Developing new tools in community detection and graph-based signal analysis

在许多情况下，数据自然地作为图中各个节点之间的连接出现（例如，社交媒体中的友谊或协作网络）。或者，在其他空间（如图像）中出现的数据可以被强制转换为类似于图的结构进行分析，其优点是可以解锁替代信息，如在原始域中不明显的依赖结构，或者可以利用网络稀疏性进行更简单的分析。通过上述两种方法，建模和分析网络的文献现在已经很成熟。然而，在这一研究领域仍有一些悬而未决的问题需要解决。例如，我们如何在网络相关分析中构建节点或边成员约束？目前用于分析图（如小波）上数据的变换方法能否用于分析静态和动态网络？这是否会导致更有效的工具，如变点技术或在线设置？在网络及其特征的统计模型中存在缺失数据的情况下，是否有更稳健的参数估计方法？该项目的目的是提出一系列潜在的问题，在一般领域的决策网络数据。具体地说，我们要考虑的问题，有一个缺乏，或不满意，方法的发展的实际利益。

In many settings, data naturally arise as connections between individual nodes in a graph (for example, friendship or collaboration networks in social media). Alternatively, data arising in other spaces (such as images) can be coerced into a graph-like structure for analysis, the suggested advantage being that one can unlock alternative information such as dependency structure not obvious in the original domain, or that network sparsity can be exploited for simpler analysis.The literature for modelling and analysing networks is now well-established via both of the approaches described above. However, there are still open questions in this research area which need to be addressed. For example, how can we build nodal or edge membership constraints into network-related analysis? Can transformation methods currently employed in analysing data arising on a graph (such as wavelets) be exploited for the analysis of static and dynamic networks? Could this result in more efficient tools, such as change-point techniques or online settings? Are there more robust ways of parameter estimation in the presence of missing data in statistical models for networks and their characterisation?The aim of this project is to present a range of potential problems arising in the general area of decision-making for network data. Specifically, we want to consider problems where there is a lack of, or unsatisfactory, methodological development of practical interest.