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The visualization of relational data is at the heart of information visualization. The prevalence of visual representations for this kind of data is based on many real world examples spread over many application domains: protein-protein interaction networks in the field of bioinformatics, hyperlinked documents in the World Wide Web, call graphs in software systems, or co-author networks are just four instances of a rich source of relational datasets. The most common visual metaphor for this kind of data is definitely the node-link approach, which typically suffers from visual clutter caused by many edge crossings. Many sophisticated algorithms have been developed to layout a graph efficiently and with respect to a list of aesthetic graph drawing criteria. Relations between objects normally change over time. Visualizing the dynamics means an additional challenge for graph visualization researchers. Applying the same layout algorithms for static graphs to intermediate states of dynamic graphs may also be a strategy to compute layouts for an animated graph sequence that shows the dynamics. The major drawback of this approach is the high cognitive effort for a viewer of the animation to preserve his mental map. To tackle this problem, a sophisticated layout algorithm has to inspect the whole graph sequence and compute a layout with as little changes as possible between subsequent graphs. The main contribution and ultimate goal of this thesis is the visualization of dynamic compound weighted multi directed graphs as a static image that targets at visual clutter reduction and at mental map preservation. To achieve this goal, we use a radial space-filling visual metaphor to represent the dynamics in relational data. As a side effect the obtained pictures are very aesthetically appealing. In this thesis we firstly describe static graph visualizations for rule sets obtained by extracting knowledge from software archives under version control. In a different work we apply animated node-link diagrams to code-developer relationships to show the dynamics in software systems. An underestimated visualization paradigm is the radial representation of data. Though this kind of data has a long history back to centuries-old statistical graphics, only little efforts have been done to fully explore the benefits of this paradigm. We evaluated a Cartesian and a radial counterpart of a visualization technique for visually encoding transaction sequences and dynamic compound digraphs with both an eyetracking and an online study. We found some interesting phenomena apart from the fact that also laymen in graph theory can understand the novel approach in a short time and apply it to datasets. The thesis is concluded by an aesthetic dimensions framework for dynamic graph drawing, future work, and currently open issues.
The reduction of information contained in model time series through the use of aggregating statistical performance measures is very high compared to the amount of information that one would like to draw from it for model identification and calibration purposes. It is readily known that this loss imposes important limitations on model identification and -diagnostics and thus constitutes an element of the overall model uncertainty as essentially different model realizations with almost identical performance measures (e.g. r-² or RMSE) can be generated. In three consecutive studies the present work proposes an alternative approach towards hydrological model evaluation based on the application of Self-Organizing Maps (SOM; Kohonen, 2001). The Self-Organizing Map is a type of artificial neural network and unsupervised learning algorithm that is used for clustering, visualization and abstraction of multidimensional data. It maps vectorial input data items with similar patterns onto contiguous locations of a discrete low-dimensional grid of neurons. The iterative training of the SOM causes the neurons to form a discrete, data-compressed representation of the high-dimensional input data. Using appropriate visualization techniques, information on distributions, patterns and relationships in complex data sets can be extracted. Irrespective of their potential, SOM applications have earned very little attention in hydrological modelling compared to other artificial neural network techniques. Therefore, the aim of the present work is to demonstrate that the application of Self-Organizing Maps has very high potential to address fundamental issues of model evaluation: It is shown that the clustering and classification of model time series by means of SOM can provide useful insights into model behaviour. In combination with the diagnostic properties of Signature Indices (Gupta et al., 2008; Yilmaz et al., 2008) SOM provides a novel tool for interpreting the model parameters in the hydrological context and identifying parameter sets that simultaneously meet multiple objectives, even if the corresponding model realizations belong to different models. Moreover, the presented studies and reviews also encourage further studies on the application of SOM in hydrological modelling.