Social networks have become an indispensable part of modern life. Signed networks, a class of social network with positive and negative edges, are becoming increasingly important. Many social networks have adopted the use of signed networks to model like (trust) or dislike (distrust) relationships. Consequently, how to rank nodes from positive and negative views has become an open issue of social network data mining. Traditional ranking algorithms usually separate the signed network into positive and negative graphs so as to rank positive and negative scores separately. However, much global information of signed network gets lost during the use of such methods, e.g., the influence of a friend’s enemy. In this paper, we propose a novel ranking algorithm that computes a positive score and a negative score for each node in a signed network. We introduce a random walking model for signed network which considers the walker has a negative or positive emotion. The steady state probability of the walker visiting a node with negative or positive emotion represents the positive score or negative score. In order to evaluate our algorithm, we use it to solve sign prediction problem, and the result shows that our algorithm has a higher prediction accuracy compared with some well-known ranking algorithms.
Signed network [
How to measure the importance of nodes in a social network has always been an important issue in many data mining fields such as collaborative filtering [
A classical node ranking method is known as PageRank [
In this paper, we propose a novel ranking method for signed network. Our contributions are as follows:
This paper is organized as follows. Section
In recent years, signed networks have attracted more and more attention for its ability to specify trust or distrust relationships between nodes. Network modeling and network topology analysis are important foundations for the study of signed networks. BSCL [
PageRank [
In order to make traditional methods applicable to negative edges, researchers have proposed some new methods. Modified PageRank [
At first, a signed network is denoted by a weighted graph
We will introduce a novel random walk model for signed network (RWSN for short) and simulate the behavior of users accessing online social network sites. RWSN supposes a walker randomly visits a user’s home page. After that, the walker will visit one of the neighbors of this page.
The walker could have a positive or negative emotion when accessing social networks, and the edges of social networks have positive or negative signs. The reasons why the walker has positive emotion may be the following ones:
In contrast, the walker gets into negative emotion because of the following:
In our model, if a walker travels through a negative link, he/she will flip his/her sign, whereas the walker will keep the sign unchanged if he/she travels through a positive link. We define such rules according to structure balance theory of sign network [
For example, Figure
An example of RWSN. Alice starts walking with positive emotion.
Figure
An example of RWSN. Alice starts walking with negative emotion.
We say that
We say that the subscripts
Figure
An example of trap.
We use hopping probability
Then we can use an iterative approach to update
In this section, we will prove the convergence of (
where
where
According to Markoff’s convergence theorem [
We can calculate
First, we initialize
In the experiment, first we use a simple example to verify the effectiveness of the algorithm; then we compare our algorithm with some other ranking algorithms to prove that SignRank is better.
An example of signed network is shown in Figure
An illustration of signed network. The positive relationships are marked with red plus, and negative relationships are marked with green minus sign.
The positive and negative scores of four nodes according to SignRank. The tired probability
The positive and negative scores of four nodes according to SignRank. The tired probability
The positive and negative scores of four nodes according to SignRank. The tired probability
In Figure
It is very difficult to give a direct proof that our ranking algorithm is better than other algorithms, so we adopted an indirect method that has been used by many researchers to prove the superiority of their algorithm [
Reputation and optimism can be calculated through the ranking score
In this paper, we can measure a node with its positive and negative scores, so we can extend
Correspondingly,
Therefore, in this paper, we generate eight features denoted by vector v for each edge and then use logistic regression for sign prediction.
We choose accuracy, recall, precision, and F1 to evaluate the quality of our method and comparative methods. And their definitions are as follows: Accuracy is the proportion of correctly predicted edges. Recall is the proportion of correctly predicted edges in actually positive edges. Precision is the proportion of correctly predicted edges in predicted positive edges. F1 is the harmonic mean of precision and recall.
To study the performance of our algorithm, we apply it in sign prediction and compare it with ranking algorithms as follows. PageRank [ Hits [ Modified PageRank [ TrollTrust [
In the experiment, we used three signed network datasets described in Table
Datasets statistics.
Datasets | Nodes | Edges | Edges+(%) | Edges-(%) |
---|---|---|---|---|
|
131828 | 841372 | 85.3 | 14.7 |
|
81867 | 545671 | 77.4 | 22.6 |
|
11258 | 178096 | 78.3 | 21.7 |
Epinions: Epinions.com is a consumer review website where members present their opinions toward each other, and these opinions can be trusted or distrusted. Epinions records these trust or distrust relationships.
Slashdot: slashdot.org is a technology-related news website where users could tag each other as friend or foe. Slashdot records these friend or foe relationships.
Wiki-RFA: Wikipedia is a free online encyclopedia. If a Wikipedia editor wants to become an administrator, a request for adminship (RfA) must be submitted. Any Wikipedia member may cast a supporting, neutral, or opposing vote. Wiki-RFA records these supporting or opposing relationships.
We execute SignRank and comparison methods (PageRank, Hits, MPR, and TrollTrust) on Slashdot, Epinions, and Wiki-RFA datasets. Then we calculate features according to (
Figures
Accuracy, precision, recall, and f1 score of sign prediction on Slashdot.
Accuracy, precision, recall, and f1 score of sign prediction on Epinions.
Accuracy, precision, recall, and f1 score of sign prediction on Wiki-RFA.
This paper presents a novel random walk model for signed network. It simulates the action of visiting online social network websites with emotion. When the visitor feels unhappy, he/she leaves. In this way, our model has a clear semantic interpretation of the ranking score, which is the steady probability of the walker visiting the node with emotion. Furthermore, this paper presents an iterative algorithm described in Algorithm
The datasets (Epinions, Slashdot, and Wiki-RFA) used to support the findings of this study are open access and they can be downloaded from
The authors declare no conflicts of interest.
This work was supported by the National Natural Science Foundation of China under Grants 61702089 and 61501102 and the Basic Scientific Research Operating Foundation of central universities under Grant N182304021, and the Science and Technology Support Program of Northeastern University at Qinhuangdao (XNK201401).