AF:Small:Algorithms for visualizing data with contact graphs and data maps

该项目的目标是开发用于可视化静态和动态数据的新技术。可视化使我们能够感知大型互联数据集中的关系。虽然统计数据可以确定数据之间的相关性，但这些相关性的直观可视化可以帮助我们构建关于数据的问题。此外，随着时间的推移，用于可视化过程的算法将具有超越探索性数据分析和搜索模式和趋势的信息可视化传统用途的应用。图通常用于捕获对象之间的关系，并可视化为节点链接图。接触图提供了另一种更直观的方式来可视化平面图形。在接触图中，节点由区域表示，边缘由共享公共边界的两个区域表示。这样的表现方式让人联想到一幅熟悉的地理地图。在这个研究项目中，pi将研究允许接触图表示的图类的特征，其中节点具有“漂亮”的形状（例如，凸，具有小复杂性，具有预定区域）和创建这种表示的技术。虽然接触图仅限于平面图，但pi将使用聚类和嵌入方法将概念扩展到一般图。作为这个项目的一个组成部分，研究生和本科生将参与所描述的研究活动的各个方面。这延续了将本科生纳入研究项目的传统，这些项目容易获得且具有视觉吸引力。与过去的项目一样，所有开发的新软件都将提供给更广泛的社区。

The goal of this project is to develop new techniques for visualizing static and dynamic data. Visualization allows us to perceive relationships in large interconnected datasets. While statistics may determine correlations among the data, intuitive visualizations of these correlations helps us frame what questions to ask about the data. Moreover, algorithms for visualizing processes that evolve over time will have applications beyond the traditional uses of information visualization in exploratory data analysis and searching for patterns and trends.Graphs are often used to capture relationships between objects and visualized as node-link diagrams. Contact graphs provide an alternative and often more intuitive way to visualize planar graphs. In contact graphs, nodes are represented by regions and edges are represented by two regions sharing a common border. Such representation suggests the familiar metaphor of a geographical map. In this research project the PIs will study characterizations of the classes of graphs that admit contact graph representations where nodes have "nice" shapes (e.g., convex, with small complexity, with predetermined areas) and techniques for creating such representations. While contact graphs are restricted to planar graphs, the PIs will extend the notion to general graphs using clustering and embedding methods.As an integral part of this project, graduate and undergraduate students will be involved in all aspects of the described research activities. This continues a tradition of integrating undergraduates into research projects that are easily accessible and visually appealing. As with past projects, all new software developed will be made available to the broader community.