Efficient Point Clustering for Visualization

The visualization of large spatial point data sets constitutes a problem with respect to runtime and quality. A visualization of raw data often leads to occlusion and clutter and thus a loss of information. Furthermore, particularly mobile devices have problems in displaying millions of data items. Often, thinning via sampling is not the optimal choice because users want to see distributional patterns, cardinalities and outliers. In particular for visual analytics, an aggregation of this type of data is very valuable for providing an interactive user experience. This thesis defines the problem of visual point clustering that leads to proportional circle maps. It furthermore introduces a set of quality measures that assess different aspects of resulting circle representations. The Circle Merging Quadtree constitutes a novel and efficient method to produce visual point clusterings via aggregation. It is able to outperform comparable methods in terms of runtime and also by evaluating it with the aforementioned quality measures. Moreover, the introduction of a preprocessing step leads to further substantial performance improvements and a guaranteed stability of the Circle Merging Quadtree. This thesis furthermore addresses the incorporation of miscellaneous attributes into the aggregation. It discusses means to provide statistical values for numerical and textual attributes that are suitable for side-views such as plots and data tables. The incorporation of multiple data sets or data sets that contain class attributes poses another problem for aggregation and visualization. This thesis provides methods for extending the Circle Merging Quadtree to output pie chart maps or maps that contain circle packings. For the latter variant, this thesis provides results of a user study that investigates the methods and the introduced quality criteria. In the context of providing methods for interactive data visualization, this thesis finally presents the VAT System, where VAT stands for visualization, analysis and transformation. This system constitutes an exploratory geographical information system that implements principles of visual analytics for working with spatio-temporal data. This thesis details on the user interface concept for facilitating exploratory analysis and provides the results of two user studies that assess the approach

A Phase Field Model for Continuous Clustering on Vector Fields

A new method for the simplification of flow fields is presented. It is based on continuous clustering. A well-known physical clustering model, the Cahn Hilliard model, which describes phase separation, is modified to reflect the properties of the data to be visualized. Clusters are defined implicitly as connected components of the positivity set of a density function. An evolution equation for this function is obtained as a suitable gradient flow of an underlying anisotropic energy functional. Here, time serves as the scale parameter. The evolution is characterized by a successive coarsening of patterns-the actual clustering-during which the underlying simulation data specifies preferable pattern boundaries. We introduce specific physical quantities in the simulation to control the shape, orientation and distribution of the clusters as a function of the underlying flow field. In addition, the model is expanded, involving elastic effects. In the early stages of the evolution shear layer type representation of the flow field can thereby be generated, whereas, for later stages, the distribution of clusters can be influenced. Furthermore, we incorporate upwind ideas to give the clusters an oriented drop-shaped appearance. Here, we discuss the applicability of this new type of approach mainly for flow fields, where the cluster energy penalizes cross streamline boundaries. However, the method also carries provisions for other fields as well. The clusters can be displayed directly as a flow texture. Alternatively, the clusters can be visualized by iconic representations, which are positioned by using a skeletonization algorithm.