CIF: Small: A comprehensive framework for dynamic network tracking and clustering with applications to functional brain connectivity

复杂网络理论已被证明是一个通用的框架来表示和分析关系数据，这些数据在许多学科中非常丰富，包括社会科学，信息系统，生物学和神经科学。直到最近，网络理论的研究主要集中在静态图上，即网络节点之间的关系不随时间而变化。然而，几乎所有的真实的网络本质上都是动态的，例如连接随时间变化的社交网络，或者响应刺激而快速重组的功能性神经网络。当前动态网络的研究主要集中在两个相互关联的问题上：时间序列图中的异常或变点检测和识别网络时变结构的进化聚类。这项研究解决了这两个问题，同时在一个统一的框架，以监测和跟踪网络拓扑结构的变化，并表征每个？网络状态？一个单一的社区结构。本研究针对人脑中在感知、认知和执行过程中动态重组的功能连接网络（Functional Connectivity Networks，FCN），提出了两种互补的动态网络监测方法：1）时变网络中的联合异常检测和网络状态识别的多尺度框架;一致谱聚类方法沿着与张量分解的简洁拓扑表示的网络状态。最后，这个动态的网络监测框架被应用到脑电图（EEG）数据收集使用的实验协议，旨在评估知名的显着性和控制功能网络与情感调节和认知控制。

Complex network theory has proved to be a versatile framework to represent and analyze relational data that is abundant in many disciplines including the social sciences, information systems, biology and neuroscience. Until recently, the research on network theory has mainly focused on static graphs, i.e. the relationships between nodes of the network do not change with time. However, almost all real networks are dynamic in nature such as social networks with connections that change over time or functional neural networks that reorganize rapidly in response to stimuli. Most of the current studies of dynamic networks focuses on two major and interrelated problems: anomaly or change point detection in a time series of graphs and evolutionary clustering to identify the time-varying structure of networks. This research addresses these two problems simultaneously in a unified framework to monitor and track the changes in network topology and to characterize each ?network state? with a single community structure. In particular, this research focuses on the functional connectivity networks (FCNs) of the human brain that reorganize themselves dynamically during perception, cognition and execution of mental processes.The investigator develops two complementary approaches to address dynamic network monitoring problem: 1) A multi-scale framework for joint anomaly detection and network state identification in time-varying networks; and, 2) Consensus spectral clustering methods along with tensor decomposition for succinct topographic representation of network states. Finally, this dynamic network monitoring framework is applied to electroencephalogram (EEG) data collected using an experimental protocol designed to assess well-known salience and control functional networks associated with affective regulation and cognitive control.