基于矩阵优化模型的社交网络分析研究及其应用

近些年来，随着以互联网技术为代表的科学技术的迅猛发展，如何从海量的数据中挖掘社交网络的底层结构信息，并在实际生活中加以有效的利用，逐渐成为大数据背景下社交网络分析的核心问题。随着实际应用的不断涌现，经典模型与方法已经无法应对复杂数据及其产生的各种新型应用问题带来的挑战。矩阵优化是一类自变量为矩阵约束优化问题。它在统计、数据挖掘、机器学习、图像和信号处理、金融工程、控制理论等领域有广泛的应用。本项目将基于矩阵优化模型，围绕大数据背景下的社交网络分析问题的模型、统计误差分析以及算法设计展开研究。通过与高维统计分析等相关数据科学领域相融合，根据社交网络问题的特点，建立合理的统计优化模型，系统分析相应矩阵优化模型的非渐近式统计误差界，设计实际可行的求解社交网络分析的有效算法。

Recently, the progress of development of science and technology, especially the Internet technology, makes the following question the key issue of the social network analysis (SNA) in the era of Big Data: how to explore the underlying structure information from the large-scale data, and use this information effectively in the applications. With the rapid development of applications, the classical models and methods are not able to cope with the new challenges posed by the complexity of data and a variety of new applications. Matrix optimization problems (MOPs) are a class of constraint optimization problems, whose unknown variables are matrices. MOPs have recently found many important applications in many different fields, such as statistics, data mining, machine learning, imagine and signal processing, financial engineering and system control. This project will focus on the study of the MOP based SNA models, the statistical error bound analysis of the corresponding models, and the algorithm design and analysis. By connecting with the related data science technology, such as the high dimensional statistical analysis, we will extract suitable statistical optimization models based on the features of social network applications, establish the non-asymptotic error bound of the proposed MOP based models, and design effective algorithms for solving the corresponding SNA problem.