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

本研究项目的目的是通过图形绘制模型来研究信息可视化的主要方面。基本方法是将复杂数据(具有层次结构和/或时间和空间组件)建模为图形，然后将可视化问题描述为图形绘制问题。所得到的数据表示的质量由表征拟合质量的适当目标函数来衡量。将开发高效和健壮的算法来解决基本的优化问题。此外，还评估了数据在其结果图形表示中的微小扰动的影响。这些算法在各种各样的合成数据和来自社会科学、物理学和生命科学的真实数据上进行了测试。该方法是在Gravis中实现的，这是一个概念验证工具，将在http://www.stat.lsa.umich.edu/~gmichail/gravis.上免费提供该项目的最终目标是为信息可视化问题奠定坚实的方法学和数学基础。

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.