CIF: Small: Community Detection in Multilayer Networks with Applications to Functional Connectivity Brain Networks

网络为相互作用的代理组成的复杂系统的内部结构提供了强大而紧凑的表示。例子包括社会网络、万维网和分子、细胞或整个物种的生物网络。传统的网络科学假设网络节点是由一条捕获它们之间所有交互的单一边缘连接起来的。然而，这是一种过度简化，因为大多数现实世界的网络都是通过节点之间不同类型的交互构建的。例子包括社交网络，其中两个人可以通过源自友谊、合作或家庭关系的不同类型的社会关系联系在一起；航空运输网络，不同的机场可以通过不同的航空公司连接起来；在大脑中，不同的区域可以在不同的频带或时间点上相互作用。近年来，引入了包含多个连接通道的多层网络来模拟这些不同的通信模式。网络分析的核心任务是识别和理解社区，因为它们可以揭示有意义的结构，并提供对网络整体功能的更好理解，例如发现代谢网络中的功能途径，万维网中的相关页面或社交网络中的朋友群等等。简单图上的社区检测方法不能充分利用节点间的多种交互模式，不足以处理多层网络的复杂性。本项目旨在借助启发式质量函数优化和统计推断两种互补的方法，开发一个全面的多层社区检测框架。这两种方法之间的联系将建立在具有不同复杂程度的多层网络模型上，从时间网络开始，到完全耦合的多层网络。该项目通过三个研究重点来解决多层网络中的社区检测问题。首先，将为时间、多路和多层网络定义新的基于归一化切的质量函数，并开发计算效率高的算法来优化这些新的成本函数。将研究所得算法的收敛性和一致性。接下来，将开发时间、多路和多层网络的广义随机块模型。将建立从这些模型中得到的后验概率最大化与启发式质量函数优化之间的联系。最后，将新的社区检测方法应用于多层功能连通性网络，例如由脑电图数据构建的时间和多频网络，以评估已知的任务相关网络。这种新的多层网络社区检测计算框架可以应用于不同类型的网络，包括社会网络、生物网络和生态网络；我们希望通过与密歇根州立大学的神经科学家合作，对大脑连接组学和认知神经科学领域产生影响。作为该项目的一部分，将培训一个多元化的跨学科研究小组，并将组织旨在吸引女学生的K-12外展活动。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。

Networks provide a powerful and compact representation of the internal structure of complex systems consisting of agents that interact with each other. Examples include social networks, the World Wide Web and biological networks of molecules, cells or entire species. Traditional network science assumes that the network nodes are connected by a single edge that captures all interactions between them. However, this is an oversimplification as most real-world networks are built through different types of interactions among the nodes. Examples include social networks, where two individuals can be connected through different types of social ties originating from friendship, collaboration or family relationships; air transportation networks, where different airports can be connected through different airlines; and the brain, where different regions can be interacting across different frequency bands or time points. In recent years, multilayer networks, which incorporate multiple channels of connectivity, have been introduced to model these different modes of communication. A core task in network analysis is to identify and understand communities as they can reveal meaningful structure and provide a better understanding of the overall functioning of networks, such as uncovering functional pathways in metabolic networks, related pages in the World Wide Web or groups of friends in social networks and more. Community detection methods on simple graphs are not sufficient to deal with the complexity of multilayer networks for they cannot leverage the multiple modes of interaction between nodes. This project aims to develop a comprehensive multilayer community detection framework with the help of two complementary approaches, namely heuristic quality function optimization and statistical inference. The connections between these two approaches will be established for multilayer network models with varying degrees of complexity starting with temporal networks going to fully coupled multilayer networks.This project addresses the problem of community detection in multilayer networks through three research thrusts. First, novel normalized-cut based quality functions will be defined for temporal, multiplex and multilayer networks, and computationally efficient algorithms will be developed to optimize these new cost functions. The convergence and consistency of the resulting algorithms will be studied. Next, generalized stochastic block models for temporal, multiplex and multilayer networks will be developed. Connections between maximizing a posteriori probabilities derived from these models and optimizing the heuristic quality functions will be established. Finally, the new community detection methods will be applied to multilayer functional connectivity networks, e.g. temporal and multi-frequency networks, constructed from electroencephalogram (EEG) data to assess well-known task-related networks. This new computational framework for multilayer network community detection can be applied to different types of networks including social, biological and ecological networks; we expect an impact on the fields of brain connectomics and cognitive neuroscience through collaborations with neuroscientists at Michigan State University. As part of the project, a diverse group of interdisciplinary researchers will be trained, and K-12 outreach activities that seek to engage female students will be organized.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.