Hidden features and information diffusion in large social networks

在社交网络中，用户之间的联系是建立在一定程度的社区基础上的。通常，如果用户共享共同的功能或属于同一个社区，则链接更有可能出现。网络形成可以通过假设节点嵌入在特征空间中来建模，并且通过一个随机过程来形成链接，该过程取决于底层空间中节点之间的距离。提出的研究目的是开发模型和算法，允许从大型网络的链接结构中提取潜在特征空间。我将使用理论工具来研究节点的空间特征与链路结构之间的关系，使用无限极限来理解网络变大时的行为。我还将进一步开发和分析基于优先依恋原则的增长网络的空间模型，该模型导致图形显示出常见的特征，如幂律度分布、高聚类和导致小世界属性的长链接的存在。******本研究的第一个目标是开发方法来测试给定的图是否可能是空间知情链接形成过程的结果，以及底层空间的特征是什么。一旦为给定的网络类别建立了适当的空间模型，发展的理论将导致改进公共链路挖掘任务的方法，如社区提取和节点相似性的量化。这可以有重要的应用在分析在线社会网络的目标营销，或识别欺诈或犯罪分子。这些方法也可用于分析生物网络，如蛋白质相互作用网络或食物网。******本研究的第二个目的是研究网络及其潜在空间结构对信息扩散和行为策略演变的影响。特别有趣的是基于博弈论的模型。在网络中，节点采用博弈策略，与相邻节点进行战略博弈。每个节点收到的回报取决于其邻居的策略。然后，节点有机会将其策略更改为具有更高收益的邻居的策略。这导致成功的策略通过网络传播。我的兴趣是研究网络结构如何影响这种动态过程。此外，使用空间网络模型，我将重点关注底层空间在多大程度上影响了这些过程。******简而言之，提出的研究目标是研究随机空间模型，以获得对大型复杂网络的链接结构所表达的隐藏深层信息的细致理解，以及沿着其链接传播的动态过程

In social networks, connections are made based on a degree of communality between the users. Typically, links are more likely if users share common features or belong to the same community. Network formation can be modelled by assuming the nodes to be embedded in a feature space, and links to be formed through a stochastic process which depends on the distance between the nodes in the underlying space. The aim of the proposed research is to develop models and algorithms that will allow for the extraction of the latent feature space from the link structure of large networks. I will use theoretical tools to study the relationship between spatial features of the nodes and the link structure, using the infinite limit to understand the behaviour as the network gets large. I will also further develop and analyze a spatial model for growing networks, built on the principle of preferential attachment, which leads to graphs that exhibit commonly observed features such as a power law degree distribution, high clustering, and the presence of long links that lead to the small world property.******The first objective of this research is to develop methods to test whether a given graph is likely the result of a spatially informed link formation process, and what are the characteristics of the underlying space. Once an appropriate spatial model for a given class of networks has been established, the developed theory will lead to improved methods for common link mining tasks, such as community extraction and quantification of node similarity. This can have important applications in the analysis of on-line social networks towards targeted marketing, or identification of fraudulent or criminal elements. These methods may also be of use in the analysis of biological networks, such as protein interaction networks or food webs.******A second aim of the proposed work is to study the effect of the network and its underlying spatial structure on the diffusion of information and the evolution of behavioural strategies. Of particular interest are models based on game theory. On a network, nodes adopt a game strategy, and play a strategic game with their neighbours. Each node receives a pay-off that depends on the strategy of its neighbours. Nodes then are given a chance to change their strategy to that of a neighbour with a higher pay-off. This leads to a spread of successful strategies through the network. My interest is in studying how the network structure affects such dynamic processes. Moreover, using spatial network models, I will focus on the question to what extend the underlying space informs these processes.******In short, the goal of the proposed research is to study stochastic spatial models to gain a nuanced understanding of the hidden deep information that is expressed by the link structure of a large complex network, and of the dynamic processes that propagate along its links.**