CAREER:Computational Frameworks for Higher-order Graph and Network Data Analysis

网络中的连接是社会、技术和基础设施的一个重要方面。例如，社会关系影响着我们的日常活动，家里的电是通过连接的电线输送的，大脑中的连接促进了我们处理信息的能力。理解、设计、控制和预测这些类型的连接和网络系统的能力对于改善物理基础设施、国防和经济健康至关重要。该项目将开发新的人工智能功能，以利用来自广泛网络连接的大数据。该研究的关键新颖之处在于直接考虑多个实体之间的联系。例如，小团体聚会中的联系影响疾病的传播，多种药物之间的联系是许多医疗的关键，金融交易往往涉及多方。通过利用这些多路连接，我们可以在许多情况下改进和发现网络内部的机制。例如，这项研究有可能改进预测疾病传播的模型，提出新的药物组合类型，并提高我们在网络上检测对抗性和恶意群体的能力。该项目还包括在一个以研究为基础的互动式夏季研讨会上教授这些思想，旨在扩大大学生对计算机相关研究生教育的参与。图或网络是整个科学中复杂关系数据的基本抽象。网络模型的基本思想是通过一组节点来表示数据的组件，并使用连接节点对的边来建模这些组件之间的关系。设计用于挖掘和学习图形数据的计算已经在生物医学、经济学、交通运输、社会学和其他领域得到了广泛的应用。然而，对两两关系的关注，如图中的边编码，固有地限制了传统的网络模型。复杂数据中的许多结构涉及同时发生在两个以上实体之间的高阶关系。例如，人们通过电子邮件或短信进行群体交流，学生在教室里聚集在一起，生物相互作用发生在一组分子之间，而不仅仅是两个分子。要充分认识数据中普遍存在的高阶交互的丰富性，有必要超越图形方法。该项目通过直接对网络数据中的高阶交互进行建模，并开发数据挖掘和机器学习算法，从而从这些模型中生成有意义的数据见解，从而开创了下一代网络数据分析。研究集中在高阶网络数据的三种模型，超图，张量和简单复合体，它们很有希望让我们思考与数据相关的计算方式。对于每个模型，该项目将开发数据挖掘和机器学习方法，为网络数据提供新的见解。这些方法将应用于各种真实世界的数据，以演示在社交网络、电子商务、生物医学和信息管理中的应用。该奖项反映了美国国家科学基金会的法定使命，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。

Connections in networks are an essential aspect of society, technology, and infrastructure. For example, social connections influence our daily activities, electricity in our homes is delivered by connected power lines, and connections in the brain facilitate our ability to process information. The ability to understand, design, control, and make predictions about these types of connections and networked systems is crucial to improving physical infrastructure, the national defense, and the health of the economy. This project will develop new artificial intelligence capabilities for leveraging big data coming from connections within a wide range of networks. The key novelty in the research is the direct consideration of connections among several entities at once. For example, connections in small group gatherings affect the spread of disease, connections between multiple drugs are key to many medical treatments, and financial transactions often involve several parties. By harnessing these multiway connections, we can make improvements to and make discoveries about mechanisms within networks in many settings. For instance, the research has the potential to improve models that forecast disease spread, propose new types of drug combinations, and enhance our ability to detect adversarial and malicious groups on the Web. This project also involves teaching these ideas in a research-based, interactive summer workshop for college students that is designed to broaden participation in computing-related postgraduate education.Graphs or networks are a fundamental abstraction for complex relational data throughout the sciences. The basic idea of network models is to represent components of the data by a set of nodes, and to model the relationships among these components using edges that connect pairs of nodes. Computations designed to mine and learn from graph data have resulted in diverse applications within biomedicine, economics, transportation, sociology, and other fields. However, the focus on pairwise relationships, as encoded by edges in a graph, inherently limits traditional network models. Much of the structure in complex data involves higher-order relationships that take place among more than two entities at once. For example, people communicate in groups over email or text message, students gather in groups in classrooms, and biological interactions occur between a set of molecules rather than just two. Going beyond graph methods is necessary to fully realize the richness of such higher-order interactions that are pervasive in data. This project ushers in the next generation of network data analysis by directly modeling higher-order interactions in network data and developing data mining and machine learning algorithms for generating meaningful data insights from such models. The research focuses on three models for higher-order network data, hypergraphs, tensors, and simplicial complexes, which are promising for the way in which they make us think about computations associated with the data. For each model, the project will develop data mining and machine learning methods that offer new insights into network data. These methods will be applied to a variety of real-world data to demonstrate applications in social networks, e-commerce, biomedicine, and information management.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.