基于复杂网络图模型的信号处理

发布时间：2019-04-28 20:44

【摘要】：复杂网络的研究在很多领域取得了巨大的成功,如:网络的建模,聚类分析等等。现今大多数的研究或是偏重于网络结构分析或是偏重于网络节点性质的研究。图滤波理论很好的解决了网络结构分析和网络节点性质分析分离的研究现状。本文首先介绍了图滤波算法的基本原理,图滤波算法将节点性质映射为图信号,并通过定义图傅里叶变换,将图信号变换到另一个维度进行分析。但是已有的图滤波算法只适用于同构网络。即:只包含一种类型节点的网络。针对异构网络的场景,本文提出了张量图滤波算法,将图滤波算法推广至异构网络。张量图滤波算法首先使用邻接张量对异构网络进行建模;其次分析图信号在异构网络上的滤波规律;最后通过张量分解定义图傅里叶变换,提出了适用于异构网络的图滤波器。张量图滤波算法因为基于异构网络的场景,所以比起只能够分析同构网络的图滤波,该算法考虑了不同类型节点之间的拓扑结构,最大程度地利用了已知的节点连接关系。因此,张量图滤波算法不仅拓展了图滤波算法的适用范围,并且可以更加准确地分析图信号的滤波规律。在算法仿真验证方面,本文基于张量图滤波提出了一种半监督分类算法,通过分类的准确度证明算法的有效性。本文分别在DBLP数据库,新浪微博数据库以及构造的异构网络上对张量图滤波算法进行了仿真。与只适用于同构网络的图滤波算法相比,张量图滤波算法实现了更高的分类准确度。并且在已知节点比例较小时,张量图滤波算法的优势更加明显。
[Abstract]:The research of complex network has achieved great success in many fields, such as network modeling, cluster analysis and so on. Nowadays, most researches focus on network structure analysis or network node properties. The graph filtering theory solves the problem of separation between network structure analysis and network node property analysis. In this paper, the basic principle of the graph filtering algorithm is introduced firstly. The graph filtering algorithm maps the property of the node to the graph signal, and by defining the graph Fourier transform, the graph signal is transformed into another dimension for analysis. However, the existing graph filtering algorithms are only suitable for homogeneous networks. That is, a network that contains only one type of node. In this paper, a tensor graph filtering algorithm is proposed for heterogeneous networks, and the graph filtering algorithm is extended to heterogeneous networks. Tensor graph filtering algorithm first uses adjacent Zhang Liang to model heterogeneous networks, secondly analyzes the filtering law of graph signals on heterogeneous networks, and finally defines graph Fourier transform by Zhang Liang decomposition, and proposes a graph filter suitable for heterogeneous networks. Because the scene of heterogeneous network is based on the tensor graph filtering algorithm, compared with the graph filtering algorithm which can only analyze the isomorphic network, the algorithm takes into account the topology structure of different types of nodes and makes the best use of the known node connection relationship. Therefore, the tensor graph filtering algorithm not only extends the scope of application of the graph filtering algorithm, but also can more accurately analyze the filtering law of graph signals. In the aspect of algorithm simulation, this paper presents a semi-supervised classification algorithm based on Zhang Liang graph filtering, which proves the effectiveness of the algorithm through the accuracy of classification. In this paper, the tensor filter algorithm is simulated on DBLP database, Sina Weibo database and heterogeneous network. Compared with the graph filtering algorithm which is only suitable for isomorphic networks, tensor graph filtering algorithm achieves higher classification accuracy. And when the proportion of known nodes is small, the advantage of tensor graph filtering algorithm is more obvious.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5;TN911.7

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