CAREER: Reeb graph learning: Classification, Clustering, and Embedding of Graphical Signatures

职业：Reeb 图学习：图形签名的分类、聚类和嵌入

• 批准号: 2142713
• 负责人: Elizabeth Munch
• 金额: $ 50.75万
• 依托单位: Michigan State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-05-01 至 2027-04-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2142713&HistoricalAwards=false
• 关键词: CAREER; Reeb; graph; learning; Classification

The constant increase in available data is a ubiquitous feature of modern life. This data comes in many forms such as points, images, and networks. Networks (equivalently called graphs in mathematical terminology) can themselves be data points in a large data set. For instance, one may wish to compare gene regulatory networks across many different species, or compare embedded graphs from different molecules to predict therapeutic properties. This research focuses on graphs with additional structure, which arise in the field of Topological Data Analysis (TDA), a modern take on data analysis that encodes shape and structure in data. The research objective of this project is to build the machine-learning theory necessary to utilize the rich structure of this kind of graph data which comes with both theoretical guarantees and practical algorithms. This research plan is combined with a fully integrated education plan including a series of workshops to stimulate interdisciplinary collaborations between starting researchers in TDA with domain scientists, as well as creation of open source code and educational materials to make the newly developed methods available to more interdisciplinary researchers. In more detail, this project focuses on graphical signatures, which are topological graphs equipped with a real-valued function further encoding some aspect of the topology or geometry of the structure represented. These include highly utilized constructions such as Reeb graphs, mapper graphs, merge trees, and contour trees. Recent work has developed metrics for comparing these objects, allowing for treating the space of, e.g., Reeb grahs as a metric space. The machine-learning interfaces developed for this project will utilize and respect the metrics available. While there is work aimed interfacing general graphs with machine learning, and separately for other topological signatures such as persistent homology, no tools yet exist for graphical signatures which take the additional function structure into account. The project team will further develop a theory of random Reeb graphs to generate data sets on which we can test the methods, as well as test the results in applications arising from the field of plant morphology.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

可用数据的不断增加是现代生活的一个普遍特征。这些数据有多种形式，如点、图像和网络。 网络（在数学术语中相当于图形）本身可以是大型数据集中的数据点。例如，人们可能希望比较许多不同物种的基因调控网络，或者比较来自不同分子的嵌入图以预测治疗特性。本研究的重点是具有附加结构的图，这些结构出现在拓扑数据分析（TDA）领域，这是一种对数据中的形状和结构进行编码的现代数据分析。该项目的研究目标是建立必要的机器学习理论，以利用这种图形数据的丰富结构，既有理论保证，又有实用算法。该研究计划与一个完全整合的教育计划相结合，包括一系列研讨会，以刺激TDA的研究人员与领域科学家之间的跨学科合作，以及创建开源代码和教育材料，使新开发的方法可供更多的跨学科研究人员使用。更详细地说，这个项目的重点是图形签名，这是一个拓扑图配备了一个实值函数进一步编码的拓扑结构或几何结构的某些方面表示。这些包括高度利用的结构，如Reeb图，映射图，合并树和轮廓树。最近的工作已经开发了用于比较这些对象的度量，允许处理例如，作为度量空间的Reeb Grahs。为该项目开发的机器学习界面将利用并尊重现有的指标。虽然有工作旨在将一般图与机器学习接口，并且单独用于其他拓扑签名，例如持久同源性，但还没有工具用于考虑额外功能结构的图形签名。该项目团队将进一步开发随机Reeb图理论，以生成数据集，我们可以在这些数据集上测试方法，并测试植物形态学领域的应用结果。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

The shape of aroma: Measuring and modeling citrus oil gland distribution

香气的形状：柑橘油腺分布的测量和建模

• DOI: 10.1002/ppp3.10333
• 发表时间: 2022
• 期刊: PLANET
• 作者: Amézquita, Erik J.;Quigley, Michelle Y.;Ophelders, Tim;Seymour, Danelle;Munch, Elizabeth;Chitwood, Daniel H.
• 通讯作者: Chitwood, Daniel H.