基于属性图的社交网络建模与态势分析理论研究
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摘要
随着互联网的迅速发展，对基于Web的社交网络的研究引起了越来越多的研究者的关注，并取得了一批研究成果。但目前对社交网络的研究大多数是基于典型的图论理论，忽略了顶点和边的属性及其关联关系，不能很好地反映出Web上社交网络的动态性、隐含模糊性、信息粗糙性、不确定性以及关系多维性的特征。本文针对社交网络的复杂特征，研究构建社交网络数学模型的理论基础，探索对社交网络上个体及其结构进行态势分析的有效方法，从而达到全面、准确地了解多维不确定社交网络的状态，对社交网络进行高效挖掘、态势分析的目的。
首先，针对社交网络中个体和链接均具有属性的特征，在传统图论的基础上，构建一种描述复杂社交网络的新结构——属性图，并对属性图的基本性质进行了研究。在属性图的基础上，运用粗糙集理论，研究构建了粗糙属性图模型，以描述社交网络中结点和链接属性的不完备性和关系的多样性。进一步结合社交网络的动态性，融合S-粗糙集理论，构建S-粗糙属性图模型，分析S-粗糙属性图、粗糙属性图、属性图以及传统图之间的关系。
其次，基于属性图模型，研究社交网络进行图查询、图搜索时的子图匹配问题，提出了粗匹配属性子图的随机游走判定算法；基于粗糙属性图模型，提出了粗糙中心区挖掘算法；基于S-粗糙属性图，定义了S-图精度和粗糙度，并证明了迁移函数与图粗糙度的关系，提出了一种社交网络的动态分析方法；通过实例验证了粗糙属性图和S-粗糙属性图在实际应用中的有效性。
再次，在已构建的社交网络数学模型基础上，考虑社交网络中结点及其关系的多维性、不确定性等特征，从复杂系统思想出发，运用集对分析方法构建集对社交网络分析模型，提出λ网络中心区和α关系社区等概念，并设计了相应的静态和动态挖掘算法，通过实验验证方法的有效性和合理性。
最后，拓展集对势为广义集对势，构建对应的态势级别表，对社交网络结点关系与个体关系强度进行态势分析；拓展联系熵为广义联系熵，定义了社交网络关系社区的联系熵，提出了一种对社交网络态势及稳定性进行分析的方法。基于广义集对势同时考虑社交网络上实体间结点和边属性存在的差异性，提出了一种基于属性-关系的网络实体相似度计算方法，并设计基于此方法的网络社团检测算法，通过实例验证方法的合理性。
With the constant growth of internet, it has great significance to study the socialnetwork based on Web which has attracted more and more wide attention and anumber of research results have been made. However, the most researches on socialnetwork are based on the typical graph theory which ignores the attribute of node,edge and their relationship, so it could not well reflect the characteristic of dynamic,implicit fuzziness, information roughness and uncertainty and multidimensionalrelation of social network on the Web.In allusion to the complex features of socialnetwork, the theory foundation of modeling the social network is studied and theefficient method for analyzing the trend of the entity on the social and its structure,so as to achieve the purposes that can understand the state of the multi-dimensionaluncertain social networks accurately, and mining the social network efficiently.
First, in allusion to the feature that individual and link have attributes in thesocial network, on the basis of traditional graph theory, it is built a new structure todescribe the complex social network—“attribute graph”. The basic property of theattribute graph is studied. On the basis of the attribute graph theory, the model ofrough attribute graph is built by integrating the rough set so as to describe theincomplete nodes and links relationship in the social network. Further more,considering the dynamic of nodes and links relationship in the social network, theS-rough attribute graph model is built by integrating the S-rough set theory. Therelationship between the S-rough attribute graph and rough attribute graph isdemonstrated.
Secondly, it studies the sub graph matching problem in graph query and graphsearch of social networks based on the attribute graph.The decision algorithms areput forward. Based on the rough graph, the rough center area is defined and itsmining algorithm is designed which is proved efficient by an example.Based on theS-rough attribute graph, the relation between the transfer function and the graphroughness is proved so that there will have a simple and convenient method for analyzing the social network dynamically.
Thirdly, On the basis of mathematical model constructed in the social network,considering the characteristic of multi-dimensional, uncertainty of nodes and theirrelationships in the social network, the model of set pair social network analysis isbuilt by applying the set pair analytical method. In view of the model, the conceptsof λ network central community and α relationship community are proposed.Further more, the mining algorithms of static and dynamic are designed which isdemonstrated the effectiveness and rationality by the experiments.
Finally, the set pair potential is expanded into the generalized set pair potentialand the corresponding trend level table is built. The relation entropy is expanded intothe generalized relation entropy. The trends of the individual, relationship and thewhole social network are analyzed.In view of the generalized set pair potential, themethod is given how to calculate the network entity similarity based on attributesand relationships. It is demonstrated the method is reasonable by an example.
首先，针对社交网络中个体和链接均具有属性的特征，在传统图论的基础上，构建一种描述复杂社交网络的新结构——属性图，并对属性图的基本性质进行了研究。在属性图的基础上，运用粗糙集理论，研究构建了粗糙属性图模型，以描述社交网络中结点和链接属性的不完备性和关系的多样性。进一步结合社交网络的动态性，融合S-粗糙集理论，构建S-粗糙属性图模型，分析S-粗糙属性图、粗糙属性图、属性图以及传统图之间的关系。
其次，基于属性图模型，研究社交网络进行图查询、图搜索时的子图匹配问题，提出了粗匹配属性子图的随机游走判定算法；基于粗糙属性图模型，提出了粗糙中心区挖掘算法；基于S-粗糙属性图，定义了S-图精度和粗糙度，并证明了迁移函数与图粗糙度的关系，提出了一种社交网络的动态分析方法；通过实例验证了粗糙属性图和S-粗糙属性图在实际应用中的有效性。
再次，在已构建的社交网络数学模型基础上，考虑社交网络中结点及其关系的多维性、不确定性等特征，从复杂系统思想出发，运用集对分析方法构建集对社交网络分析模型，提出λ网络中心区和α关系社区等概念，并设计了相应的静态和动态挖掘算法，通过实验验证方法的有效性和合理性。
最后，拓展集对势为广义集对势，构建对应的态势级别表，对社交网络结点关系与个体关系强度进行态势分析；拓展联系熵为广义联系熵，定义了社交网络关系社区的联系熵，提出了一种对社交网络态势及稳定性进行分析的方法。基于广义集对势同时考虑社交网络上实体间结点和边属性存在的差异性，提出了一种基于属性-关系的网络实体相似度计算方法，并设计基于此方法的网络社团检测算法，通过实例验证方法的合理性。
With the constant growth of internet, it has great significance to study the socialnetwork based on Web which has attracted more and more wide attention and anumber of research results have been made. However, the most researches on socialnetwork are based on the typical graph theory which ignores the attribute of node,edge and their relationship, so it could not well reflect the characteristic of dynamic,implicit fuzziness, information roughness and uncertainty and multidimensionalrelation of social network on the Web.In allusion to the complex features of socialnetwork, the theory foundation of modeling the social network is studied and theefficient method for analyzing the trend of the entity on the social and its structure,so as to achieve the purposes that can understand the state of the multi-dimensionaluncertain social networks accurately, and mining the social network efficiently.
First, in allusion to the feature that individual and link have attributes in thesocial network, on the basis of traditional graph theory, it is built a new structure todescribe the complex social network—“attribute graph”. The basic property of theattribute graph is studied. On the basis of the attribute graph theory, the model ofrough attribute graph is built by integrating the rough set so as to describe theincomplete nodes and links relationship in the social network. Further more,considering the dynamic of nodes and links relationship in the social network, theS-rough attribute graph model is built by integrating the S-rough set theory. Therelationship between the S-rough attribute graph and rough attribute graph isdemonstrated.
Secondly, it studies the sub graph matching problem in graph query and graphsearch of social networks based on the attribute graph.The decision algorithms areput forward. Based on the rough graph, the rough center area is defined and itsmining algorithm is designed which is proved efficient by an example.Based on theS-rough attribute graph, the relation between the transfer function and the graphroughness is proved so that there will have a simple and convenient method for analyzing the social network dynamically.
Thirdly, On the basis of mathematical model constructed in the social network,considering the characteristic of multi-dimensional, uncertainty of nodes and theirrelationships in the social network, the model of set pair social network analysis isbuilt by applying the set pair analytical method. In view of the model, the conceptsof λ network central community and α relationship community are proposed.Further more, the mining algorithms of static and dynamic are designed which isdemonstrated the effectiveness and rationality by the experiments.
Finally, the set pair potential is expanded into the generalized set pair potentialand the corresponding trend level table is built. The relation entropy is expanded intothe generalized relation entropy. The trends of the individual, relationship and thewhole social network are analyzed.In view of the generalized set pair potential, themethod is given how to calculate the network entity similarity based on attributesand relationships. It is demonstrated the method is reasonable by an example.
引文
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