Institute for Data Analysis and Visualization

Clustering is a powerful analysis technique used to detect structures in data sets. The output of a clustering process can be very large. However, if presented in a textual form, the amount of information that can be understood i s limited. An alternative approach is to display the data in a graphical way. An advantage of visualization is that a larger amount of information can be perceived. Supporting user interaction and manipulation of the object space enables exploration of large data sets. We present a technique for the visualization of cluster hierarchies. The input to our technique is a finite set of n-dimensional points. All points are initially placed in one cluster, which is recurisively split, creating a hieracrhy of clusters. Principal component analysis is used to determine how to optimally biset a cluster. After splitting a cluster, a local reclassification scheme based on the Gabriel graph is applied to improve the quality of the classification. As a byproduct of the generation of the cluster hierarchy, we compute and store the eigendirections. eigenvalues and local centers for each cluster at each level of the hierarchy. For the visualization of the cluster hierarchy, the user has to specify the three dimentions that are used for the rendering process. The local coordinate systems (centroids, eigenvalues, and eigendirections) of each cluster induce a local metric that can be utilized to define ''density functions''. These functions describe hyperellipsoids that we render in two different ways: (1) we apply ''ray casting'' to simulate the behavior of X-rays penetrating the density fields implied by the clusters. In order to show the different levels in the hierarchy, one can either render only thoese clusters belonging to the same level or, alternatively, use transparency to be able to see through the 'outer shell' of a cluster and see the finer, more detailed structures inside.