Social Network Information Propagation Model Based on Individual Behavior

Lejun Zhang , Hongjie Li , Chunhui Zhao , Xiaoying Lei ＊

1 College of Information Engineering, Yangzhou University, Yangzhou, 225127,China

2 College of Computer Science and Technology, Harbin Engineering University Harbin 150001,China* The corresponding author, email： xylei@yzu.edu.cn

I. INTRODUCTION

Social networking has become the most popular means of information exchange in people’s daily lives. Therefore, information dissemination in social networks has attracted the attention of many researchers. Traditional research mostly focuses on the macroscopic characteristics of the network and less on the traits of individual behavior in social networks.However, there is a significant link between information dissemination in social networks and the behavior of individuals. Because of the complexity of social networks, research and modeling can be difficult in a real network environment and requires establishing an information propagation model in line with the real network characteristics and propagation mechanisms. Building an information dissemination model for social networks based on individual behavior provides the prerequisite and foundation for the future of social network analysis.

The rapid rise of social media has attracted a large number of researchers to model the behavior of users on social media[1], the users’ forwarding behavior on Twitter[2], their review behavior of pictures on Flickr[3], their interaction behavior on MySpace[4], scholars’cooperative behavior on paper research[5],and users’ behavior when citing research documents. A maximized influence can actually attribute to individual behavior modeling.Anagnostopoulos et al.[2]and Wang et al.[6]proposed methods to quantify the influence of users. Goyal et al.[7]constructed a user behavior model using the user behavior logs of social networks. While national studies of individual behavior based on social networks lag behind those of other countries, tracking and development are more rapid and have produced a series of research results. For instance,Cao Jianxun verified the differences in individual behavior between accessing common sites and accessing porn sites and designed a method of porn site identi fication based on individual behavior[8]. Liu Guohua conducted empirical research on the behavior of mobile phone users when sending text messages and conducted a statistical analysis of users’ behavioral characteristics[9]. Tang Yu analyzed the relationship between online and offline networking and provided metrics and analysis methods based on structures and relationships[10]. Individual behavior models also play an important role in practical applications. Hong Wenxing established a recruitment system for the city of Xiamen by analyzing individual behavior, which is of considerable practical value[11]. Tang Jie built a probability model that models and predicts human behavior by studying internet users, and veri fied its validity with a real data set from social networks[12].From the above-discussed research approaches, we can see achievements in the study of individual behavior; however, an information dissemination model based on individual behavior has not been reported yet. This paper aims to establish an information dissemination model for social networks based on individual behavior.

In this paper, the authors show a social-network information dissemination model based on individual behaviors and propose a classification and identi fication method for individual behaviors.

II. INDIVIDUAL BEHAVIOR CLASSIFICATION AND RECOGNITION METHOD

There are many researches about user behavior in online social networks and information dissemination exists. One of the common methods is extracting user behavior characteristics and use machine learning algorithm to classify and predict user behavior[13]. The features they widely use are the in fluence of user,the intimacy between the users, the interest similarity of user, Weibo content importance,and so forth. In online social network, individuals usually have different behavior, which will influence the information dissemination.For example, an inactive user will not forward the message received. So the behavior of individuals will decide the dissemination direction and span. But most of the existing methods consider that the individual’s behavior in the social network is the same during the process of information dissemination.

The individuals in social networks play different roles in the information dissemination process. We consider the individual behavior of homogeneous and heterogeneous groups,which is the basis for conducting the individual classi fication. First, we classify individual behavior based on the acts of individuals in the information dissemination process. Then,we extract factors that in fluence individual behavior and quantify the feature value of these factors. Finally, we use machine-learning methods to identify the type of individual.

2.1 Individual behavior classi fication

Since every individual has his/her own way of thinking, emotion, and will, individual behavior will have a variety of manifestations. This article classifies the behavior of individuals based on how they performed when receiving and forwarding information in social networks, which directly relates to the dissemination of information. We found that some individuals are accustomed to receiving information, but do not like forwarding information. Some individuals receive and forward information while other individuals do not.Therefore, we divided the test subjects into Spreader, Terminator, and Ignorant based on how they disseminate information.

1.Spreader： The test subjects accepted information from other individuals in social networks and spread the information to their adjacent individuals; abbreviated as S.

2.2 Factors affecting individual behavior

Different individuals have different habits,and the same individual will demonstrate a different behavior depending on the sources of information. In the following, we extract four features from individuals who released information and individuals who received the information and from their relationship. The features can be quanti fied and build the basis for identifying an individual’s behavior and type. The four features are described below.

2.2.1 Individual in fluence

Different individuals have different in fluence in social networks, so their impact on the choices and behavior of other individuals vary.To study the influence of an individual who has published information on the sharing behavior of other individuals, the paper analyzes the characteristics associated with the individual’s in fluence, such as professional authority and popularity. However, these features are qualitative and difficult to quantify. Therefore,this paper presents an index to measure an individual’s in fluence that is easy to quantify and is a generalization of the features described above.

Since this article is about an individual’s performance in the dissemination of information, we characterize the individual by his/her ability to influence other individuals to disseminate information in the network. The more information is shared, the greater the individual’s influence. The average time an information is shared can be used as indicator to measure the individual’s in fluence. In addition, the individual’s position in the network is directly related to the individual’s in fluence.This is mainly re flected by the degree of network topology. Studies have shown that the number of Twitter fans indirectly reflects the user’s in fluence[14]. The higher the number, the more users can directly see the information published by him/her. The more users see the information, the more likely it is that the information is forwarded. The more often the information is forwarded, the quicker it spreads to a larger audience.

In this paper, we estimate an individual’s influence by determining the average probability that his/her information is shared. This is calculated by the ratio of the average share time and the average number of individuals who obtain the information. The number of individuals who receive the information is obtained by traversing the whole spread tree and is not easy to obtain. Therefore, in this article,we approximate this number by the number of fans. It is worth noting that the in fluence of the most in fluential individual may be overestimated due to this approximation because the number of fans may be far less than the number of individuals who received information.To reduce this effect, we added an exponential according to reference [1]. Through a thorough analysis, we set the value to 1/3.

2.2.2 Forwarding preference

To extract the features that in fluence an individual to receive or forward information, we need to consider the individual’s forwarding preferences. Some individuals prefer forwarding behavior, like sharing information with friends. Other individuals just like to read information or express their feelings and views,but do not like to forward information. We use the forwarding preference of individuals to characterize the forwarding possibility when receiving information. Whether an individual chooses to forward information depends on his/her habits, personality, and preferences. We can identify a pattern in an individual’s behavior from historical records of his/her behavior.If the historical data reveals that the individual frequently forwarded information, it indicates a high degree of individual forwarding preferences.

In this paper, we express an individual’s forwarding preference by the ratio of his/her average daily forwarding amount and the average daily release amount. To reflect the individual’s recent dynamics, we consider the amount of his/her forwarding and releasing activities in the past month. Because an individual’s behavior varies over time, the individual’s preferences or behavior may change.Selecting the individual’s behavior in the past month can re flect the current status of the individual.

2.2.3 Individual activity

Not all registered users in a social network are active users. There are also non-active users and zombie users. The amount of time an individual spends online can re flect the activity of the individual to a certain extent because the individual’s activity is directly related to the ability of receiving information. Obviously, if the individual has not been online for a while,he/she is not able to receive, read, or forward information.

We focus on an individual’s activity to characterize his/her ability to receive information. An individual’s activity can also change over time because the individual may no longer be curious about or interested in the social networking site, and therefore his/her activity will naturally drop. We use the individual’s online time within the past week (7 days) to quantify the individual’s activity as follows.

We divide one day into eight periods： 0：00-3：00 marks the first period, 3：00-6：00 marks the second period, 6：00-9：00 marks the third period, 9：00-12：00 marks the fourth period,12：00-15：00 marks the fifth period, 15：00-18：00 marks the sixth period, 18：00～21：00 marks the seventh period, and 21：00～24：00 marks the eighth period.

Suppose

Definition 3: Assume that individualube expressed as：

2.2.4 Forwarding intimacy

Because every individual has his/her own feelings and way of thinking, an individual’s acceptance of information from different individuals differs. Just as in real life, where relationships between people can be close, alienated, important, or unimportant, the users of social networks can have strong or weak ties.People tend to be more concerned with close relationships. In social networks, individuals are more likely to share information coming from users with whom they have a close relationship. If in the past individualufrequently forwarded information that was released by individualv, then he/she is more likely to forward information from individualvin the future.

We use forwarding intimacy to characterize an individual’s preference for the information source. We can determine an individual’s intimacy from his/her historical records. The more information individualuforwarded that he/she had received from individualv, the higher the forwarding intimacy between individualuand individualv. To take the characteristics of an individual’s change of behavior over time into account, we consider the interaction record between the two individuals from the last month.

2.3 Individual behavior recognition method

The accumulation of real-time individual behavior logs in social networks makes the research on individual behavior models more convenient and effective. An individual’s past behavior reflects his/her behavior pattern to a certain extent. Based on the characteristics of the individual’s past behavior, we can predict his/her behavior and decisions. Based on their information dissemination behavior, we divided the test subjects into three categories：Spreader, Terminator, and Ignorant. Therefore,the task of identifying an individual’s behavior is mapped into the task of classifying the individual’s behavior characteristics.

Details of the individual classi fication process are as follows：

III. INFORMATION PROPAGATION MODEL BASED ON INDIVIDUAL BEHAVIOR

The classi fication and identi fication method of an individual’s behavior lays the foundation for constructing an information transmission model. Figure 1 shows the flow chart of the model construction.

3.1 Random time generation method

Previous studies have shown that the time delay in information dissemination has a significant impact on the scale and speed of information dissemination [15, 16]. However,the traditional information dissemination model does not take into account the time delay of the information dissemination process, or it cannot reproduce the process reliably. Therefore, this paper proposes a method for generating a random time to simulate an individual’s behavior when receiving information with a delay.

Individuals cannot immediately receive information when it is released because they are not likely to remain online at any time.We call the time that passes between releasing of information and the individual reading the information the receiving delay. Because the behavior of the individual receiving the information is random, it is impossible to determine the exact receiving delay. Although the receiving delay is random, it has certain stability in general. It can count the frequency of the individual’s activities in each period according to the behavior of the individual on social networking sites. We then simulate the individual’s receiving delay behavior based on the statistical results. We introduce our simulation method of an individual’s receiving delay in detail below, which is the method for generating a random time.

We obtain the individual’s frequencies of activity for the respective periods, where a period is divided into 24 hours and represented researchers found that 75% of the information was forwarded in the first twenty-four hours after its release on Twitter, and this proportion has increased year by year. This means that the vast majority of the forwarding behavior occurs within twenty-four hours after the release of the information. To keep our method simple, we assume that the individual’s reading and forwarding behavior occurs in the first twenty-four hours after the information is pushed to the individual’s home page.

Our random time generation steps are as follows：

Fig. 1 Flow chart of model construction

(2)Randomly generate a number i between 1 and 100 and take out the element arr [i].

(3)Determine the random interval

The unit of time used is minutes; it has some randomness to it but is consistent with the individual’s activity frequency, which we

3.2 Information visibility prediction method

An individual receives a lot of information every day, but his/her energy is limited, and the individual will miss reading some of the information since he/she cannot pay attention to all of this information all the time. The traditional information dissemination model is based on the assumption that information will be seen and read when it is pushed to the individual’s home page. This is not the case, because the visibility of information has an important influence on the scale and speed of information dissemination. In this paper, we propose an information visibility prediction method, which makes the design of the information dissemination model more appropriate to the actual process of information dissemination. The design of the information visibility prediction method is given below.

3.3 Information dissemination model based on individual behavior

The method we introduced above lays the foundation for an information dissemination model based on individual behavior. We describe the model’s design and algorithm below.

To facilitate the description, we consider four properties (＜＞,＜＞,＜Type＞,＜Status＞)for each individual. Propertyrefers to the total delay from the beginning of the information release to the reading time of the upper level individual that directly forwarded the information to him/her. Propertyrefers to the delay from the time when the upper level individual forwarded the information to the time that the individual read the information.The sum ofandis the total delay of the individual from the beginning of the information release, and it is used as propertyfor the next level individual. Type refers to the type of the individual that we de fined as Spreader(S), Terminator (T), or Ignorant (I) in Section 2.1. Status refers to the state of the individual.We distinguish between two states： known and unknown. State “known” means that the individual has read the information. State “unknown” means that the individual did not see the information.

Figure 2 is a schematic diagram of information dissemination, whereis the individual who released the information,is of the Terminator (T) type who reads the information(i.e., the state of the individual is known) but does not forward it,is of the Ignorant (I)type who does not see the information (i.e.,the individual is in the unknown state) and does not transfer the information, andis the of Spreader (S) type who sees the information and forwards it. As can be seen in the figure,it can get the scale of information dissemination as long as the individuals who are in the known state are counted.

(1) At the initial moment, the information is not released, all individuals in the network do not know the information, the state of all individuals is unknown, K is the individual set of individuals in the known state who read the information and is empty, R is the set of individuals who forwarded the information and is empty, and set A is empty.

(2) One individual in the network (whom we call the release individual) has released a new message. The release individual’s attributes at the moment when he/she released the information (i.e., at the initial moment of information dissemination) are (0, 0, S, known),so the values ofandare 0 and the release individual wants to spread the information and is of type S. Because the release individual must have read the information, his/her state is known. We can calculate the in fluence of the release of the individual when determining the release individual.

(3) The information will be pushed to all the fans of the individual after the information is released or forwarded, then all the fans of the individual can be added to the set A.

Fig. 2 Schematic diagram of information transmission

(5) After the random delay time, the individualjvisits his/her home page, but does not necessarily read the information released by the release individual. We can predict the probability that individualjsees the information according to the information visibility prediction method introduced in Section 3.2.The probability that individualjwill read this information is, which is calculated using the formula described in Step 6.

(6) Calculate the characteristic value of the individual which includes the forwarding preference, individual activity, forwarding intimacy to the upper individual, and the individual type determined by the individual identification method introduced in Section 3.1.

(7) If individualjwho read this message is an S-type individual, add him/her to sets K and R, and go back to step 3. If individualjwho read this message is a T-type individual,add him/her to set K, and continue to the next step. If individualjwho read this message is an I-type individual, continue to step (8).

(8) When the collection A is empty, the calculation ends.

3.4 Result evaluation method of information dissemination

The information dissemination model designed in this paper can be used to predict the scale of information dissemination and the time of propagation. Since the results cannot be the same as the real results, it is effective as long as the prediction results are in a reasonable range, and the difference between the predicted results and the real results can be explained.

We found that the forwarding scale follows the power-law distribution from existing research results[18]：

Equation (10) is equivalent to (11)：

In order to better evaluate the prediction results, the accuracy of the prediction is used as the evaluation index of the prediction results.The prediction accuracy is de fined as the ratio of the correct number to the total number of predictions：

The evaluation method is cited by other articles many times. In order to facilitate comparison we use formula (12) as evaluation method.

IV. RESULT AND DISCUSSION

4.1 Data description

Sina Weibo is the country’s largest domestic micro-blogging site. It has many registered and online users, and has become the most common means of spreading information. Its excellent social networking features and information dissemination capabilities are very relevant for our research, and it is the ideal platform for data collection.

Sina Weibo contains an enormous amount of data and is the ideal platform for social network analysis and data mining research,but its open platform limits the external API interface used to access the data. The complete information cannot be accessed through the API interface only, and, therefore, the APIs do not meet the demand for this study. Although Sina Weibo makes some of the data sets publicly available, these data sets contain either only user data or only some of the micro blog content data. The user data and content data do not correspond, and we cannot obtain the complete dissemination routes and user relationship topologies. Therefore, we use crawler technology to imitate the client operations and collect the data from the hard disk.

We use a breadth- first strategy to extract the data. We first select a user as seed node and then get the user’s fans and a list of fans. Next,we obtain the attentions and Weibo messages of each node from October 1, 2014 to March 1, 2015. Finally, we clean up the data, which results in 20853 remaining users and 846573 pieces of Weibo information.

4.2 Information dissemination prediction

Because the scale of information dissemination cannot be easily determined, the information dissemination model constructed in this paper cannot assess the scale of information dissemination. However, we can obtain the forwarding scale from the data set and we can use the information dissemination model proposed in this paper to predict the accuracy of the forwarding scale. We randomly sampled 1000 users from the data set, filtered out those users with less than 10 original messages, and predicted the forwarding size for each user.Figure 3 shows the accuracy of prediction for each user.

As can be seen in Figure 3, the prediction accuracy of the information dissemination model proposed in this paper lies in the range of 0.8-0.9 and has a good accuracy. It also indirectly proves the rationality and validity of the information dissemination model constructed from the aspects of individual behavior.

Figure 3 also shows that while the prediction of the forwarding scale is accurate in general, some individuals’ predictions are not ideal. We analyzed the outliers whose accuracy is low and found that these nodes share common features： (1) the number of fans is small (2) the number of messages released recently is low,and (3) the level of activity is low.

We analyzed the common features of the outliers and found that the impact of fewer fans will lead to a greater impact, the activity is low because they have fewer recent release messages and therefore less information of the individual is exposed and we cannot fully extract the behavior characteristics of the individual. However, the prediction accuracy of the information forwarding scale equals the average of all messages of the individual and therefore the prediction result is not sufficiently stable.

Some researchers used machine learning algorithm to classify and predict user behavior,such as Support Vector Machine (SVM)[13]and Extreme Learning Machine (ELM)[19]. The features they widely use are the influence of user, the intimacy between the users, the interest similarity of user; We compared our work with them in Table 1.

Fig. 3 Forwarding scale prediction accuracy

We discussed the prediction of the scale of information dissemination above. The infor-mation dissemination model proposed in this paper can also provide us a time prediction of information dissemination. To better describe the propagation time information, we propose an indicator as de fined below：

De finition 4: Assume that the number of pressed as：

As can be seen in Figure 4, the difference of most of the predicted values and true values is not large, indicating that the information propagation time prediction and the actual situation is similar. The information propagation model proposed in this paper can effectively predict the information propagation time. However,Figure 4 also shows that there are several differences between the predictive value and the real value. Through repeated analysis, we conclude that the individuals, whose propagation time predictions are not sufficiently accurate,have a common feature their number of fans is small. The relationship between the number of individual fans and the prediction accuracy of the propagation time is analyzed below.

Before calculating individual time prediction accuracy of information dissemination,we must first establish a method to judge the prediction accuracy. We de fine that the prediction is correct as long as Formula (14) is met.

Based on the statistics, the accuracy of the individual corresponding to the number of different fans, the relationship between the number of fans, and the time of propagation prediction are established as shown in Figure 5. As can be seen in Figure 5, when the number of fans of an individual is small, the rate of time prediction accuracy of information dissemination is low. When the number of fans increases, the prediction accuracy also gradually increases. When the number of fans reached a certain size, the prediction results have a stable accuracy. The generated random time is highly random, and this is particularly evident when the number of fans is small.However, with an increasing number of fans,the original contingency exhibits a certain degree of inevitability and reduces the predicted distortion due to the large sample.

4.3 In fluence of individual type distribution on information transmission

In the network, different individuals play different roles in the process of information transmission. Therefore, this paper classifies the individual and constructs the information dissemination model based on the individual’s behavior. If the proportion of various individ-uals in the network is different, what is the impact on the scale and speed of information dissemination?

Table I Comparison experiment table

Fig. 4 Information propagation time prediction

We re-predict the spread scale of information by modifying the distribution of the individual types of proportion. First, we reduce the number of type-S individuals, and then we increase the number of type-S individuals.These two situations of individual type distributions are shown in Table 2.

In Table 1, the default row corresponds to the distribution proportion of the individual’s type under normal conditions. For the Type1 row, we take the default row and replace half of type-S individuals by type T. For the Type2 row, we take the default row and randomly replace some of the type-T individuals by type S, so that the proportion of type-S individuals is 2%. These cases are predicted and we obtain a variety of information dissemination scales. The prediction results of the information dissemination scales are shown in Figure 6, where the x-axis represents the propagation time of the information, the y-axis represents the proportion of the information that is received by the individual, and each line corresponds to one of the three cases shown in Table 1.

By analyzing the in fluence of different individual behaviors on the information dissemination of social networks, we found that when different proportions of individuals are used,the influence on the information dissemination process and the results are also different.From the experimental results we can clearly conclude that the more type-S individuals we have i.e., the more individuals who are willing to accept information and spread it the greater and faster the spread of information.

4.4 Eff ect of forwarding delay on information transmission

The information dissemination model proposed in this paper considers the impact of forwarding delay on the process of information dissemination and is more appropriate to the true communication process. The necessity and effectiveness of the forwarding delay is verified based on real data sets. The random times when individuals receive information is reduced by half. We use this model to predict the transmission of information and compare the results of the forecast and the original pre-diction results in Figure 7. The “default” line shows the normal delay in the case of information dissemination of the results and the “modify” line shows the case where the propagation delay time has been changed.

Table II Distribution proportion of individuals

Fig. 5 Relationship between individual fans account and the propagation time prediction accuracy

Fig. 6 Effect of individual type change on the spread scale

As can be seen in Figure 7, the forwarding delay will not only affect the speed of information propagation, but will also affect the scale of information dissemination. It is consistent with the view mentioned in the literature [17], i.e., the closer the time when the individual sees the information is to the release time of the information, the greater the probability that the information is forwarded.This is consistent with the observed individual forwarding behavior, i.e., people like to forward the latest news.

4.5 Eff ect of information visibility on information dissemination

Individuals may not see all the information,because their attention and concern is limited,and they receive a lot of information every day. Information that is not looked at is naturally not known and cannot be forwarded. This means that the visibility of the information directly affects the spread of the information.We conducted the following experiments to verify the results.

To verify that changes in information visibility affect the outcome of information propagation, we conducted an experiment where we reduced information visibility by half and re-predicted the results of information dissemination. Figure 8 compares the prediction results with the original predictions. The “default” line shows the results for the original information visibility, and the “alter” line shows the results for the modi fied visibility.

As can be seen in Figure 8, decreasing the information visibility reduces the speed and size of information dissemination. This is consistent with people’s perception that the more people see the information, the more likely that they will pay attention and forward that information. It also con firms the necessity and rationality of considering the visibility of the information when constructing an information dissemination model.

V. CONCLUSION

Fig. 7 Effect of forwarding delay on the process of information transmission

Fig. 8 Effect of the spread of information visibility

The main contributions of this paper are as follows： (1) constructing a social-network information dissemination model based on individual behavior, (2) proposing a classi fication and identification method for individual behavior, (3) illustrating the dissemination of information when constructing the model, and(4) presenting a model that not only predicts the scale of information dissemination, but also the propagation time. For the dissemination of information, we presented a method for generating a random time to simulate the delay in propagating the information and raising the information visibility in the prediction method.

This paper provides a new perspective on the importance of individual behavior on the dissemination of information. The random time generation method simulates the delay characteristics of the information dissemination process. This allows us to predict the propagation time and to bring the scale prediction of information dissemination closer to the actual situation. The method of forecasting the information visibility can predict the likelihood that the individual will see the information, describe the propagation of information more accurately, and improve the forecast accuracy of the information dissemination time and scale. The model is based on the classi fication and identi fication of individual behavior and takes into account the delay characteristics of information dissemination. Combined with the information visibility prediction method,we can predict the scale and velocity of information propagation quite accurately. Although the proposed information propagation model provides several achievements, it can still be improved. We plan to conduct further research and will use complex text analysis techniques,such as sentiment analysis, to build a more detailed information dissemination model.

ACKNOWLEGEMENTS

The authors would like to thank the reviewers for their detailed reviews and constructive comments, which have helped improve the quality of this paper. This work is sponsored by the National Natural Science Foundation of China under grant number No. 61100008;the Natural Science Foundation of Heilongjiang Province of China under Grant No.LC2016024.

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