EAGER: Define and Construct an Enhanced Graph Representation for Multiscale Vector Field Data Summarization

矢量场数据分析在科学和工程的许多应用中是不可或缺的，从气候研究，物理，化学，汽车设计到医疗实践。大多数现有的矢量场数据的分析技术是不可扩展的，以不断增加的规模和复杂性的真实世界的数据。更重要的是，固有的有限的视觉感知通道在很大程度上限制了整体或细节上理解矢量场的复杂几何和物理行为的能力。 为了解决这些挑战，这个探索性的项目研究了一个基于图形的矢量场数据减少的多尺度矢量场数据摘要的后续提取。摘要作为原始矢量场的浓缩但信息丰富的表示，支持数据解释和交互，并使用户免受流体动力学的潜在复杂性的影响。计算这种摘要表示的关键是构造一种新的增强的图形表示，该图形表示对向量场的全局结构信息和局部特征以及其他派生信息进行编码。该方法侧重于基于图的向量场数据约简中关键问题的开发和验证，包括：（1）识别用于构建增强图的向量场的关键信息;（2）图的有效存储;以及（3）用于从所获得的图中提取感兴趣特征的新的图算法。 为了解决这些问题，从动力系统，代数拓扑，张量演算，信息论，图论的理论和算法扩展和集成在一个新的框架。为了验证该方法，PI正在与机械工程和空气动力学领域的科学家密切合作，以获得有关摘要的表示及其在特定应用中的实用性的建议。向量场摘要表示的预期结果将产生一个重要的除了现有的摘要技术的各种数据形式。这种分析和抽象是基于增强图的，可以丰富传统的图论和图论算法。处理稳定和非稳定矢量场的能力提高了描述流体动力学现象的动力系统的理论和实践，使各种学科受益。从向量场概括中学习到的知识可以适用于更复杂的几何数据（例如张量场数据）的概括表示的研究。此外，向量场摘要的研究代表了一个统一的框架，从异构数据形式的知识发现和完整性的一步。预计开发的技术将作为一个软件工具，将适用于更广泛的科学和工程领域。 此外，这项工作产生的新理论有望丰富现有的数据分析和可视化教育，使许多学科的本科生和研究生阶段的新课程得以开发。该项目的网站（http：//www2.cs.uh.edu/cnchengu/vf_summary/vf_summary.html）将提供项目成果，包括开发的软件工具。

Vector field data analysis is indispensable for many applications in science and engineering, ranging from climate study, physics, chemistry, automobile design, to medical practice. Most existing analysis techniques for vector field data are not scalable to the real-world data with ever-increasing sizes and complexity. More importantly, the inherent limited visual perception channel largely constrains the ability to understand the complex geometric and physical behaviors of vector fields as a whole or in detail. To address these challenges, this exploratory project investigates a graph-based vector field data reduction for the subsequent extraction of a multi-scale vector field data summary. The summary serves as a condensed, yet informative, representation of the original vector field, supporting data interpretation and interaction and shielding the user from the underlying complexity of the flow dynamics. The key to computing such a summary representation is the construction of a novel, enhanced graph representation that encodes both the global structural information and local characteristics of the vector field, as well as other derived information. The approach focuses on development and validation of critical issues in graph-based vector field data reduction , including; (1) identification of the key information of a vector field for the construction of the enhanced graph: (2) efficient storage of the graph; and (3) new graph algorithms for extracting features of interest from the obtained graph. To address these issues, theories and algorithms from dynamical system, algebraic topology, tensor calculus, information theory, and graph theory are extended and integrated in a novel framework. To validate the approach, the PI is working closely with domain scientists from mechanical engineering and aerodynamics to receive advice on the representation of the summary and its utility in specific applications. The expected results in vector field summary represents will yield an important addition to the existing summarization techniques for various data forms. The analysis and abstraction are based on the enhanced graph and can enrich the conventional graph theory and graph algorithms. The ability to handle both steady and unsteady vector fields improves the theory and practice of dynamical systems in describing fluid dynamic phenomena, benefiting a wide variety of disciplines. Knowledge learned from the vector field summarization can be adapted to the study of summarized representation of more complex geometric data, such as tensor field data. In addition, the research on vector field summary represents one step towards a unified framework of knowledge discovery and integrity from heterogeneous data forms. The developed techniques are expected to be implemented as a software tool that will be applicable in a wider range of scientific and engineering domains. Furthermore, the new theory stemming from this work is expected to enrich the existing education on data analysis and visualization, enabling the development of new courses at both undergraduate and graduate levels in many academic disciplines. The project web site (http://www2.cs.uh.edu/~chengu/vf_summary/vf_summary.html) will provide access to project results, including developed software tools.