網路嵌入目的在於學習網路中每個節點的低維向量表示式，並且同時保留網路的內在信息，網路嵌入有助於進一步的網路分析，例如社群偵測 (community detection)和鏈接預測 (link prediction)等應用。然而，大多數的社群網路具有節點特性或邊特性來表示節點和邊的資訊。對於有號網路 (signed network)，邊特性代表著點與點之間的友誼/敵人或信任/不信任的關係。雖然已經有許多有號網路的嵌入模型被提出，但它們只支援其中一種關係的有號網路做嵌入，因此較難應用在大多數有號網路中使用。在這本論文中，我們提出了一個靈活且有效的特性網路的模組性嵌入（SiME），它利用指數隨機圖模型取樣保留網路中兩種關係的訊息，並且得到取樣網路 (sampled graph)。基於取樣網路，模組性 (modularity)的概念也可以被定義。然後，利用模塊性我們可以解決模塊化嵌入問題並獲得特性網路的嵌入結果。最後，利用真實網路資料進行實驗以說明我們的方法的有效性。

Network embedding aims to learn a low-dimensional vector representation for each node in a network that can preserve specific intrinsic information of the network. It facilitates further embedding tasks such as community detection and link prediction. However, most social networks have node attributes or edge attributes that represent the features of nodes and edges. For the signed network, the edge attributes indicate the friendship/enemy or trust/distrust relationships. Although there are many existing signed network embedding models, they only focus on one of the relationships. So it is hard to support most of the signed network.
In this thesis, we propose a flexible and effective Signed Network Modularity Embedding (SiME) framework which can capture two relationships information of network by using exponentially twisted sampling and obtain the sampled graph. Based on the sampled graph, the modularity of the graph can be defined. Then, using the modularity, we can solve the modularity embedding problem and obtain the embedding results of the attributed network. Experiments are conducted on real datasets to illustrate the effectiveness of our approach.

Abstract
Contents 1
List of Figures 3
1 Introduction 4
2 Related work 9
3 Sampled graph 11
3.1 Review of the probabilistic framework of sampled graphs . . . . . . . . . 11
3.2 Exponentially twisted sampling . . . . . . . . . . . . . . . . . . . . . . . 14
3.3 Generalized modularity embedding . . . . . . . . . . . . . . . . . . . . . 16
3.4 Estimating the generalized modularity matrix . . . . . . . . . . . . . . . 18
4 Signed network modularity embedding 22
4.1 Friendship embedding module . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2 Trust relationship embedding module . . . . . . . . . . . . . . . . . . . . 25
1
4.2.1 Proposed model - SiME . . . . . . . . . . . . . . . . . . . . . . . 26
5 Attributed network modularity embedding 28
6 Applications of exponentially twisted sampling 30
7 Experiments 32
7.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.2 Baseline algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.2.1 Signed network baseline algorithms . . . . . . . . . . . . . . . . . 34
7.2.2 Attributed network baseline algorithms . . . . . . . . . . . . . . . 35
7.3 Parameter settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.4 Evaluation metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.5 Results and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.5.1 Performance on Three Clusters . . . . . . . . . . . . . . . . . . . 37
7.5.2 Performance on Political blogs . . . . . . . . . . . . . . . . . . . . 38
7.5.3 Performance on BlogCatalog . . . . . . . . . . . . . . . . . . . . . 43
7.5.4 Parameters Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . 43
8 Conclusions 47
9 Bibliography 48

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