抽样技术在复杂网络中的应用研究

发布时间：2018-09-07 19:24

【摘要】：近年来,复杂网络的研究由于具有广泛的应用背景而受到许多领域学者的高度关注,人们对很多实际网络的拓扑共性与数学模型展开了深入的研究。然而,实际网络往往规模巨大,受限于技术和成本,我们很难获得网络的完全信息,许多复杂网络的实证研究实际上是基于非完全网络数据展开的。因此,如何对网络进行合理抽样,获得较好的抽样网络以实现对完全网络性质的准确推断,是复杂网络研究面临的一个重要问题,大数据下网络的抽样方法设计与抽样效果分析具有十分重要的价值。本文通过使用不同的抽样法分别在三个不同类型的复杂网络中进行抽样,并计算不同抽样法所得样本网络的拓扑特征量,比较其对总体初始值的估计效果,总结出适合于不同网络拓扑性质估计的抽样方法。本文第一部分(1)是背景研究,介绍了复杂网络抽样在目前时代背景下的重要性和必要性,同时分析了当前国内外在复杂网络抽样领域的研究成果和现状,并阐述了本课题研究的目的。第二部分(2)是理论分析,首先介绍了复杂网络抽样的理论基础,包括复杂网络的历史发展过程、经典复杂网络模型的特征和构建方法、常用网络拓扑特征量的介绍。然后介绍了常见的三种抽样方法的抽样思路,以及基于滚雪球抽样法和完全随机抽样法结合得到的两阶段抽样法。第三部分(3-5)是方法应用,分别将完全随机抽样法、随机游走抽样法、滚雪球抽样法、两阶段抽样法以不同的抽样率分别在BA无标度网络、WS小世界网络、欧盟邮件通讯网络中进行抽样,利用所得样本网络计算拓扑特征量并比较其对总体的估计效果,总结出不同抽样方法的特点,以及其在各网络中估计不同拓扑性质时的优劣。最后一部分(6)是总结,结合上述分析总结列举适合不同网络拓扑性质估计的抽样方法,本文结尾部分指出了论文的创新点以及不足之处。
[Abstract]:In recent years, the research of complex network has been highly concerned by many scholars because of its wide application background. People have deeply studied the topology commonness and mathematical model of many practical networks. However, the actual network is often large, limited by technology and cost, so it is difficult to obtain the complete information of the network. Many empirical studies of complex networks are actually based on incomplete network data. Therefore, how to reasonably sample the network and obtain a better sampling network to accurately infer the nature of the complete network is an important problem in the study of complex networks. The network sampling method design and sampling effect analysis under big data has very important value. In this paper, different sampling methods are used to sample three different types of complex networks, and the topological characteristic quantities of the sample networks obtained by different sampling methods are calculated, and the estimation results of the initial values of the samples are compared. A sampling method suitable for different network topology property estimation is summarized. The first part of this paper (1) is the background research. It introduces the importance and necessity of complex network sampling in the background of the present era, and analyzes the current research results and present situation in the field of complex network sampling at home and abroad. The purpose of this research is expounded. The second part (2) is the theoretical analysis. Firstly, the theoretical basis of complex network sampling is introduced, including the historical development process of complex network, the characteristics and construction methods of classical complex network model, and the introduction of common network topology characteristic quantity. Then it introduces the sampling ideas of three common sampling methods and the two-stage sampling method based on the combination of snowball sampling method and complete random sampling method. The third part (3-5) is the application of the method, which applies the complete random sampling method, random walk sampling method, snowball sampling method and two-stage sampling method respectively in BA scale free network and WS small world network with different sampling rates. Sampling is carried out in the EU mail communication network. The topological characteristic quantity is calculated by using the obtained sample network and its estimation effect on the whole is compared. The characteristics of different sampling methods and their advantages and disadvantages in estimating different topological properties in each network are summarized. The last part (6) is a summary. Combined with the above analysis, the sampling methods suitable for different network topology properties estimation are listed. At the end of this paper, the innovations and shortcomings of the paper are pointed out.
【学位授予单位】：桂林理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5

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