CRII:III:Towards Advanced Filtering and Pooling Operations for Graph Neural Networks

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。近年来，我们见证了从网络世界的众多平台和物理世界的各种传感器中生成和收集数据的能力的快速增长。图提供了各种数据的通用表示，包括在线社会网络、知识图、交通网络和化合物。实体通常可以表示为节点，而它们的关系可以表示为边。在这些数据上的许多重要的实际应用程序可以被视为图上的计算任务。促进这些任务的关键步骤是学习节点或图的良好向量表示。近年来，将深度学习技术推广到图的图神经网络被广泛应用于图的表示学习。尽管图神经网络已经在各个领域推进了许多实际应用，但在功效和效率方面仍然存在许多局限性。本项目旨在通过进行理论分析和开发创新算法来解决这些限制。这个项目特别受到计算社会科学、计算生物学和电子商务中的欺诈检测的应用的激励。此外，该项目将涉及研究生和本科生进行他们的论文或荣誉项目。该项目的发现和研究成果将紧密地整合到新泽西理工学院的几门现有和新课程中。该项目的技术目标分为两个任务，对应于图神经网络的两个主要构建组件：图过滤操作和图池操作。图过滤操作的目的是细化图中所有节点的节点表示。另一方面，图池化操作旨在总结节点表示以获得图表示。第一个任务是研究在异交性条件下的图过滤操作，这种情况通常对图过滤操作提出了很大的挑战。特别是，研究者将对图过滤操作进行理论分析，以更深入地了解其内在机制，特别是在异质性情况下。然后，基于这些理解，将提出更高级的图神经网络模型来处理异恋图。第二个任务旨在开发更高效和有效的图池操作。研究人员将探索和开发基于聚类和下采样过程的图池操作。为了提高图池化操作的有效性和效率，聚类/下采样过程将以端到端的方式很好地整合到整个学习框架中。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。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).In recent years, we have witnessed a rapid growth in our ability to generate and gather data from numerous platforms in the online world and various sensors in the physical world. Graphs provide a universal representation for a variety of data including online social networks, knowledge graphs, transportation networks, and chemical compounds. Entities can usually be represented as nodes while their relations can be denoted represented as edges. Many important real-world applications on these data can be treated as computational tasks on graphs. A crucial step to facilitate these tasks is to learn good vector representations either for nodes or graphs. Recently, graph neural networks, which generalize deep learning techniques to graphs, have been widely adopted to learning representations for graphs. Though graph neural networks have advanced numerous real-world applications from various fields, they still suffer from many limitations in terms of efficacy and efficiency. This project aims to address these limitations by conducting theoretical analysis and developing innovative algorithms. This project is specifically motivated by applications to computational social science, computational biology, and fraud detection in e-commerce. Furthermore, this project will involve graduate and undergraduate students in pursuing their theses or honor projects. Discoveries and research findings of this project will be tightly integrated into several current and new courses at the New Jersey Institute of Technology.The technical aims of the project are divided into two tasks corresponding to the two major building components of graph neural networks: graph filtering operations and graph pooling operations. The graph filtering operation aims to refine node representations for all nodes in a graph. On the other hand, the graph pooling operation aims to summarize node representations to obtain a graph representation. The first task aims to investigate graph filtering operations under heterophily—a setting typically poses great challenges for graph filtering operations. In particular, the investigator will conduct theoretical analyses on graph filtering operations to gain deeper insights into their intrinsic mechanism, especially under the scenario of heterophily. Then, based on these understandings, more advanced graph neural networks models will be proposed to handle heterophilous graphs. The second task aims to develop more efficient and effective graph pooling operations. The investigators will explore and develop graph pooling operations based on clustering and down-sampling process. To improve the efficacy and efficiency of the graph pooling operations, the clustering/down-sampling process will be nicely incorporated into the entire learning framework in an end-to-end way.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.