融合先验结构信息的复杂动态网络重构及算法研究

现实世界中复杂网络处处存在，有效刻画节点间的相互作用关系并构建网络结构是研究复杂网络结构性质的基础。本项目针对网络重构所面临的实现不唯一、大规模网络维数灾、结构动态变化等特点，研究融合先验结构信息的复杂动态网络重构问题。具体的，分析度分布先验信息的融合方式，构建融合小世界、无标度等先验结构信息的重构框架。针对大型复杂网络，研究基于先验社团结构信息的重构方法，刻画不同团之间的作用关系，设计并行算法。分析层级网络的模型构建方式，设计由上层动态交互网络推断下层关系网络的优化算法。对于时变动态网络重构，给出跳变点的估计方法，分析先验信息在时间域的嵌入方式，得到时变参数的递推算法。项目综合利用关联网络、概率图模型、动力学系统的优势，围绕先验结构信息的嵌入发展新的重构方法，为从大量数据中发现和挖掘复杂网络的结构提供新的途径和有效的算法，为更好地理解各类复杂网络、优化网络结构、改善网络性能提供技术支持。

In the real world, complex networks are everywhere. It is a fundamental problem for the structural properties of complex networks, on how to efficiently characterize the interactions between nodes. With the facts that non-unique realizations for network reconstruction, dimensional disaster for large-scale networks, dynamic change of network structures and so on, in this project, we will investigate the reconstruction problem of complex dynamic networks by making use of prior structure information. Specifically, we will analyze the fusion ways of prior information on degree distribution, and present a theoretical framework for network reconstruction with informative structure priors such as small world and scale free. For large complex networks, we will study the reconstruction approaches based on the prior community information, model the interactions between different communities, and design parallel reconstruction algorithms. We will analyze the reconstructions of hierarchical networks, and design optimal algorithms that used to infer the underlying relation network from the top-layer dynamical interacting networks. For the reconstruction of time-varying dynamic networks, we will present the estimation methods for jump points, analyze the embedded ways of prior information in the time-domain, and obtain the iterative algorithms for time-variant parameters. By integrating the advantages of correlation networks, probability graphical models and dynamic systems, the project will provide new approaches and efficient algorithms through the embedding of informative structure priors. It will benefit the discovering and mining of complex network structure from large data sets, and will provide technical support for better understanding of diverse complex networks, optimizing of network structure, and improving of network performance.