  • 9.
    • To avoid overlapping we introduce new parameters to represent uniquely transformed points
    • The constant c was varied between from 1000 to 10000. The transformed points can be visualized using polyhedrons in three dimensions and polygons in two dimension.
    • When many points are mapped to same point, we can visualize using wire frame view or different opacity.
  • 10. Pipeline of the 3D Star Coordinate Algorithm
  • 11. Visualization of Iris using 3D star coordinates
  • 12. Visualization of Iris using 3D star coordinates using polygons
  • 13. Visualization of Iris using 3D star coordinates and wire frames
  • 14. Visualization of two overlapped objects using different opacity
  • 15. Visualization of Iris data set with labels THE INSTANCE 42 IS DETECTED AS OUTLIER
  • 16. References
    • P. Hoffman, G. Grinstein, and D. Pinkney. Visualizing multi-dimensional clusters trends, and outliers using star coordinates. Proc. ACM SIGKDD, New York, NY, USA, pages 107–116, 2001.
    • R. Kandogan. Visualizing Multi-Dimensional Clusters Trends, and Outliers using Star Coordinates. Proceedings ACM SIGKDD ’01, pages 107–116,2001
    • S. Tee and K-L Ma, StarClass: Interactive Visual Classification Using Star Coordinates. In Proceedings of the 3rd SIAM International Conference on Data Mining, May 1-3, 2003, pp. 178-185.
    • H. Theisel and M. Kreusel. An Enhanced Spring Model for Information Visualization. In Proceedings Eurographics Ferreira and M. Gobel, 17(3):335–344, 1999.
    • E. J. Wegman. Hyperdimensional Data Analysis Using Parallel Coordinates.Journal of the American Statistical Association, 85(411):664–675,1990.