Information Visualization Through Graph Drawing: Modeling, Analysis and Optimization Issues

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The purpose of this research project is to study the main aspects of information visualization through graph drawing models. The basic approach is to model complex data (having a hierarchical structure and/or temporal and spatial components) as graphs, and then formulate the visualization problem as a graph drawing problem. The quality of the resulting data representation is measured by an appropriate objective function that characterizes the quality of the fit. Efficient and robust algorithms will be developed for solving the underlying optimization problem. Furthermore, the effects of small perturbations of the data in their resulting graphical representation are assessed. The algorithms are tested on a wide variety of synthetic data and real data from the social, physical and life sciences. The methodology is implemented in GRAVIS, a proof-of-concept tool that will be freely available at http://www.stat.lsa.umich.edu/~gmichail/gravis. The ultimate goal of the project is to establish a solid methodological and mathematical foundation for the problem of information visualization.