Density Surface Module: the First Session

A density surface is a surface, which encloses the data points of a and higher density. An example of density surface for a three-dimensional normal distribution is shown in Figure 1 (the last two figures). In the figures the most dense point is in the center of the figure. The density level parameter is chosen so that the surface encloses almost all data points. The APDF-DS module computes, and visualizes density surfaces.

The APDF-DS module of the 3DVDM system can be run with the following command:

• $ 3dvdm/bin/apdf

The executable opens a VR++ window and a GUI of the density surfaces module (cf. Figure 1).

Computation of density surfaces is done in two steps: (i) the apdf tree is computed for the database, and (ii) a density surface is computed from the apdf tree. In order to compute the apdf tree one needs to select the database, the X, Y, Z attributes of the database, shape error, and the size initial partition. Once these parameters are selected the the apdf tree is computed with the press of the ``Compute PDF'' button. Density surface is visualized immediatelly after the APDF tree is computed.

The data source controls the data for which density surfaces are calculated. The estimation error controls the precision of the estimation of the probability density function (PDF) of the dataset. The density level parameter controls the level of the density surface. As the parameter changes from 0.0 to 1.0 the biggest surface (the surface, which envelops all the data points) to the smallest (the surface, which envelops only the most dense data points) is visualized.

A more elaborate discussion of the DS module and its parameters can be found in the manual of the DS module.

Screen Shots

This section presents a number of screen shots of the DS module for various datasets.

Figure 3 presents a scatter plot together with density surfaces for the click stream data for the http://www.sunsite.dk/ site. In the figures, the document dimension is mapped to the Z axe (blue axe), time dimension is mapped to the Y axe (green axe), and domain dimension is mapped to the X axe (red dimension). The red surface represents .com clicks, while the green surface represents the .dk clicks. Density surfaces show the dynamics of the clicks (increase and decrease of the number of clicks during certain time periods of the day), which is impossible to see in the scatter plot. Click on the image to see the animated version of the picture.