Large-scale structure in complex networks

这位研究人员和他的同事们研究了现实世界网络的大规模结构，如社会、生物和信息网络。将开展几个具体项目。第一部分将集中讨论网络中的社区检测这一经典问题，并开发出用于评估社区质量的紧凑目标函数和优化它们的有效策略。提出的方法在严格激励、尽可能利用存储在网络中的信息以及避免以前方法的一些缺陷(如分辨率限制)方面有所改进。第二个项目将开发基于期望最大化(EM)算法与蒙特卡罗和信任传播方法相结合的网络通用结构推理方法。这些方法的一个特别优点是，因为它们优化了边际概率，它们具有避免过度拟合的潜力，并为解决模型选择问题提供了策略。几个进一步的项目集中于将这些技术扩展到更复杂的网络结构形式，包括重叠的顶点类、层次结构和对隐藏变量的一般类的依赖。许多具有科学意义的系统可以表示为网络，从互联网到生物网络再到社会网络。在过去的十年中，海量的网络数据出现在不同的领域，但在许多情况下，这些数据是密集和令人困惑的，这给试图理解其结构的用户带来了巨大的挑战。这项研究的基本问题是我们如何从物理、生物和社会系统的网络结构中获得新的理解。例如，调查者和他的合作者将开发用于检测网络中密切交互的节点组的方法，例如社交网络中的个人集团或网络上的相关网站组。它们还将解决使用网络结构来推断网络节点的未知属性的一般问题。例如，如果网络中有几种不同类型的节点，例如细胞中新陈代谢网络中的化学物质类别，我们如何才能仅从网络结构中识别类型，而不直接测量它们(这可能很困难或成本很高)？这项资助的研究将创造一系列数学工具，可以应用于这一领域的问题。将开发的方法有许多可能的应用，包括帮助研究生物和社交网络的研究人员的新技术，在线社交网络的商业应用，以及数据可视化和自动数据汇总的软件应用等。

The investigator and his colleagues study the large-scale structure of real-world networks, such as social, biological, and information networks. Several specific projects will be undertaken. The first will focus on the classic problem of community detection in networks and the development of compact objective functions for assessing community quality and effective strategies for their optimization. The methods proposed improve on previous ones in being rigorously motivated, utilizing as much as possible of the information stored in a network, and avoiding some of the pitfalls of previous approaches, such as resolution limits. A second project will develop methods for general structural inference in networks based on a combination of expectation--maximization (EM) algorithms with Monte Carlo and belief propagation methods. A particular strength of these approaches is that, because they optimize marginal probabilities, they have the potential to avoid overfitting and offer strategies for solving model selection problems. Several further projects focus on the extension of these techniques to more complex forms of network structure, including overlapping vertex classes, hierarchical structure, and dependence on general classes of hidden variables.Many systems of scientific interest can be represented as networks, from the Internet to biological networks to social networks. In the last decade copious amounts of network data have become available in different fields, but in many cases these data are dense and bewildering, presenting a substantial challenge to the user trying to make sense of their structure. The fundamental question addressed in this research is how we can gain new understanding about physical, biological, and social systems from their network structure. For instance, the investigator and his collaborators will develop methods for detecting groups of closely interacting nodes in networks, such as cliques of individuals in social networks, or groups of related web sites on the web. They will also tackle general questions of using network structure to deduce unknown properties of network nodes. If, for instance, there are several different types of nodes in a network, such as classes of chemicals in a metabolic network in the cell, how can we identify the types from network structure alone, without measuring them directly (which may be difficult or costly)? The funded research will create a range of mathematical tools that can be applied to problems in this area. The methods to be developed have a number of possible applications, including new techniques to aid researchers working on biological and social networks, commercial applications in online social networks, and software applications in data visualization and automatic data summarization, among others.