CAREER: Spatial Network Deep Generative Modeling, Transformation, and Interpretation

随着现代大数据时代的到来，空间数据和网络数据分别是具有连续和离散属性的高维数据。跨越这两种数据类型，空间网络代表了一种重要的数据结构，其中节点和边嵌入在几何空间中。如今，空间网络数据变得越来越流行和重要，范围从微观尺度（例如，蛋白质结构），到中等规模（例如，生物神经网络），到宏观尺度（例如，移动网络）。空间网络的建模是非常困难的，由于涉及的重大挑战，包括：1）连续空间属性和离散网络属性之间的处理不兼容，2）空间和网络拓扑之间的密切相互作用，以及3）它们的极高维度。这些挑战反映了真实的世界中许多尚未解决的关键问题，例如对“蛋白质结构折叠过程”和“大脑网络中的精神疾病机制”进行建模和理解。到目前为止，在我们缺乏强大的模型和对空间网络生成进行建模所涉及的极其复杂的研究问题之间存在着巨大的差距。为了填补这一空白，本项目致力于开发一个空间网络生成建模的变革性框架，该框架可以从海量空间网络数据集中自动学习底层复杂的生成过程。本项目将现有的空间网络生成模型推广到深度和表达性架构。该框架的目标是：1）自动学习新的空间网络生成和转换过程; 2）嵌入用户指定的规则来约束和规则化生成的空间网络; 3）追求模型的可解释性，自动提取新的空间网络过程的可理解规则。研究活动沿着以下主题进行：i）用于大型空间网络的新颖的空间和谱图解码器，ii）具有空间和拓扑约束以及正则化的深度生成建模和优化，iii）各种新颖的空间和谱图变换策略，以及iv）用于在人类和模型之间交互预定义和提取原则的新颖系统。该项目开发的技术旨在通过高效准确地发现和合成复杂的空间网络行为，使各种社会和自然科学领域受益。该项目的成功可以使药物设计、精神疾病早期诊断和灾害管理等关键领域受益。该项目的核心产品，包括出版物，软件和数据集，在各种网站上发布，并得到用户的积极支持，以便在很大程度上使研究界和社会受益。拟议的统一框架还用于教授空间和网络数据挖掘概念，以及为研究生和本科生提供新课程、研究和实习机会。该项目积极包括代表性不足的学生和推广到当地高中。该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

As we enter the modern big data era, spatial data and network data are popular types of high-dimensional data with continuous and discrete properties, respectively. Spanning these two data types, spatial networks represent a crucial data structure where the nodes and edges are embedded in a geometric space. Nowadays, spatial network data is becoming increasingly popular and important, ranging from micro-scale (e.g., protein structures), to middle-scale (e.g., biological neural networks), to macro-scale (e.g., mobility networks). The modeling of spatial networks is extremely difficult due to the significant challenges involved, including: 1) incompatibility between the treatments for continuous spatial properties and discrete network properties, 2) the close interactions between spatial and network topologies, and 3) their extremely high dimensionality. These challenges echo numerous unsolved critical issues in the real world such as modeling and understanding the "protein structure folding process" and "mental disease mechanisms in brain networks". Until now, there has been a significant gap between our lack of powerful models and the extremely complex research issues involved in modeling the generation of spatial networks. To fill this gap, this project focuses on developing a transformative framework for spatial network generative modeling, which can automatically learn the underlying complex generation process from massive spatial network datasets.This project generalizes existing generative models of spatial networks into deep and expressive architectures. The developed framework aims at: 1) automatically learning new generation and transformation process of spatial networks, 2) embedding user-specified principles to constrain and regularize the generated spatial networks, and 3) pursuing the model interpretability and automatically distill new understandable principles of spatial network process. The research activities are conducted along the following themes: i) novel spatial and spectral graph decoders for large spatial networks, ii) deep generative modeling and optimization with spatial and topological constraints and regularization, iii) a variety of novel spatial- and spectral- graph transformation strategies, and iv) a novel system for interacting the predefined and distilled principles between human and models. The techniques developed in this project aim at benefiting various social and natural science domains by enabling efficient and accurate discovery and synthesis of complex spatial network behavior. The success of this project can benefit crucial domains including medicine design, mental disease early diagnoses, and disaster management. Core products of this project, including publications, software, and datasets, are published in various websites with active user support, in order to largely benefit the research communities and the society. The proposed unified framework is also used for teaching spatial and network data mining concepts, as well as providing graduate and undergraduate students with new courses, research, and internship opportunities. This project actively includes underrepresented students and outreach to local high schools.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.