III: Medium: Collaborative Research: Topological Data Analysis for Large Network Visualization

该项目利用拓扑学方法开发了一类新的数据分析和可视化技术，以了解网络结构。网络通常用于对社会、生物和技术系统进行建模，并捕获个人、企业和基因组实体之间的关系。了解如此庞大、复杂的数据源在脑连接学、流行病学、执法、公共政策和营销等应用领域具有高度相关性和重要性。这项拟议的研究将在多个数据来源上进行评估，包括但不限于大型社交、通信和脑网络数据集。此外，该项目制定的新方法将纳入不断增长的数据分析课程，通过举办讲习班加以分享，并作为专题继续吸引代表不足的群体进入科学、技术和经济管理领域，特别是计算机科学领域。该项目解决的科学挑战有两个：如何使用拓扑学从数据中提取特征；以及如何设计有效的可视化来将这些特征传达给领域专家和决策者。该项目的核心拓扑技术为简化和汇总复杂数据提供了强大的理论基础，同时仍然保留了关键的底层结构。它们还为面向任务的设计提供了基础，这些设计允许我们控制要在可视化中显示的数据量，这样用户就可以开发出忠实的数据心理模型，从而促进信息发现。这个项目集中在两个研究议程上。首先，提出了一套丰富的拓扑摘要技术来提取和保留大规模图结构网络中的重要拓扑特征，并获得适合可视化探索的紧凑和层次表示。特征提取过程捕捉系统中的复杂交互，在所有尺度上描述特征，对噪声具有鲁棒性，并且具有高效的计算。其次，该项目提出了对提取的拓扑结构进行显式编码的可视化设计，重点研究了在待开发的视觉隐喻中充分利用它们的特性的技术。项目网站(http://www.sci.utah.edu/networktdav))提供了更多信息，并将包括对开发的工具和测试数据集的访问。

This project leverages topological methods to develop a new class of data analysis and visualization techniques to understand the structure of networks. Networks are often used in modeling social, biological and technological systems, and capturing relationships among individuals, businesses, and genomic entities. Understanding such large, complex data sources is highly relevant and important in application areas including brain connectomics, epidemiology, law enforcement, public policy and marketing. The proposed research will be evaluated over multiple data sources, including but not limited to large social, communication and brain network datasets. Furthermore, the new approaches developed in this project will be integrated into growing data analysis curricula, shared through developing workshops, and used as topics to continue attracting underrepresented groups into STEM fields and computer science specifically. The scientific challenges this project addresses are two-fold: how to use topology to extract features from the data; and how to design effective visualizations to communicate these features to domain experts and decision makers. Topological techniques central to this project provide a strong theoretical basis for simplifying and summarizing complex data while still preserving critical underlying structures. They also provide a basis for task-oriented designs that allow us to control the volume of data to be displayed in visualizations, so users can develop faithful mental models of the data, facilitating information discovery. This project focuses on two research agendas. First, it proposes a rich body of topological summarization techniques to extract and preserve important topological features within large-scale graph-structured networks, and to obtain compact and hierarchical representations that are suitable for visual exploration. The feature extracting process captures complex interactions in the system, describes features at all scales, is robust with respect to noise, and has efficient computation. Second, this project proposes designing visualizations that encode the extracted topological structures explicitly, focusing on investigating techniques to fully exploit their properties in the visual metaphors to be developed. The project web site (http://www.sci.utah.edu/networktdav) provides additional information and will include access to developed tools and test data sets.