1. Density Surfaces Arturas Mazeika

2. Outline of the Presentation A very brief overview of the architecture of the 3DVDM system An intuition of the density surfaces and main parameters of the method. A case study: sunsite.dk click-stream data The mysterious dataset The theory behind the density surfaces Probability density functions Kernel estimation The density surfaces method The proposals

3. 24/11-2002Arturas Mazeika, WIM3 The Idea of Density Surfaces The idea is to draw a surface, which encloses the data points of a and higher density.

4. 24/11-2002Arturas Mazeika, WIM4 Probability Density Functions PDF reflects the density of the data: higher density means higher PDF value.

5. 24/11-2002Arturas Mazeika, WIM5 Estimation of the PDF Kernel functions are drawn around all observations. All values at point x are added to obtain the overall PDF. K(x)PDF

6. 24/11-2002Arturas Mazeika, WIM6 2D 1D Density Surfaces, 1-2D Cases Surface, which encloses data points of a and higher density is called Density Surface PDF PDF+Cut planeDensity Surface

7. 24/11-2002Arturas Mazeika, WIM7 Density Surfaces, 3D Case DatasetPDF Selecting the brightness level of the PDF yields the Density Surface Different density of the structures complicates the investigation

8. 24/11-2002Arturas Mazeika, WIM8 Implementation of PDF and DS PDF is implemented as an height-unbalanced tree –We start the PDF estimation at g uniformly distributed points –the values of the PDF in between grid points are interpolated linearly –In the region of high oscillation of the PDF more grid points are added to describe the PDF

9. 24/11-2002Arturas Mazeika, WIM9 Key Parameters of the Estimation g is used to detect structures (peaks of the PDF). g has to be as small as possible, but enough to describe the peaks of the PDF g=10 is suitable in most of practical applications The split criteria identifies the range of PDF where grid inadequately describes the PDF. For each 3 neighbor grid points g L, g M, and g R we calculate the difference: if the difference is larger then e then we split the interval. Essentially, the method depends on three parameters: Estimation error e, initial number of grid points g, and split criteria

10. 24/11-2002Arturas Mazeika, WIM10 The Proposals Triangular Surface Reconstruction From a Frame of Points –Envelop the frame of points with a DS –Adjust the algorithm for the tree data structure –Real-Time considerations Separation of Structures –Non-overlapping structures –Overlapping structures Visualization of Fly Through Scenarios –A simple navigational path (a curve + view directions) –(Spiral) curve on a surface –A curve connecting dense regions (visiting hot-spots)