Multi-resolution visualization (MRV) systems are widely used for handling large amounts of information. These systems look different but they share many common features. The visualization research community lacks a general framework that summarizes the common features among the wide variety of MRV systems in order to help in MRV system design, analysis, and enhancement. This dissertation proposes such a general framework. This framework is based on the definition that a MRV system is a visualization system that visually represents perceptions in different levels of detail and allows users to interactively navigate among the representations. The visual representations of a perception are called a view. The framework is composed of two essential components: view simulation and interactive visualization. View simulation means that an MRV system simulates views of non-existing perceptions through simplification on the data structure or the graphics generation process. This is needed when the perceptions provided to the MRV system are not at the user's desired level of detail. The framework identifies classes of view simulation approaches and describes them in terms of simplification operators and operands (spaces). The simplification operators are further divided into four categories, namely sampling operators, aggregation operators, approximation operators, and generalization operators. Techniques in these categories are listed and illustrated via examples. The simplification operands (spaces) are also further divided into categories, namely data space and visualization space. How different simplification operators are applied to these spaces is also illustrated using examples. Interactive visualization means that an MRV system visually presents the views to users and allows users to interactively navigate among different views or within one view. Three types of MRV interface, namely the zoomable interface, the overview + context interface, and the focus + detail interface, are presented with examples. Common interaction tools used in MRV systems, such as zooming and panning, selection, distortion, overlap reduction, previewing, and dynamic simplification are also presented. A large amount of existing MRV systems are used as examples in this dissertation, including several MRV systems developed by the author based on the general framework. In addition, a case study that analyzes and suggests possible improvements for an existing MRV system is described. These examples and the case study reveal that the framework covers the common features of a wide variety of existing MRV systems, and helps users analyze and improve existing MRV systems as well as design new MRV systems.

Traditional visualization techniques for multidimensional data sets, such as parallel coordinates, star glyphs, and scatterplot matrices, do not scale well to high dimensional data sets. A common approach to solve this problem is dimensionality reduction. Existing dimensionality reduction techniques, such as Principal Component Analysis, Multidimensional Scaling, and Self Organizing Maps, have serious drawbacks in that the generated low dimensional subspace has no intuitive meaning to users. In addition, little user interaction is allowed in those highly automatic processes. In this thesis, we propose a new methodology to dimensionality reduction that combines automation and user interaction for the generation of meaningful subspaces, called the visual hierarchical dimension reduction (VHDR) framework. Firstly, VHDR groups all dimensions of a data set into a dimension hierarchy. This hierarchy is then visualized using a radial space-filling hierarchy visualization tool called Sunburst. Thus users are allowed to interactively explore and modify the dimension hierarchy, and select clusters at different levels of detail for the data display. VHDR then assigns a representative dimension to each dimension cluster selected by the users. Finally, VHDR maps the high-dimensional data set into the subspace composed of these representative dimensions and displays the projected subspace. To accomplish the latter, we have designed several extensions to existing popular multidimensional display techniques, such as parallel coordinates, star glyphs, and scatterplot matrices. These displays have been enhanced to express semantics of the selected subspace, such as the context of the dimensions and dissimilarity among the individual dimensions in a cluster. We have implemented all these features and incorporated them into the XmdvTool software package, which will be released as XmdvTool Version 6.0. Lastly, we developed two case studies to show how we apply VHDR to visualize and interactively explore a high dimensional data set.