# A Proposed Method for Predicting User Disinformation Forwarding Behavior

Authors: Bing Fang; Fan Zhang; Limin Hou; Enpeng Hu; Jingwen Zhang; Junyang Shen; Yang Chen
Journal: Scientific Programming
 (2022)

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## Abstract

At present, social network sites (SNSs) have become the major channels by which disinformation is released and disseminated. Without the effective control of disinformation on social media, a serious threat to social stability may occur. Different from traditional media, forwarding has become the key approach to propagating information on social media. Therefore, if the users who will forward the disinformation are identified in advance, they can be prevented from forwarding the disinformation and the harmful effects of disinformation will be minimized. To identify the users who will forward the disinformation, we should predict the probability of an individual forwarding disinformation. We propose a novel method to predict the disinformation forwarding probability of individuals on a social network. The proposed method extracts the features that affect individual disinformation forwarding, especially extracting features related to the susceptibility of users to disinformation. With combining bootstrap sampling and expectation-maximization (EM) algorithm to learn unobserved features, the proposed method utilizes both observed and unobserved features to predict the disinformation forwarding probability of individuals. Using data from “Weibo,” which is the largest social media platform in China, we demonstrate the effectiveness of the proposed method.


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## Body

## 1. Introduction

At present, social network sites (SNSs), such as Facebook and Twitter, have become the major channels by which information is released and disseminated. SNSs create huge commercial value; however, they also increase the difficulty of preventing disinformation [1]. According to Oxford Dictionary, disinformation refers to “false information that is given deliberately” [2]. Compared to other credible information, the common feature of disinformation is that “the intention of mislead and spread false information about various occasions in the world” [3]. Worse still, disinformation propagates much faster than other credible information on social media [1, 4–6]. Without the effective control of disinformation on social media, a serious threat to social stability may occur [7, 8].Different from traditional media, forwarding has become the key approach to propagating information on social media. Forwarding refers to a user passing on a message written by someone else [9]. As shown in Figure 1, initially, information is posted on social media by one or a few users. Next, their follower-fans read these posts and forward it. Eventually, these posts are widely spread on social media after forwarded for multiple times. As a result, if disinformation is not forwarded for multiple times, it is not capable of spreading widely. Therefore, if we can identify the users who will forward the disinformation and take corrective actions in advance, we can prevent them from forwarding the disinformation and minimize the harmful effects of disinformation, as shown in Figure 2. To identify the users who will forward the disinformation, we should predict the probability of an individual forwarding disinformation. It is of crucial importance for both businesses and governments. If commercial organizations or governments can identify users who will forward disinformation in advance, they can spread denials of false information to target users. As a result, the probability of the large-scale spread of disinformation can be decreased effectively and the losses caused by disinformation can be reduced considerably.Figure 1
The process of propagating information on social media.Figure 2
The process of spreading denials of disinformation.Predicting the probability of an individual forwarding disinformation is also of academic importance. Disinformation forwarding is essentially a process of user behavior spreading. User behavior spreading on a social network refers to users following the behavior performed by someone else when they see it [10]. Studying the spread of behavior on an online social network “has long been a fundamental area in social sciences, particularly social computing” [11]. To better understand the spread of user behavior, a fundamental question is how to predict (future) probability of individual behavior who have not adopted by now [11].However, few previous studies have directly addressed the probability of social network disinformation forwarding. This research issue mainly involves user information forwarding behavior on social networks and disinformation spreading across social networks. Current research on user information forwarding behavior on social networks mainly treats this problem as a classification task. Specifically, they extract the features that affect user information forwarding behavior and train the classifier using the extracted features to predict user information forwarding behavior. Therefore, the extracted features will undoubtedly influence the prediction accuracy. Current research on user information forwarding behavior mainly focuses on features related to user influence and textual content. In fact, the features affecting user information forwarding are not exactly the same as those affecting user disinformation forwarding [12–14]. The key difference is that the susceptibility of users to disinformation has a clear impact on user disinformation forwarding behavior, while it has negligible impact on user information forwarding behavior. If users are able to recognize the disinformation, they will not forward it. On the contrary, if users are deluded by the disinformation, they will be very likely to forward it. In addition, current research on user information forwarding behavior rarely takes unobserved features into considerations [10, 11, 15–17]. On the other hand, current research on the spread of disinformation on social networks mainly investigates the spread of disinformation among groups. They focus on the features related to disinformation and susceptible population, while ignoring the features related to individuals [7, 18–21]. As a result, they are still inappropriate for the prediction of individual disinformation forwarding.To overcome the limitations mentioned above, we propose a novel method called user disinformation forwarding behavior prediction (DFP) method to predict the disinformation forwarding probability of individuals on a social network. The DFP method also treats this problem as a classification task: it extracts the features that affect individual disinformation forwarding, especially extracting features related to the susceptibility of users to disinformation. With combining bootstrap sampling and expectation-maximization (EM) algorithm to learn unobserved features, the DFP method utilizes both observed and unobserved features to predict the disinformation forwarding probability of individuals. Here, the bootstrap method is used for sampling training data and the EM algorithm is used for learning the parameters of unobserved variables.The remainder of this paper is organized as follows. In Section2, we review relevant previous research and discuss the differences between our proposed method and existing methods. In Section 3, we describe the method to predict the disinformation forwarding probability of individuals on social networks. To demonstrate the superiority of our proposed method, in Section 4, we evaluate its effectiveness on real data from social networks using representative existing methods as benchmarks. Finally, in Section 5, we summarize the findings of this study, discuss the theoretical and practical contributions, and conclude with the limitations of our research.


## 2. Literature Review

Previous researchers rarely directly solved the problem of predicting the disinformation forwarding probability on social networks, so we review related studies, including research on user forwarding behavior on social networks, disinformation spreading on social networks, and the spread of behavior on social networks.


### 2.1. Studies on User Forwarding Behavior on Social Networks

Studies on user forwarding behavior on social networks aim at solving the problem related to the information forwarding behavior of social network users. Researchers found that the features directly related to forwarding behavior mainly include the following: (1) intensity of influence of the information publisher on the forwarders: Wu et al. found that the strength of interaction between the publisher and forwarders correlated with the final volume of forwarding, Wang et al. used the trust between users to predict forwarding behavior [22, 23], and Asif Khan et al. used interaction between leaders and their supporters to analyze the retweet network [24]. (2) Textual content: both Wu and Shen [23] and Firdaus et al. [25] found that emotion in textual content could affect user forwarding behavior. Wang et al. used the similarity between the content of Twitter posts to predict forwarding behavior [22, 23, 25]. Wang and Yang learnt text feature from text content and combined text feature with social feature to predict forwarding behavior using multitask deep learning technology [17]. (3) Network topology indicated that when most active users belonged to the same social circle, this reduced the probability of forwarding information [26]. (4) Contextual information: Zhang et al. combined contextual information and social information to predict forwarding behavior [14]. (5) User behavior history: Lymperopoulos used users’ history behaviors and the popularity of tweets to predict forwarding behavior [16]. These studies demonstrated that the characteristics of the publisher, social network, and textual content all affected disinformation forwarding behavior. However, these results cannot be fully applied to predicting disinformation forwarding behavior because the studies mainly focused on social network data and ignored the characteristics of the disinformation itself.


### 2.2. Studies on Disinformation Spreading on Social Networks

The main way to spread information on social networks is forwarding; accordingly, most information spreading features are also disinformation forwarding features. Among them, the features that have been identified to be directly related to disinformation forwarding mainly include the following: (1) social homogeneity: M. Del Vicario et al. found that the disinformation receiver tended to make the same choice as users in the same social circle, that is, forwarding the disinformation or not [7]. Askarizadeh and Tork Ladani found that disinformation generally started from one or multiple users and spread through between the trusted friends [20]. Oh et al. further explained this phenomenon [27]. They found that people tended to emotionally trust information from acquaintances or people in the same social circle, even when its source was ambiguous. (2) Network topology: Doerr et al. found that disinformation was quickly forwarded from connections between influential users to a large number of ordinary users around them [28]. (3) People’s beliefs: Zimmermann and Kohring indicated that the less people trusted news media and politics, the more they trusted online disinformation [29]. F.B. Soares et al. suggested informational characteristics of online disinformation and the psychological mediators could promote online disinformation forwarding behavior [21]. It is noted that these studies did not utilize those findings to predict individual forwarding behavior prediction. (4) Attractiveness of disinformation: Zhang et al. mentioned that the attractiveness of disinformation had a marked impact on the transmission pattern of user forwarding [19]. (5) Characteristics of the disinformation receiver group: Liu et al. found that the ability of users to distinguish disinformation and the refutation of disinformation by users could interrupt the spread of disinformation [30]. These studies demonstrated that the characteristics of social networks, disinformation, and users on social networks could all influence disinformation forwarding behavior. However, few in-depth studies have been conducted on individual’s forwarding disinformation, and the results of the aforementioned studies cannot be directly applied to the prediction of individual disinformation forwarding behavior.


### 2.3. Studies on the Spread of Behavior on Social Networks

Disinformation forwarding is a kind of user behavior spreading. The spread of user behavior on a social network has long been a fundamental study area in social computing [11]. In many relevant studies, researchers found that the features that were directly related to disinformation forwarding mainly include the following: (1) network topology: Centola found that the size, centrality, and density of social circles were positively related to the probability of behavior spreading [10]. Wang et al. also indicated that a multiplexing network would promote behavior spreading [31]. (2) Social influence among users: Centola et al. found that social reinforcement between members could promote behavior spreading, and Bond et al. found that behavior spreading among close friends was more prominent [10, 15]. (3) Social convergence: both Centola and Aral and Nicolaides found that social convergence had a positive impact on behavior spreading [32, 33]. (4) Social persuasiveness and unobserved features: Fang et al. found that compared with social influence, social persuasiveness (composed of social interaction, entity similarity, and structural equivalence) and unobserved features could better predict the probability of user behavior spreading [11]. These studies demonstrated that the characteristics of social networks, the interaction between members, and social convergence should be taken into consideration when predicting disinformation forwarding. However, these studies rarely considered the susceptibility of individual users to disinformation. They were also not fully applicable to predicting disinformation forwarding behavior.From the above analysis, current studies have significantly contributed in the prediction of disinformation forwarding. However, there are still mainly three limitations in these studies. First, few studies address the susceptibility of users to disinformation. They mainly focus on some social network data features, particularly the social influence of information publishers. However, the susceptibility of users to disinformation is an essential feature that affects disinformation forwarding. Second, few studies consider the unobserved features when predicting user forwarding behavior. Most studies treat the prediction of user information forwarding as a classification task. Regular classification algorithms cannot handle unobserved features. It will influence the prediction accuracy inevitably. Final, current research on the spread of disinformation on social networks mainly investigates the spread of disinformation among groups, with ignoring the features related to individuals. They are inappropriate for the prediction of individual disinformation forwarding.To overcome the limitations mentioned above, we propose a novel method to predict the probability of individual disinformation forwarding on social networks. This method systematically explores the key features that affect the forwarding of disinformation and measurement methods of each feature and combines bootstrap sampling and EM algorithm to learn unobserved features.


## 2.1. Studies on User Forwarding Behavior on Social Networks

Studies on user forwarding behavior on social networks aim at solving the problem related to the information forwarding behavior of social network users. Researchers found that the features directly related to forwarding behavior mainly include the following: (1) intensity of influence of the information publisher on the forwarders: Wu et al. found that the strength of interaction between the publisher and forwarders correlated with the final volume of forwarding, Wang et al. used the trust between users to predict forwarding behavior [22, 23], and Asif Khan et al. used interaction between leaders and their supporters to analyze the retweet network [24]. (2) Textual content: both Wu and Shen [23] and Firdaus et al. [25] found that emotion in textual content could affect user forwarding behavior. Wang et al. used the similarity between the content of Twitter posts to predict forwarding behavior [22, 23, 25]. Wang and Yang learnt text feature from text content and combined text feature with social feature to predict forwarding behavior using multitask deep learning technology [17]. (3) Network topology indicated that when most active users belonged to the same social circle, this reduced the probability of forwarding information [26]. (4) Contextual information: Zhang et al. combined contextual information and social information to predict forwarding behavior [14]. (5) User behavior history: Lymperopoulos used users’ history behaviors and the popularity of tweets to predict forwarding behavior [16]. These studies demonstrated that the characteristics of the publisher, social network, and textual content all affected disinformation forwarding behavior. However, these results cannot be fully applied to predicting disinformation forwarding behavior because the studies mainly focused on social network data and ignored the characteristics of the disinformation itself.


## 2.2. Studies on Disinformation Spreading on Social Networks

The main way to spread information on social networks is forwarding; accordingly, most information spreading features are also disinformation forwarding features. Among them, the features that have been identified to be directly related to disinformation forwarding mainly include the following: (1) social homogeneity: M. Del Vicario et al. found that the disinformation receiver tended to make the same choice as users in the same social circle, that is, forwarding the disinformation or not [7]. Askarizadeh and Tork Ladani found that disinformation generally started from one or multiple users and spread through between the trusted friends [20]. Oh et al. further explained this phenomenon [27]. They found that people tended to emotionally trust information from acquaintances or people in the same social circle, even when its source was ambiguous. (2) Network topology: Doerr et al. found that disinformation was quickly forwarded from connections between influential users to a large number of ordinary users around them [28]. (3) People’s beliefs: Zimmermann and Kohring indicated that the less people trusted news media and politics, the more they trusted online disinformation [29]. F.B. Soares et al. suggested informational characteristics of online disinformation and the psychological mediators could promote online disinformation forwarding behavior [21]. It is noted that these studies did not utilize those findings to predict individual forwarding behavior prediction. (4) Attractiveness of disinformation: Zhang et al. mentioned that the attractiveness of disinformation had a marked impact on the transmission pattern of user forwarding [19]. (5) Characteristics of the disinformation receiver group: Liu et al. found that the ability of users to distinguish disinformation and the refutation of disinformation by users could interrupt the spread of disinformation [30]. These studies demonstrated that the characteristics of social networks, disinformation, and users on social networks could all influence disinformation forwarding behavior. However, few in-depth studies have been conducted on individual’s forwarding disinformation, and the results of the aforementioned studies cannot be directly applied to the prediction of individual disinformation forwarding behavior.


## 2.3. Studies on the Spread of Behavior on Social Networks

Disinformation forwarding is a kind of user behavior spreading. The spread of user behavior on a social network has long been a fundamental study area in social computing [11]. In many relevant studies, researchers found that the features that were directly related to disinformation forwarding mainly include the following: (1) network topology: Centola found that the size, centrality, and density of social circles were positively related to the probability of behavior spreading [10]. Wang et al. also indicated that a multiplexing network would promote behavior spreading [31]. (2) Social influence among users: Centola et al. found that social reinforcement between members could promote behavior spreading, and Bond et al. found that behavior spreading among close friends was more prominent [10, 15]. (3) Social convergence: both Centola and Aral and Nicolaides found that social convergence had a positive impact on behavior spreading [32, 33]. (4) Social persuasiveness and unobserved features: Fang et al. found that compared with social influence, social persuasiveness (composed of social interaction, entity similarity, and structural equivalence) and unobserved features could better predict the probability of user behavior spreading [11]. These studies demonstrated that the characteristics of social networks, the interaction between members, and social convergence should be taken into consideration when predicting disinformation forwarding. However, these studies rarely considered the susceptibility of individual users to disinformation. They were also not fully applicable to predicting disinformation forwarding behavior.From the above analysis, current studies have significantly contributed in the prediction of disinformation forwarding. However, there are still mainly three limitations in these studies. First, few studies address the susceptibility of users to disinformation. They mainly focus on some social network data features, particularly the social influence of information publishers. However, the susceptibility of users to disinformation is an essential feature that affects disinformation forwarding. Second, few studies consider the unobserved features when predicting user forwarding behavior. Most studies treat the prediction of user information forwarding as a classification task. Regular classification algorithms cannot handle unobserved features. It will influence the prediction accuracy inevitably. Final, current research on the spread of disinformation on social networks mainly investigates the spread of disinformation among groups, with ignoring the features related to individuals. They are inappropriate for the prediction of individual disinformation forwarding.To overcome the limitations mentioned above, we propose a novel method to predict the probability of individual disinformation forwarding on social networks. This method systematically explores the key features that affect the forwarding of disinformation and measurement methods of each feature and combines bootstrap sampling and EM algorithm to learn unobserved features.


## 3. A Proposed Method for Predicting User Disinformation Forwarding Behavior

We propose a novel method called DFP to predict the disinformation forwarding probability of individuals on a social network. As illustrated in Figure3, the DFP method consists of three stages:(1)
Identifying features: we identify features that affect user disinformation forwarding behavior on social networks based on the theory related to behavior spreading on social networks and measure these features(2)
Predicting the probability of user being persuaded to forward a disinformation: we predict the probability that a user is persuaded to forward a disinformation(3)
Predicting the probability of user forwarding disinformation: we predict the probability of a user forwarding a disinformation with considering unobserved featuresFigure 3
The DFP method for predicting user disinformation forwarding behavior.


### 3.1. Identify Features That Affect User Disinformation Forwarding Behavior on Social Networks

#### 3.1.1. Theoretical Basis

Aral et al. indicated that behavior spreading on social networks could be regarded as a result of the interaction between social influence, user susceptibility, and user self-publishing [34]. Users create social influence that affects their opinions, attitudes, and behaviors within a social network. Chaiken et al. found that the influence is essentially social persuasiveness [35]. Fang et al. further suggested that social persuasiveness originated not only from social influence, but also the combination of social influence, entity similarity, and social structural equivalence [11, 36]. According to social comparison theory, people adjust their behavior according to the information released by other people around them to reduce uncertainty when they made decisions. Pfeffer et al., Friedkin, and Festinger further proposed the social influence network theory [37–39]. According to this theory, users on social networks usually have their own ideas about events from the beginning and then further consolidate or change their opinion or attitude by interacting with other members in the social network. These theories all suggest that social influence is generated in the interaction between users on social networks [40], and it could affect the views and behaviors of users [40–42]. Therefore, when people invest a great deal of time and energy in establishing solid social connections with each other, they tend to trust members with strong social connections. It means that social influence between members with strong social connections is much stronger than that between other members [43–45].Social comparison theory and social influence network theory suggest that entity similarity also has an impact on behavior spreading. They found that the behaviors or opinions of social network users were similar simply because their characteristics were similar [46, 47]. Generally, entity similarity refers to the degree to which two entities in a social network are similar demographically and behaviorally [48]. People with similar demographic characteristics usually have similar needs and preferences [49]. People with similar behavior usually have similar views on products or services [33, 49]. McPherson et al. found that the similarity in behavior between members was even independent of their interaction behavior [50]. Generally, the more similar the members are, the more likely they are to take concerted actions [11].The characteristics of social network topology also affect the views and behaviors of users on this social network [51, 52]. Studies have shown that network structure characteristics could affect the similarity of views and behaviors between users on this social network [52, 53]. Structural equivalence is a basic feature of social network topology. Users with equivalent structures tend to have similar views and behaviors because they tend to learn from users with equivalent structures when they make decisions [51]. Additionally, the topological structure characteristics of communities and the characteristics of individual users also affect the degree of similarity of views and behaviors between members [10, 54].Previous studies rarely took the susceptibility of users into consideration when predicting user behavior. Instead, they often used social influence to indirectly measure susceptibility [54, 55]. In fact, the awareness of received information is also essentially a type of susceptibility of users, which is independent of social influence, and also affects the views and behaviors of users [56–58]. Researchers have found that people believe disinformation and actively spread them on social networks only when they are susceptible to disinformation, whereas other people do not respond to disinformation because they detect disinformation or believe disinformation but are not interested in them [59]. The reason that people are susceptible to disinformation is that the content of disinformation is consistent with their original cognition. Specifically, the degree of agreement between the characteristics of disinformation content and their cognition (i.e., susceptibility) determines their susceptibility to disinformation [60]. This also means that exploring the susceptibility of people to disinformation features can help to predict the susceptibility of people to disinformation. The characteristics of a disinformation include the following: the information form of the disinformation, such as the #, @, URL, length, and picture; semantics; confounding, such as fuzziness and clear behavior; and emotion [1].It is difficult to measure the spontaneous behavior of users directly, which can be regarded as the unobserved features of disinformation forwarding. Additionally, the disinformation forwarding behavior of users may also be affected by other confounding features [46, 61] that include the specific content about the interaction of people and the spread of disinformation offline [62]. In addition to the features that can be traced to a clear source, there are many unobserved features that can significantly influence the disinformation forwarding behavior of people [63].Based on the above analysis, we first measure the features that affect the disinformation forwarding of social network users in addition to confounding features and then use the features that influence the disinformation forwarding of social network users, including confounding features, to predict the disinformation forwarding probability of social network users.


#### 3.1.2. Operationalization

Based on the above discussion, we divide the features of the disinformation forwarding behavior of social network users into four categories: the strength of social influence of the disinformation publisher on the disinformation forwarder, the entity similarity between the disinformation publisher and disinformation forwarder, the structural equivalence between the disinformation publisher and disinformation forwarder, and the susceptibility of the user to disinformation.(1) Social Influence. Suppose V=v1,v2,…,vn is a group of users on a social network. Users are connected by two-way or one-way links. The social influence of user vi on user vj (hereinafter referred to as the influence power) is denoted by Iij. Iij is measured as the interaction intensity Xij between user vi and user vj:(1)Iij=Xij−XminXmax−Xmin,where Xmax and Xmin denote the maximum and minimum social connection strengths, respectively. Additionally, standardization helps to prevent Iij from relying on the measurement unit of Xij. Interaction intensity Xij is a three-dimensional vector that measures the interaction intensity between users through the three dimensions of thumbs up, forwarding, and comments:(2)Xij=Lij−LminLmax−Lmin,Rij−RminRmax−Rmin,Cij−CminCmax−Cmin.See Table1 for the calculation formula for the interaction strength between user vivi and user vj.Table 1
The calculation formula for the interaction strength
Interaction dimensionsCalculation formulaThumbs upLij=zanij/∑vhϵV,h≠izanhjNote 1: Lij denotes the interaction intensity between user vi and user vj in thumbs upNote 2: zanij denotes the number of thumbs up received by user vi from user vjNote 3: zanhj denotes the number of thumbs up received by user vhh≠i from user vjNote 4： Lmax and Lmin denote the maximum and minimum values among all Lij, respectivelyForwardingRij=zhuanij/∑vhϵV,h≠izhuanhjNote 1: Rij denotes the interaction intensity between user vi and user vj in forwardingNote 2: zhuanij denotes the number of microblogs of user vi forwarded by user vjNote 3: zhuanhj denotes the number of microblogs of user vhh≠i forwarded by user vjNote 4: Rmax and Rmin denote the maximum and minimum values among all Rij, respectivelyCommentsCij=commentij/∑vhϵV,h≠icommenthjNote 1: Cij denotes the interaction intensity of user vi and user vj in commentsNote 2: commentij denotes the number of microblogs of user vi commented by user vjNote 3: commenthj denotes the number of microblogs of user vhh≠i commented by user vjNote 4: Cmax and Cmin denote the maximum and minimum values among all Cij, respectively(2) Entity Similarity. The entity similarity between user i and user j is denoted by Sij. Sij is measured as the similarity of each feature between user i and user j, that is, the distance between each feature:(3)Sij=dmax1−dvi1,vj1dmax1−dmin1,dmax2−dvi2,vj2dmax2−dmin2,dmax3−dvi3,vj3dmax3−dmin3,dmax4−dvi4,vj4dmax4−dmin4,where dmax1,dmax2,dmax3,anddmax4 denote the maximum value of each feature distance among all users and dmin1,dmin2,dmin3,anddmin4 denote the minimum value of each feature distance among all users.The features that we use to measure the entity similarity of users can be divided into three categories: the profile similarity of users, the behavior similarity of users, and the comprehensive similarity of users. Additionally, the corresponding calculation formula for the entity similarity between usersvi and vj is shown in Table 2.Table 2
The calculation formula for the entity similarity.
The feature types to measure user entity similarityFeature nameCalculation formulaProfile similarity between usersNumber of followeesdvi1,vj1=num_guanzhuvi−num_guanzhuvj/maxnum_guanzhu−minnum_guanzhuNote 1: dvi1,vj1 denotes the similarity between user vi and user vj in the number of followeesNote 2: num_guanzhuvi and num_guanzhuvJ denote the number of followees of user vi and user vj, respectivelyNote 3: maxnum_guanzhu and minnum_guanzhu denote the maximum and minimum values among all dvi1,vj1, respectivelyNumber of followersdvi2,vj2=num_fensivi−num_fensivi/maxnum_fensi−minnum_fensiNote 1: dvi2,vj2 denotes the similarity between user vi and user vj in the number of followersNote 2: num_fensivi and num_fensivi denote the number of followers of user vi and user vj, respectivelyNote 3: maxnum_fensi and minnum_fensi denote the maximum and minimum values among all dvi2,vj2, respectivelyBehavior similarity between usersForwarding behaviorSen_disvik,vj=maxSenviknSenvj1/SenvikSenvj1,SenviknSenvj2/SenvikSenvj2,…,SenviknSenvjn/SenvikSenvjn, dvi3,vj3=∑k=1mSen_disvik,vj/mNote 1: Senvik denotes the paragraph vector of the kth blog post forwarded by user viNote 2: Sen_disvik,vj denotes the semantic similarity between the kth blog post forwarded by user vi and all the blog posts forwarded by user vj, and n denotes the number of blog post forwarded by user vjNote 3: dvi3,vj3 denotes the similarity of forwarding behavior between user vi and user vj, and m denotes the number of blog posts forwarded by user viComprehensive similarity between usersComprehensive of usersdvi4,vj4=∑k=13dvik,vjk/3Note 1: dvi4,vj4 denotes the comprehensive similarity of all features between user vi and user vj(3) Structural Equivalence. The structural equivalence between user i and user j is denoted by Eij. Eij is measured as the similarity of each topological structure feature between user i and user j, that is, the distance between each topological structure feature:(4)Eij=emax1−evi1,vj1emax1−emin1,emax2−evi2,vj2emax2−emin2,…,dmax13−dvi13,vj13dmax13−dmin13,where emax1,emax2,…,emax11 denote the maximum value of each topology feature distance among all users and emin1,emin2,…,emin11 denote the minimum value of each topology feature distance among all users.The features that we use to measure the user structure equivalence can be divided into three categories: topological structure equivalence, the individual topological structure feature similarity between users, and the topological feature similarity for the community of users. The corresponding calculation formula for the structural equivalence of uservi and user vj is shown in Table 3.Table 3
The calculation formula for the feature types to measure structural equivalence.
The feature types to measure user structure equivalenceFeature nameCalculation formulaUser topological structure equivalenceUser topological structureevi1,vj1=∑Vz∈V/Vi，VjIiz−Ijz2+Izi−Izj2Note 1: if there exists a link from user va to user vb, Iab  = 1; otherwise, Iab  = 0Note 2: evi1,vj1 denotes user topological structure equivalence between user vi and user vjIndividual topological structure feature similarityDegree centralitydegvi=∑j=1naij/n−1, evi2,vj2=degvi−degvj/maxdegv−mindegvNote 1: degvi and degvj denote the degree centrality of user vi and user vj, respectivelyNote 2: if there exists a link between entity vi and vj, then aij=1; otherwise, aij=0, and n denotes the number of users on social networkNote 3: evi2,vj2 denotes the equivalence of user vi and user vj in degree centralityNote 4: maxdegv and mindegv denote the maximum and minimum values among all degvi, respectivelyCloseness centralityclsvi=n−1/∑j=1ndij, evi3,vj3=clsvi−clsvj/maxclsv−minclsvNote 1: clsvi and clsvj denote the closeness centrality of user vi and user vj, respectivelyNote 2: dij denotes the distance from entity vi to entity vj, and n denotes the number of users on social network Note 3: evi3,vj3 denotes the equivalence of user vi and user vj in closeness centralityNote 4: maxclsv and minclsv denote the maximum and minimum values among all clsvi, respectivelyBetweenness centralitybjkvi=gjkvi/gjk, btnvi=∑j=1n∑k=1,k>jnbjkvi/nn−1/2, evi4,vj4=btnvi−btnvj/maxbtnv−minbtnvNote 1: gik denotes the number of shortest paths linking entity vj and entity vk, and gjkvi denotes the total number of shortest paths from entity vj to entity vk, and these paths also traverse entity vi, where i≠j≠kNote 2: btnvi and btnvj denote the betweenness centrality of user vi and user vj, respectivelyNote 3: evi4,vj4 denotes the equivalence of user vi and user vj in betweenness centralityNote 4: maxbtnv and minbtnv denote the maximum and minimum values among all btnvi, respectivelyPercolation centralitypcvi=1/n−2∑j=1n∑k=1,k>jnbjkviDj/∑h=1nDh−Di, evi5,vj5=pcvi−pcvj/maxpcv−minpcvNote 1: pcvi and pcvj denote the percolation centrality of user vi and user vj, respectivelyNote 2: if user vj forwards the disinformation published by user vi, Dj=1; otherwise, Dj=0, where i≠j≠kNote 3: evi5,vj5 denotes the equivalence of user vi and user vj in percolation centralityNote 4: maxpcv and minpcv denote the maximum and minimum values among all pcvi, respectivelyEigenvector centralityEgnvi=xvi=∑j=1naijxvj, evi6,vj6=Egnvi−Egnvj/maxEgnv−minEgnvNote 1: Egnvi and Egnvj denote the eigenvector centrality of user vi and user vj, respectivelyNote 2: xvi and xvj denote the influence of user vi and user vj, respectively, if there exists a link between entity vi and entity vj, then aij=1; otherwise, aij=0Note 3: evi6,vj6 denotes the equivalence of user vi and user vj in eigenvector centralityNote 4: maxEgnv and minEgnv denote the maximum and minimum values among all Egnvi, respectivelyPageRankPrvi=d+1+d∑vjϵIviPrvj/Οvj, evi7,vj7=prvi−prvj/maxprv−minprvNote 1: Prvi and Prvj denote PageRank values of user vi and user vj, respectivelyNote 2: Οvj denotes the number of followers of entity vj. To ensure guarantees global convergence, the attenuation factor d is usually set to 0.15Note 3: evi7,vj7 denotes the equivalence of user vi and user vj in PageRankNote 4: maxprv and minprv denote the maximum and minimum values among all Prvi, respectivelyClustering coefficientcvi=Ei/Cki2=2Ei/kiki−1, evi8,vj8=cvi−cvj/maxcv−mincvNote 1: cvi and cvj denote the clustering coefficient of user vi and user vj, respectivelyNote 2: ki denotes the number of nodes directly connected to entity vi, Ei denotes the actual number of edges of these nodes, and Cki2 denotes the maximum number of edges that may existNote 3: evi8,vj8 denotes the equivalence of user vi and user vj in clustering coefficientNote 4: maxcv and mincv denote the maximum and minimum values among all cvi, respectivelyThe topological feature similarity for the community of usersDegree centralizationDEGvi=∑i=1ndegvimax−degvi/max∑i=1ndegvimax−degvi, evi9,vj9  =  DEGvi−DEGvj/maxDEGv−minDEGvNote 1: DEGvi denotes the degree centralization of the communities which user vi and user vj belong toNote 2: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in degree centralizationNote 3: maxDEGv and minDEGv denote the maximum and minimum values among all DEGvi, respectivelyCloseness centralizationCLSvi=∑i=1nclsvimax−clsvi/max∑i=1nclsvimax−clsvi, evi10,vj10  =  CLSvi−CLSvj/maxCLSv−minCLSvNote 1: CLSvi denotes the closeness centralization of the communities which user vi and user vj belong toNote 2: evi10,vj10 denotes the equivalence of the communities which user vi and user vj belong to in closeness centralizationNote 3: maxCLSv and minCLSv denote the maximum and minimum values among all CLSvi, respectivelyBetweenness centralizationBTNvi=∑i=1nbtnvimax−btnvi/max∑i=1nbtnvimax−btnvi, evi11,vj11  =  BTNvi−BTNvj/maxBTNv−minBTNvNote 1: BTNvi denotes the betweenness centralization of the communities which user vi and user vj belong toNote 2: evi11,vj11 denotes the equivalence of the communities which user vi and user vj belong to in betweenness centralizationNote 3: maxBTNv and minBTNv denote the maximum and minimum values among all BTNvi, respectivelyCommunity clustering coefficientCvi=∑i=1ncvimax−cvi/max∑i=1ncvimax−cvi, evi12,vj12  =  Cvi−CvjmaxCv−minCvNote 1: Cvi denotes the clustering coefficient of the communities which user vi and user vj belong toNote 2: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in clustering coefficientNote 3: maxDEGv and minDEGv denote the maximum and minimum values among all Cvi, respectivelyCommunity sizeSvi=∑Vz1,Vz2∈VIz1z2, evi13,vj13  =  Svi−Svj/maxSv−minSvNote 1: Svi denotes the size of the communities which user vi and user vj belong toNote 2: if there exists a link from user vZ1 to user vZ2, IZ1Z2  = 1; otherwise, IZ1Z2  = 0Note 3: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in community sizeNote 4: maxSv and minSv denote the maximum and minimum size among all Svi, respectively(4) Susceptibility to Disinformation. The susceptibility of users to disinformation refers to the susceptibility of users to various characteristics of disinformation. The susceptibility of user vj to disinformation Mi is denoted by Fij. Fij is measured as the satisfaction degree of disinformation to various features and the susceptibility of the user to various features of disinformation. The calculation formula is as follows:(5)Fij=Mi1∗YGj1,Mi2∗YGj2,…,Mik∗YGjk,∑p=1kMip∗YGjp,where Mip denotes the satisfaction degree of disinformation Mi to a certain feature and YGjp denotes the susceptibility of user vj to a certain feature of the disinformation.The characteristics of disinformation mainly belong to three categories: formal features, popularity, and semantic features. The formula for calculating disinformationMi that corresponds to the feature satisfaction degree Mip is shown in Table 4.Table 4
The susceptibility of users to disinformation features.
The feature types of disinformationFeature nameCalculation formulaFormal featuresHashtagMi1=1if the rumorMihas a  hashtag，0   if the rumorMidoes not have  a  hashtag.MentionMi2=1if  rumorMimentions  uservj，0  if  rumorMidoes not  mention uservj.HyperlinksMi3=1if  rumorMihas hyperlinks，0  if  rumorMidoes not have  hyperlinks.With pictures or videosMi4=1if  rumorMihas pictures  or videos，0  if  rumorMidoes not  have   pictures  or videos.LengthMi5=lengthi−minlength/maxlength−minlengthNote 1: lengthi denotes the length of disinformation Mi, and maxlength and minlength denote the maximum and minimum values among all lengthi, respectivelyNote 2: Mi5 denotes the relative length of disinformation Mi among all disinformationPopularityForwarding numberMi6=retweeti−minretweet/maxretweet−minretweetNote 1: retweeti denotes the forwarding number of disinformation Mi, and maxretweet and minretweet denote the maximum and minimum values among all retweeti, respectivelyNote 2: Mi6 denotes the relative forwarding number of disinformation Mi among all disinformationComment numberMi7=commenti−mincomment/maxcomment−mincommentNote 1: commenti denotes the comment number of disinformation Mi, and maxcomment and mincomment denote the maximum and minimum values among all commenti, respectivelyNote 2: Mi7 denotes the relative comment number of disinformation Mi among all disinformationLike numberMi8=likei−minlike/maxlike−minlikeNote 1: likei denotes the like number of disinformation Mi, and maxlike and minlike denote the maximum and minimum values among all disinformation likei, respectivelyNote 2: Mi8 denotes the relative like number of disinformation Mi among all disinformationSemantic featuresAmbiguityMi9=1if  rumorMihas  amphibolous  words,0  if  rumorMidoes not  have  amphibolous  words. Note: constructing an amphibolous dictionary to check whether disinformation contains amphibolous wordsInductivityMi10=1if  rumorMihas  inductivity words,0  if  rumorMidoes not have  inductivity  words. Note: constructing an inductivity dictionary to check whether disinformation contains inductivity wordsEmotional intensityMi11=∑1nemotionn/nNote 1: emotioni denotes the emotional intensity of words in disinformationNote 2: Mi11 denotes the emotional intensity of disinformation MiNote 3: the emotional intensity of a word is determined by using an emotional dictionaryThe susceptibility of users to disinformation features is calculated as the mean value of the corresponding features of all Weibo posts forwarded by them, which is then normalized. The calculation formula is as follows:(6)YGjp=∑p=1mMjp/m−min∑p=1mMjp/mmax∑p=1mMjp/m−min∑p=1mMjp/m,where Mip denotes the value of the p-th attribute of each microblog forwarded by user Vi and max∑p=1mMjp/m and min∑p=1mMjp/m denote the maximum and minimum susceptibility of users to the p attribute, respectively, p = 1, 2, …, 10.


### 3.2. Predict the Probabilityp_persuadeik of User vi Being Persuaded to Forward Disinformation Mk

Becausep_persuadeik is determined by the power of all friends to persuade a user to forward disinformation, we first calculate the probability p_persuadeik that user vi is persuaded by each friend to forward disinformation Mk.According to the analysis in the previous section, the features that influence whether uservi forwards disinformation mk published by friend vj comprise mainly four aspects: the social influence intensity Iij of user vj on user vi, the entity similarity Sij between user vi and user vj, the structural equivalence Eij between user vi and user vj, and the susceptibility Fik of user vi to disinformation mk. Therefore, the calculation formula of p_persuadeijk is as follows:(7)ppersuadeijk=Ppersuadeijk=1=PRetweetijk=1|Iij,Sij,Eij,Fik,where Retweetijk=1 indicates that user vi forwards disinformation mk published by friend vj and persuadeijk=1 indicates that user vj persuades user vi to forward disinformation mk.We predictpijk using the random forest algorithm. To improve the prediction accuracy of pijk, we predict p_persuadeijk using the bagging method and M-estimation. In particular, we extract training samples using the bootstrap method from the original sample set and obtain 50 training sets after 50 rounds of extraction. Then, we train 50 decision trees from these sample data and calculate p_persuadeijk as the average value of the probability estimation of the 50 decision trees. The training process and prediction process are shown in Figures 4 and 5, respectively.Figure 4
Construction of the training data algorithm.Figure 5
Prediction process.Then, we calculate the probabilityp_persuadeijk of user vi being persuaded to forward disinformation Mk. The calculation formula of p_persuadeik is as follows:(8)ppersuadeik=Ppersuadeik=1=1−∏vj∈V1−ppersuadeik,where persuadeik=1 indicates that user vi is persuaded to forward disinformation Mk.


### 3.3. Predict the Probabilityp_retweetik of User vi Forwarding Disinformation Mk

We denote the unobserved variable that affects uservi forwarding disinformation Mk by Hik and combine it with the probability p_persuadeik of user vi being persuaded to forward disinformation Mk. Then, according to the Bayesian probability formula, the calculation formula of p_retweetik is as follows:(9)pRetweetik=PRetweetik=1|ppersuadeik,Hik=PRetweetik=1Pppersuadeik,Hik|Retweetik=1∑r=0,1PRetweetik=rPppersuadeik,Hik|Retweetik=r.For the naive Bayesian estimation, we assume thatHik and p_persuadeik are independent. Then,(10)pRetweetik=PRetweetik=1Pppersuadeik|Retweetik=1PHik|Retweetq=1∑r=0,1PRetweetik=rPppersuadeik|Retweetik=rPHik|Retweetik=r.In the naive Bayes algorithm, a common approach is to make the probability density of each input variable obey the exponential distribution [64]. Then, we can describe the probability density function of PRetweetik=r as follows: fRetweetik=λRetweetike−λRetweetikx,x≥0, where λRetweetik is the parameter of the probability density function, r=0,1. Then, we can estimate PRetweetik=r as fRetweetik.We can estimate Pp_persuadeik|Retweetik=r and PHq||Retweetik=r in the same manner. Therefore, to compute p_retweetik, we need to learn the following vector of parameters from TRAIN:(11)θ=p1,λppersuadeik|1,λHik|1,p0,λppersuadeik|0,λHik|0,where p1 and p0 are the estimates of prior probability PRetweetik=1 and PRetweetik=0, respectively, and λp_persuadeik|1, λHik|1, λp_persuadeik|0, and λHik|0 are the density parameters for friends persuading users and unobserved power H given disinformation forward decision a, respectively, where a = 0 or 1.Simultaneously, the confounding features are indispensable in a prediction. The problem is how to learn the parameterθ in the case of missing training data.To overcome this obstacle, we combine bootstrap sampling and EM algorithm to learn parameterθ. The bootstrap method is mainly used for sampling training data, whereas the EM algorithm is used for learning the parameters of unobserved variables.The EM algorithm is the most common implicit variable estimation method. It is an iterative process from the initial parameter estimation. Each iteration of EM is composed of Steps E and M. In Step E, the maximum likelihood estimation value is calculated using the existing estimation value of the unobserved variable, whereas in Step M, the value of the parameter is calculated by maximizing the maximum likelihood value obtained in Step E. Additionally, the parameter estimates found in Step M are used in the next Step E calculation and they are conducted alternately.In our study, the specific steps for learning parameters are shown in Figure6.Figure 6
The learning parameter process of the DFP method.As mentioned above, we consider three cases when setting the initial value of the unobserved variable parameters. Therefore, we perform cyclic training for the three cases in the iteration of Steps E and M. The training algorithm for parameterθ is shown in Figure 7.Figure 7
Parameter training algorithm.We can predict the probability of disinformation forwarding after training the parameters. Given parameter estimationθ^, for user vi and disinformation mk,(12)p_retweetik=PRetweetik=1|p_persuadeik,Hik=PRetweetik=1Pppersuadeik|Retweetik=1PHik|Retweetik=1∑r=0,1PRetweetik=rPPsdik|Retweetik=rPHik|Retweetik=r=p^1λ^ppersuadeik|1exp−λ^ppersuadeik|1ppersuadeikλ^Hik|1exp−λ^Hik|1Hik∑r=0,1p^rλ^ppersuadeik|rexp−λ^ppersuadeik|rppersuadeikλ^Hik|rexp−λ^Hik|rHik,where the probability density function of Hik is(13)fHik|θ^=fHik|Rik=1,θ^PRik=1|θ^+fHik|Rik=0,θ^PRik=0|θ^.Therefore, we can use the expected value based onHik to approximately calculate the disinformation forwarding probability. As shown in Figure 8, the forwarding probability inference algorithm generates Hik samples repeatedly and calculates the disinformation forwarding probability using the sample data and equation (12) until it converges. The output of this algorithm is the expected value of the disinformation forwarding probability based on Hq.Figure 8
Inferencing retweet probability.


## 3.1. Identify Features That Affect User Disinformation Forwarding Behavior on Social Networks

### 3.1.1. Theoretical Basis

Aral et al. indicated that behavior spreading on social networks could be regarded as a result of the interaction between social influence, user susceptibility, and user self-publishing [34]. Users create social influence that affects their opinions, attitudes, and behaviors within a social network. Chaiken et al. found that the influence is essentially social persuasiveness [35]. Fang et al. further suggested that social persuasiveness originated not only from social influence, but also the combination of social influence, entity similarity, and social structural equivalence [11, 36]. According to social comparison theory, people adjust their behavior according to the information released by other people around them to reduce uncertainty when they made decisions. Pfeffer et al., Friedkin, and Festinger further proposed the social influence network theory [37–39]. According to this theory, users on social networks usually have their own ideas about events from the beginning and then further consolidate or change their opinion or attitude by interacting with other members in the social network. These theories all suggest that social influence is generated in the interaction between users on social networks [40], and it could affect the views and behaviors of users [40–42]. Therefore, when people invest a great deal of time and energy in establishing solid social connections with each other, they tend to trust members with strong social connections. It means that social influence between members with strong social connections is much stronger than that between other members [43–45].Social comparison theory and social influence network theory suggest that entity similarity also has an impact on behavior spreading. They found that the behaviors or opinions of social network users were similar simply because their characteristics were similar [46, 47]. Generally, entity similarity refers to the degree to which two entities in a social network are similar demographically and behaviorally [48]. People with similar demographic characteristics usually have similar needs and preferences [49]. People with similar behavior usually have similar views on products or services [33, 49]. McPherson et al. found that the similarity in behavior between members was even independent of their interaction behavior [50]. Generally, the more similar the members are, the more likely they are to take concerted actions [11].The characteristics of social network topology also affect the views and behaviors of users on this social network [51, 52]. Studies have shown that network structure characteristics could affect the similarity of views and behaviors between users on this social network [52, 53]. Structural equivalence is a basic feature of social network topology. Users with equivalent structures tend to have similar views and behaviors because they tend to learn from users with equivalent structures when they make decisions [51]. Additionally, the topological structure characteristics of communities and the characteristics of individual users also affect the degree of similarity of views and behaviors between members [10, 54].Previous studies rarely took the susceptibility of users into consideration when predicting user behavior. Instead, they often used social influence to indirectly measure susceptibility [54, 55]. In fact, the awareness of received information is also essentially a type of susceptibility of users, which is independent of social influence, and also affects the views and behaviors of users [56–58]. Researchers have found that people believe disinformation and actively spread them on social networks only when they are susceptible to disinformation, whereas other people do not respond to disinformation because they detect disinformation or believe disinformation but are not interested in them [59]. The reason that people are susceptible to disinformation is that the content of disinformation is consistent with their original cognition. Specifically, the degree of agreement between the characteristics of disinformation content and their cognition (i.e., susceptibility) determines their susceptibility to disinformation [60]. This also means that exploring the susceptibility of people to disinformation features can help to predict the susceptibility of people to disinformation. The characteristics of a disinformation include the following: the information form of the disinformation, such as the #, @, URL, length, and picture; semantics; confounding, such as fuzziness and clear behavior; and emotion [1].It is difficult to measure the spontaneous behavior of users directly, which can be regarded as the unobserved features of disinformation forwarding. Additionally, the disinformation forwarding behavior of users may also be affected by other confounding features [46, 61] that include the specific content about the interaction of people and the spread of disinformation offline [62]. In addition to the features that can be traced to a clear source, there are many unobserved features that can significantly influence the disinformation forwarding behavior of people [63].Based on the above analysis, we first measure the features that affect the disinformation forwarding of social network users in addition to confounding features and then use the features that influence the disinformation forwarding of social network users, including confounding features, to predict the disinformation forwarding probability of social network users.


### 3.1.2. Operationalization

Based on the above discussion, we divide the features of the disinformation forwarding behavior of social network users into four categories: the strength of social influence of the disinformation publisher on the disinformation forwarder, the entity similarity between the disinformation publisher and disinformation forwarder, the structural equivalence between the disinformation publisher and disinformation forwarder, and the susceptibility of the user to disinformation.(1) Social Influence. Suppose V=v1,v2,…,vn is a group of users on a social network. Users are connected by two-way or one-way links. The social influence of user vi on user vj (hereinafter referred to as the influence power) is denoted by Iij. Iij is measured as the interaction intensity Xij between user vi and user vj:(1)Iij=Xij−XminXmax−Xmin,where Xmax and Xmin denote the maximum and minimum social connection strengths, respectively. Additionally, standardization helps to prevent Iij from relying on the measurement unit of Xij. Interaction intensity Xij is a three-dimensional vector that measures the interaction intensity between users through the three dimensions of thumbs up, forwarding, and comments:(2)Xij=Lij−LminLmax−Lmin,Rij−RminRmax−Rmin,Cij−CminCmax−Cmin.See Table1 for the calculation formula for the interaction strength between user vivi and user vj.Table 1
The calculation formula for the interaction strength
Interaction dimensionsCalculation formulaThumbs upLij=zanij/∑vhϵV,h≠izanhjNote 1: Lij denotes the interaction intensity between user vi and user vj in thumbs upNote 2: zanij denotes the number of thumbs up received by user vi from user vjNote 3: zanhj denotes the number of thumbs up received by user vhh≠i from user vjNote 4： Lmax and Lmin denote the maximum and minimum values among all Lij, respectivelyForwardingRij=zhuanij/∑vhϵV,h≠izhuanhjNote 1: Rij denotes the interaction intensity between user vi and user vj in forwardingNote 2: zhuanij denotes the number of microblogs of user vi forwarded by user vjNote 3: zhuanhj denotes the number of microblogs of user vhh≠i forwarded by user vjNote 4: Rmax and Rmin denote the maximum and minimum values among all Rij, respectivelyCommentsCij=commentij/∑vhϵV,h≠icommenthjNote 1: Cij denotes the interaction intensity of user vi and user vj in commentsNote 2: commentij denotes the number of microblogs of user vi commented by user vjNote 3: commenthj denotes the number of microblogs of user vhh≠i commented by user vjNote 4: Cmax and Cmin denote the maximum and minimum values among all Cij, respectively(2) Entity Similarity. The entity similarity between user i and user j is denoted by Sij. Sij is measured as the similarity of each feature between user i and user j, that is, the distance between each feature:(3)Sij=dmax1−dvi1,vj1dmax1−dmin1,dmax2−dvi2,vj2dmax2−dmin2,dmax3−dvi3,vj3dmax3−dmin3,dmax4−dvi4,vj4dmax4−dmin4,where dmax1,dmax2,dmax3,anddmax4 denote the maximum value of each feature distance among all users and dmin1,dmin2,dmin3,anddmin4 denote the minimum value of each feature distance among all users.The features that we use to measure the entity similarity of users can be divided into three categories: the profile similarity of users, the behavior similarity of users, and the comprehensive similarity of users. Additionally, the corresponding calculation formula for the entity similarity between usersvi and vj is shown in Table 2.Table 2
The calculation formula for the entity similarity.
The feature types to measure user entity similarityFeature nameCalculation formulaProfile similarity between usersNumber of followeesdvi1,vj1=num_guanzhuvi−num_guanzhuvj/maxnum_guanzhu−minnum_guanzhuNote 1: dvi1,vj1 denotes the similarity between user vi and user vj in the number of followeesNote 2: num_guanzhuvi and num_guanzhuvJ denote the number of followees of user vi and user vj, respectivelyNote 3: maxnum_guanzhu and minnum_guanzhu denote the maximum and minimum values among all dvi1,vj1, respectivelyNumber of followersdvi2,vj2=num_fensivi−num_fensivi/maxnum_fensi−minnum_fensiNote 1: dvi2,vj2 denotes the similarity between user vi and user vj in the number of followersNote 2: num_fensivi and num_fensivi denote the number of followers of user vi and user vj, respectivelyNote 3: maxnum_fensi and minnum_fensi denote the maximum and minimum values among all dvi2,vj2, respectivelyBehavior similarity between usersForwarding behaviorSen_disvik,vj=maxSenviknSenvj1/SenvikSenvj1,SenviknSenvj2/SenvikSenvj2,…,SenviknSenvjn/SenvikSenvjn, dvi3,vj3=∑k=1mSen_disvik,vj/mNote 1: Senvik denotes the paragraph vector of the kth blog post forwarded by user viNote 2: Sen_disvik,vj denotes the semantic similarity between the kth blog post forwarded by user vi and all the blog posts forwarded by user vj, and n denotes the number of blog post forwarded by user vjNote 3: dvi3,vj3 denotes the similarity of forwarding behavior between user vi and user vj, and m denotes the number of blog posts forwarded by user viComprehensive similarity between usersComprehensive of usersdvi4,vj4=∑k=13dvik,vjk/3Note 1: dvi4,vj4 denotes the comprehensive similarity of all features between user vi and user vj(3) Structural Equivalence. The structural equivalence between user i and user j is denoted by Eij. Eij is measured as the similarity of each topological structure feature between user i and user j, that is, the distance between each topological structure feature:(4)Eij=emax1−evi1,vj1emax1−emin1,emax2−evi2,vj2emax2−emin2,…,dmax13−dvi13,vj13dmax13−dmin13,where emax1,emax2,…,emax11 denote the maximum value of each topology feature distance among all users and emin1,emin2,…,emin11 denote the minimum value of each topology feature distance among all users.The features that we use to measure the user structure equivalence can be divided into three categories: topological structure equivalence, the individual topological structure feature similarity between users, and the topological feature similarity for the community of users. The corresponding calculation formula for the structural equivalence of uservi and user vj is shown in Table 3.Table 3
The calculation formula for the feature types to measure structural equivalence.
The feature types to measure user structure equivalenceFeature nameCalculation formulaUser topological structure equivalenceUser topological structureevi1,vj1=∑Vz∈V/Vi，VjIiz−Ijz2+Izi−Izj2Note 1: if there exists a link from user va to user vb, Iab  = 1; otherwise, Iab  = 0Note 2: evi1,vj1 denotes user topological structure equivalence between user vi and user vjIndividual topological structure feature similarityDegree centralitydegvi=∑j=1naij/n−1, evi2,vj2=degvi−degvj/maxdegv−mindegvNote 1: degvi and degvj denote the degree centrality of user vi and user vj, respectivelyNote 2: if there exists a link between entity vi and vj, then aij=1; otherwise, aij=0, and n denotes the number of users on social networkNote 3: evi2,vj2 denotes the equivalence of user vi and user vj in degree centralityNote 4: maxdegv and mindegv denote the maximum and minimum values among all degvi, respectivelyCloseness centralityclsvi=n−1/∑j=1ndij, evi3,vj3=clsvi−clsvj/maxclsv−minclsvNote 1: clsvi and clsvj denote the closeness centrality of user vi and user vj, respectivelyNote 2: dij denotes the distance from entity vi to entity vj, and n denotes the number of users on social network Note 3: evi3,vj3 denotes the equivalence of user vi and user vj in closeness centralityNote 4: maxclsv and minclsv denote the maximum and minimum values among all clsvi, respectivelyBetweenness centralitybjkvi=gjkvi/gjk, btnvi=∑j=1n∑k=1,k>jnbjkvi/nn−1/2, evi4,vj4=btnvi−btnvj/maxbtnv−minbtnvNote 1: gik denotes the number of shortest paths linking entity vj and entity vk, and gjkvi denotes the total number of shortest paths from entity vj to entity vk, and these paths also traverse entity vi, where i≠j≠kNote 2: btnvi and btnvj denote the betweenness centrality of user vi and user vj, respectivelyNote 3: evi4,vj4 denotes the equivalence of user vi and user vj in betweenness centralityNote 4: maxbtnv and minbtnv denote the maximum and minimum values among all btnvi, respectivelyPercolation centralitypcvi=1/n−2∑j=1n∑k=1,k>jnbjkviDj/∑h=1nDh−Di, evi5,vj5=pcvi−pcvj/maxpcv−minpcvNote 1: pcvi and pcvj denote the percolation centrality of user vi and user vj, respectivelyNote 2: if user vj forwards the disinformation published by user vi, Dj=1; otherwise, Dj=0, where i≠j≠kNote 3: evi5,vj5 denotes the equivalence of user vi and user vj in percolation centralityNote 4: maxpcv and minpcv denote the maximum and minimum values among all pcvi, respectivelyEigenvector centralityEgnvi=xvi=∑j=1naijxvj, evi6,vj6=Egnvi−Egnvj/maxEgnv−minEgnvNote 1: Egnvi and Egnvj denote the eigenvector centrality of user vi and user vj, respectivelyNote 2: xvi and xvj denote the influence of user vi and user vj, respectively, if there exists a link between entity vi and entity vj, then aij=1; otherwise, aij=0Note 3: evi6,vj6 denotes the equivalence of user vi and user vj in eigenvector centralityNote 4: maxEgnv and minEgnv denote the maximum and minimum values among all Egnvi, respectivelyPageRankPrvi=d+1+d∑vjϵIviPrvj/Οvj, evi7,vj7=prvi−prvj/maxprv−minprvNote 1: Prvi and Prvj denote PageRank values of user vi and user vj, respectivelyNote 2: Οvj denotes the number of followers of entity vj. To ensure guarantees global convergence, the attenuation factor d is usually set to 0.15Note 3: evi7,vj7 denotes the equivalence of user vi and user vj in PageRankNote 4: maxprv and minprv denote the maximum and minimum values among all Prvi, respectivelyClustering coefficientcvi=Ei/Cki2=2Ei/kiki−1, evi8,vj8=cvi−cvj/maxcv−mincvNote 1: cvi and cvj denote the clustering coefficient of user vi and user vj, respectivelyNote 2: ki denotes the number of nodes directly connected to entity vi, Ei denotes the actual number of edges of these nodes, and Cki2 denotes the maximum number of edges that may existNote 3: evi8,vj8 denotes the equivalence of user vi and user vj in clustering coefficientNote 4: maxcv and mincv denote the maximum and minimum values among all cvi, respectivelyThe topological feature similarity for the community of usersDegree centralizationDEGvi=∑i=1ndegvimax−degvi/max∑i=1ndegvimax−degvi, evi9,vj9  =  DEGvi−DEGvj/maxDEGv−minDEGvNote 1: DEGvi denotes the degree centralization of the communities which user vi and user vj belong toNote 2: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in degree centralizationNote 3: maxDEGv and minDEGv denote the maximum and minimum values among all DEGvi, respectivelyCloseness centralizationCLSvi=∑i=1nclsvimax−clsvi/max∑i=1nclsvimax−clsvi, evi10,vj10  =  CLSvi−CLSvj/maxCLSv−minCLSvNote 1: CLSvi denotes the closeness centralization of the communities which user vi and user vj belong toNote 2: evi10,vj10 denotes the equivalence of the communities which user vi and user vj belong to in closeness centralizationNote 3: maxCLSv and minCLSv denote the maximum and minimum values among all CLSvi, respectivelyBetweenness centralizationBTNvi=∑i=1nbtnvimax−btnvi/max∑i=1nbtnvimax−btnvi, evi11,vj11  =  BTNvi−BTNvj/maxBTNv−minBTNvNote 1: BTNvi denotes the betweenness centralization of the communities which user vi and user vj belong toNote 2: evi11,vj11 denotes the equivalence of the communities which user vi and user vj belong to in betweenness centralizationNote 3: maxBTNv and minBTNv denote the maximum and minimum values among all BTNvi, respectivelyCommunity clustering coefficientCvi=∑i=1ncvimax−cvi/max∑i=1ncvimax−cvi, evi12,vj12  =  Cvi−CvjmaxCv−minCvNote 1: Cvi denotes the clustering coefficient of the communities which user vi and user vj belong toNote 2: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in clustering coefficientNote 3: maxDEGv and minDEGv denote the maximum and minimum values among all Cvi, respectivelyCommunity sizeSvi=∑Vz1,Vz2∈VIz1z2, evi13,vj13  =  Svi−Svj/maxSv−minSvNote 1: Svi denotes the size of the communities which user vi and user vj belong toNote 2: if there exists a link from user vZ1 to user vZ2, IZ1Z2  = 1; otherwise, IZ1Z2  = 0Note 3: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in community sizeNote 4: maxSv and minSv denote the maximum and minimum size among all Svi, respectively(4) Susceptibility to Disinformation. The susceptibility of users to disinformation refers to the susceptibility of users to various characteristics of disinformation. The susceptibility of user vj to disinformation Mi is denoted by Fij. Fij is measured as the satisfaction degree of disinformation to various features and the susceptibility of the user to various features of disinformation. The calculation formula is as follows:(5)Fij=Mi1∗YGj1,Mi2∗YGj2,…,Mik∗YGjk,∑p=1kMip∗YGjp,where Mip denotes the satisfaction degree of disinformation Mi to a certain feature and YGjp denotes the susceptibility of user vj to a certain feature of the disinformation.The characteristics of disinformation mainly belong to three categories: formal features, popularity, and semantic features. The formula for calculating disinformationMi that corresponds to the feature satisfaction degree Mip is shown in Table 4.Table 4
The susceptibility of users to disinformation features.
The feature types of disinformationFeature nameCalculation formulaFormal featuresHashtagMi1=1if the rumorMihas a  hashtag，0   if the rumorMidoes not have  a  hashtag.MentionMi2=1if  rumorMimentions  uservj，0  if  rumorMidoes not  mention uservj.HyperlinksMi3=1if  rumorMihas hyperlinks，0  if  rumorMidoes not have  hyperlinks.With pictures or videosMi4=1if  rumorMihas pictures  or videos，0  if  rumorMidoes not  have   pictures  or videos.LengthMi5=lengthi−minlength/maxlength−minlengthNote 1: lengthi denotes the length of disinformation Mi, and maxlength and minlength denote the maximum and minimum values among all lengthi, respectivelyNote 2: Mi5 denotes the relative length of disinformation Mi among all disinformationPopularityForwarding numberMi6=retweeti−minretweet/maxretweet−minretweetNote 1: retweeti denotes the forwarding number of disinformation Mi, and maxretweet and minretweet denote the maximum and minimum values among all retweeti, respectivelyNote 2: Mi6 denotes the relative forwarding number of disinformation Mi among all disinformationComment numberMi7=commenti−mincomment/maxcomment−mincommentNote 1: commenti denotes the comment number of disinformation Mi, and maxcomment and mincomment denote the maximum and minimum values among all commenti, respectivelyNote 2: Mi7 denotes the relative comment number of disinformation Mi among all disinformationLike numberMi8=likei−minlike/maxlike−minlikeNote 1: likei denotes the like number of disinformation Mi, and maxlike and minlike denote the maximum and minimum values among all disinformation likei, respectivelyNote 2: Mi8 denotes the relative like number of disinformation Mi among all disinformationSemantic featuresAmbiguityMi9=1if  rumorMihas  amphibolous  words,0  if  rumorMidoes not  have  amphibolous  words. Note: constructing an amphibolous dictionary to check whether disinformation contains amphibolous wordsInductivityMi10=1if  rumorMihas  inductivity words,0  if  rumorMidoes not have  inductivity  words. Note: constructing an inductivity dictionary to check whether disinformation contains inductivity wordsEmotional intensityMi11=∑1nemotionn/nNote 1: emotioni denotes the emotional intensity of words in disinformationNote 2: Mi11 denotes the emotional intensity of disinformation MiNote 3: the emotional intensity of a word is determined by using an emotional dictionaryThe susceptibility of users to disinformation features is calculated as the mean value of the corresponding features of all Weibo posts forwarded by them, which is then normalized. The calculation formula is as follows:(6)YGjp=∑p=1mMjp/m−min∑p=1mMjp/mmax∑p=1mMjp/m−min∑p=1mMjp/m,where Mip denotes the value of the p-th attribute of each microblog forwarded by user Vi and max∑p=1mMjp/m and min∑p=1mMjp/m denote the maximum and minimum susceptibility of users to the p attribute, respectively, p = 1, 2, …, 10.


## 3.1.1. Theoretical Basis

Aral et al. indicated that behavior spreading on social networks could be regarded as a result of the interaction between social influence, user susceptibility, and user self-publishing [34]. Users create social influence that affects their opinions, attitudes, and behaviors within a social network. Chaiken et al. found that the influence is essentially social persuasiveness [35]. Fang et al. further suggested that social persuasiveness originated not only from social influence, but also the combination of social influence, entity similarity, and social structural equivalence [11, 36]. According to social comparison theory, people adjust their behavior according to the information released by other people around them to reduce uncertainty when they made decisions. Pfeffer et al., Friedkin, and Festinger further proposed the social influence network theory [37–39]. According to this theory, users on social networks usually have their own ideas about events from the beginning and then further consolidate or change their opinion or attitude by interacting with other members in the social network. These theories all suggest that social influence is generated in the interaction between users on social networks [40], and it could affect the views and behaviors of users [40–42]. Therefore, when people invest a great deal of time and energy in establishing solid social connections with each other, they tend to trust members with strong social connections. It means that social influence between members with strong social connections is much stronger than that between other members [43–45].Social comparison theory and social influence network theory suggest that entity similarity also has an impact on behavior spreading. They found that the behaviors or opinions of social network users were similar simply because their characteristics were similar [46, 47]. Generally, entity similarity refers to the degree to which two entities in a social network are similar demographically and behaviorally [48]. People with similar demographic characteristics usually have similar needs and preferences [49]. People with similar behavior usually have similar views on products or services [33, 49]. McPherson et al. found that the similarity in behavior between members was even independent of their interaction behavior [50]. Generally, the more similar the members are, the more likely they are to take concerted actions [11].The characteristics of social network topology also affect the views and behaviors of users on this social network [51, 52]. Studies have shown that network structure characteristics could affect the similarity of views and behaviors between users on this social network [52, 53]. Structural equivalence is a basic feature of social network topology. Users with equivalent structures tend to have similar views and behaviors because they tend to learn from users with equivalent structures when they make decisions [51]. Additionally, the topological structure characteristics of communities and the characteristics of individual users also affect the degree of similarity of views and behaviors between members [10, 54].Previous studies rarely took the susceptibility of users into consideration when predicting user behavior. Instead, they often used social influence to indirectly measure susceptibility [54, 55]. In fact, the awareness of received information is also essentially a type of susceptibility of users, which is independent of social influence, and also affects the views and behaviors of users [56–58]. Researchers have found that people believe disinformation and actively spread them on social networks only when they are susceptible to disinformation, whereas other people do not respond to disinformation because they detect disinformation or believe disinformation but are not interested in them [59]. The reason that people are susceptible to disinformation is that the content of disinformation is consistent with their original cognition. Specifically, the degree of agreement between the characteristics of disinformation content and their cognition (i.e., susceptibility) determines their susceptibility to disinformation [60]. This also means that exploring the susceptibility of people to disinformation features can help to predict the susceptibility of people to disinformation. The characteristics of a disinformation include the following: the information form of the disinformation, such as the #, @, URL, length, and picture; semantics; confounding, such as fuzziness and clear behavior; and emotion [1].It is difficult to measure the spontaneous behavior of users directly, which can be regarded as the unobserved features of disinformation forwarding. Additionally, the disinformation forwarding behavior of users may also be affected by other confounding features [46, 61] that include the specific content about the interaction of people and the spread of disinformation offline [62]. In addition to the features that can be traced to a clear source, there are many unobserved features that can significantly influence the disinformation forwarding behavior of people [63].Based on the above analysis, we first measure the features that affect the disinformation forwarding of social network users in addition to confounding features and then use the features that influence the disinformation forwarding of social network users, including confounding features, to predict the disinformation forwarding probability of social network users.


## 3.1.2. Operationalization

Based on the above discussion, we divide the features of the disinformation forwarding behavior of social network users into four categories: the strength of social influence of the disinformation publisher on the disinformation forwarder, the entity similarity between the disinformation publisher and disinformation forwarder, the structural equivalence between the disinformation publisher and disinformation forwarder, and the susceptibility of the user to disinformation.(1) Social Influence. Suppose V=v1,v2,…,vn is a group of users on a social network. Users are connected by two-way or one-way links. The social influence of user vi on user vj (hereinafter referred to as the influence power) is denoted by Iij. Iij is measured as the interaction intensity Xij between user vi and user vj:(1)Iij=Xij−XminXmax−Xmin,where Xmax and Xmin denote the maximum and minimum social connection strengths, respectively. Additionally, standardization helps to prevent Iij from relying on the measurement unit of Xij. Interaction intensity Xij is a three-dimensional vector that measures the interaction intensity between users through the three dimensions of thumbs up, forwarding, and comments:(2)Xij=Lij−LminLmax−Lmin,Rij−RminRmax−Rmin,Cij−CminCmax−Cmin.See Table1 for the calculation formula for the interaction strength between user vivi and user vj.Table 1
The calculation formula for the interaction strength
Interaction dimensionsCalculation formulaThumbs upLij=zanij/∑vhϵV,h≠izanhjNote 1: Lij denotes the interaction intensity between user vi and user vj in thumbs upNote 2: zanij denotes the number of thumbs up received by user vi from user vjNote 3: zanhj denotes the number of thumbs up received by user vhh≠i from user vjNote 4： Lmax and Lmin denote the maximum and minimum values among all Lij, respectivelyForwardingRij=zhuanij/∑vhϵV,h≠izhuanhjNote 1: Rij denotes the interaction intensity between user vi and user vj in forwardingNote 2: zhuanij denotes the number of microblogs of user vi forwarded by user vjNote 3: zhuanhj denotes the number of microblogs of user vhh≠i forwarded by user vjNote 4: Rmax and Rmin denote the maximum and minimum values among all Rij, respectivelyCommentsCij=commentij/∑vhϵV,h≠icommenthjNote 1: Cij denotes the interaction intensity of user vi and user vj in commentsNote 2: commentij denotes the number of microblogs of user vi commented by user vjNote 3: commenthj denotes the number of microblogs of user vhh≠i commented by user vjNote 4: Cmax and Cmin denote the maximum and minimum values among all Cij, respectively(2) Entity Similarity. The entity similarity between user i and user j is denoted by Sij. Sij is measured as the similarity of each feature between user i and user j, that is, the distance between each feature:(3)Sij=dmax1−dvi1,vj1dmax1−dmin1,dmax2−dvi2,vj2dmax2−dmin2,dmax3−dvi3,vj3dmax3−dmin3,dmax4−dvi4,vj4dmax4−dmin4,where dmax1,dmax2,dmax3,anddmax4 denote the maximum value of each feature distance among all users and dmin1,dmin2,dmin3,anddmin4 denote the minimum value of each feature distance among all users.The features that we use to measure the entity similarity of users can be divided into three categories: the profile similarity of users, the behavior similarity of users, and the comprehensive similarity of users. Additionally, the corresponding calculation formula for the entity similarity between usersvi and vj is shown in Table 2.Table 2
The calculation formula for the entity similarity.
The feature types to measure user entity similarityFeature nameCalculation formulaProfile similarity between usersNumber of followeesdvi1,vj1=num_guanzhuvi−num_guanzhuvj/maxnum_guanzhu−minnum_guanzhuNote 1: dvi1,vj1 denotes the similarity between user vi and user vj in the number of followeesNote 2: num_guanzhuvi and num_guanzhuvJ denote the number of followees of user vi and user vj, respectivelyNote 3: maxnum_guanzhu and minnum_guanzhu denote the maximum and minimum values among all dvi1,vj1, respectivelyNumber of followersdvi2,vj2=num_fensivi−num_fensivi/maxnum_fensi−minnum_fensiNote 1: dvi2,vj2 denotes the similarity between user vi and user vj in the number of followersNote 2: num_fensivi and num_fensivi denote the number of followers of user vi and user vj, respectivelyNote 3: maxnum_fensi and minnum_fensi denote the maximum and minimum values among all dvi2,vj2, respectivelyBehavior similarity between usersForwarding behaviorSen_disvik,vj=maxSenviknSenvj1/SenvikSenvj1,SenviknSenvj2/SenvikSenvj2,…,SenviknSenvjn/SenvikSenvjn, dvi3,vj3=∑k=1mSen_disvik,vj/mNote 1: Senvik denotes the paragraph vector of the kth blog post forwarded by user viNote 2: Sen_disvik,vj denotes the semantic similarity between the kth blog post forwarded by user vi and all the blog posts forwarded by user vj, and n denotes the number of blog post forwarded by user vjNote 3: dvi3,vj3 denotes the similarity of forwarding behavior between user vi and user vj, and m denotes the number of blog posts forwarded by user viComprehensive similarity between usersComprehensive of usersdvi4,vj4=∑k=13dvik,vjk/3Note 1: dvi4,vj4 denotes the comprehensive similarity of all features between user vi and user vj(3) Structural Equivalence. The structural equivalence between user i and user j is denoted by Eij. Eij is measured as the similarity of each topological structure feature between user i and user j, that is, the distance between each topological structure feature:(4)Eij=emax1−evi1,vj1emax1−emin1,emax2−evi2,vj2emax2−emin2,…,dmax13−dvi13,vj13dmax13−dmin13,where emax1,emax2,…,emax11 denote the maximum value of each topology feature distance among all users and emin1,emin2,…,emin11 denote the minimum value of each topology feature distance among all users.The features that we use to measure the user structure equivalence can be divided into three categories: topological structure equivalence, the individual topological structure feature similarity between users, and the topological feature similarity for the community of users. The corresponding calculation formula for the structural equivalence of uservi and user vj is shown in Table 3.Table 3
The calculation formula for the feature types to measure structural equivalence.
The feature types to measure user structure equivalenceFeature nameCalculation formulaUser topological structure equivalenceUser topological structureevi1,vj1=∑Vz∈V/Vi，VjIiz−Ijz2+Izi−Izj2Note 1: if there exists a link from user va to user vb, Iab  = 1; otherwise, Iab  = 0Note 2: evi1,vj1 denotes user topological structure equivalence between user vi and user vjIndividual topological structure feature similarityDegree centralitydegvi=∑j=1naij/n−1, evi2,vj2=degvi−degvj/maxdegv−mindegvNote 1: degvi and degvj denote the degree centrality of user vi and user vj, respectivelyNote 2: if there exists a link between entity vi and vj, then aij=1; otherwise, aij=0, and n denotes the number of users on social networkNote 3: evi2,vj2 denotes the equivalence of user vi and user vj in degree centralityNote 4: maxdegv and mindegv denote the maximum and minimum values among all degvi, respectivelyCloseness centralityclsvi=n−1/∑j=1ndij, evi3,vj3=clsvi−clsvj/maxclsv−minclsvNote 1: clsvi and clsvj denote the closeness centrality of user vi and user vj, respectivelyNote 2: dij denotes the distance from entity vi to entity vj, and n denotes the number of users on social network Note 3: evi3,vj3 denotes the equivalence of user vi and user vj in closeness centralityNote 4: maxclsv and minclsv denote the maximum and minimum values among all clsvi, respectivelyBetweenness centralitybjkvi=gjkvi/gjk, btnvi=∑j=1n∑k=1,k>jnbjkvi/nn−1/2, evi4,vj4=btnvi−btnvj/maxbtnv−minbtnvNote 1: gik denotes the number of shortest paths linking entity vj and entity vk, and gjkvi denotes the total number of shortest paths from entity vj to entity vk, and these paths also traverse entity vi, where i≠j≠kNote 2: btnvi and btnvj denote the betweenness centrality of user vi and user vj, respectivelyNote 3: evi4,vj4 denotes the equivalence of user vi and user vj in betweenness centralityNote 4: maxbtnv and minbtnv denote the maximum and minimum values among all btnvi, respectivelyPercolation centralitypcvi=1/n−2∑j=1n∑k=1,k>jnbjkviDj/∑h=1nDh−Di, evi5,vj5=pcvi−pcvj/maxpcv−minpcvNote 1: pcvi and pcvj denote the percolation centrality of user vi and user vj, respectivelyNote 2: if user vj forwards the disinformation published by user vi, Dj=1; otherwise, Dj=0, where i≠j≠kNote 3: evi5,vj5 denotes the equivalence of user vi and user vj in percolation centralityNote 4: maxpcv and minpcv denote the maximum and minimum values among all pcvi, respectivelyEigenvector centralityEgnvi=xvi=∑j=1naijxvj, evi6,vj6=Egnvi−Egnvj/maxEgnv−minEgnvNote 1: Egnvi and Egnvj denote the eigenvector centrality of user vi and user vj, respectivelyNote 2: xvi and xvj denote the influence of user vi and user vj, respectively, if there exists a link between entity vi and entity vj, then aij=1; otherwise, aij=0Note 3: evi6,vj6 denotes the equivalence of user vi and user vj in eigenvector centralityNote 4: maxEgnv and minEgnv denote the maximum and minimum values among all Egnvi, respectivelyPageRankPrvi=d+1+d∑vjϵIviPrvj/Οvj, evi7,vj7=prvi−prvj/maxprv−minprvNote 1: Prvi and Prvj denote PageRank values of user vi and user vj, respectivelyNote 2: Οvj denotes the number of followers of entity vj. To ensure guarantees global convergence, the attenuation factor d is usually set to 0.15Note 3: evi7,vj7 denotes the equivalence of user vi and user vj in PageRankNote 4: maxprv and minprv denote the maximum and minimum values among all Prvi, respectivelyClustering coefficientcvi=Ei/Cki2=2Ei/kiki−1, evi8,vj8=cvi−cvj/maxcv−mincvNote 1: cvi and cvj denote the clustering coefficient of user vi and user vj, respectivelyNote 2: ki denotes the number of nodes directly connected to entity vi, Ei denotes the actual number of edges of these nodes, and Cki2 denotes the maximum number of edges that may existNote 3: evi8,vj8 denotes the equivalence of user vi and user vj in clustering coefficientNote 4: maxcv and mincv denote the maximum and minimum values among all cvi, respectivelyThe topological feature similarity for the community of usersDegree centralizationDEGvi=∑i=1ndegvimax−degvi/max∑i=1ndegvimax−degvi, evi9,vj9  =  DEGvi−DEGvj/maxDEGv−minDEGvNote 1: DEGvi denotes the degree centralization of the communities which user vi and user vj belong toNote 2: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in degree centralizationNote 3: maxDEGv and minDEGv denote the maximum and minimum values among all DEGvi, respectivelyCloseness centralizationCLSvi=∑i=1nclsvimax−clsvi/max∑i=1nclsvimax−clsvi, evi10,vj10  =  CLSvi−CLSvj/maxCLSv−minCLSvNote 1: CLSvi denotes the closeness centralization of the communities which user vi and user vj belong toNote 2: evi10,vj10 denotes the equivalence of the communities which user vi and user vj belong to in closeness centralizationNote 3: maxCLSv and minCLSv denote the maximum and minimum values among all CLSvi, respectivelyBetweenness centralizationBTNvi=∑i=1nbtnvimax−btnvi/max∑i=1nbtnvimax−btnvi, evi11,vj11  =  BTNvi−BTNvj/maxBTNv−minBTNvNote 1: BTNvi denotes the betweenness centralization of the communities which user vi and user vj belong toNote 2: evi11,vj11 denotes the equivalence of the communities which user vi and user vj belong to in betweenness centralizationNote 3: maxBTNv and minBTNv denote the maximum and minimum values among all BTNvi, respectivelyCommunity clustering coefficientCvi=∑i=1ncvimax−cvi/max∑i=1ncvimax−cvi, evi12,vj12  =  Cvi−CvjmaxCv−minCvNote 1: Cvi denotes the clustering coefficient of the communities which user vi and user vj belong toNote 2: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in clustering coefficientNote 3: maxDEGv and minDEGv denote the maximum and minimum values among all Cvi, respectivelyCommunity sizeSvi=∑Vz1,Vz2∈VIz1z2, evi13,vj13  =  Svi−Svj/maxSv−minSvNote 1: Svi denotes the size of the communities which user vi and user vj belong toNote 2: if there exists a link from user vZ1 to user vZ2, IZ1Z2  = 1; otherwise, IZ1Z2  = 0Note 3: evi9,vj9 denotes the equivalence of the communities which user vi and user vj belong to in community sizeNote 4: maxSv and minSv denote the maximum and minimum size among all Svi, respectively(4) Susceptibility to Disinformation. The susceptibility of users to disinformation refers to the susceptibility of users to various characteristics of disinformation. The susceptibility of user vj to disinformation Mi is denoted by Fij. Fij is measured as the satisfaction degree of disinformation to various features and the susceptibility of the user to various features of disinformation. The calculation formula is as follows:(5)Fij=Mi1∗YGj1,Mi2∗YGj2,…,Mik∗YGjk,∑p=1kMip∗YGjp,where Mip denotes the satisfaction degree of disinformation Mi to a certain feature and YGjp denotes the susceptibility of user vj to a certain feature of the disinformation.The characteristics of disinformation mainly belong to three categories: formal features, popularity, and semantic features. The formula for calculating disinformationMi that corresponds to the feature satisfaction degree Mip is shown in Table 4.Table 4
The susceptibility of users to disinformation features.
The feature types of disinformationFeature nameCalculation formulaFormal featuresHashtagMi1=1if the rumorMihas a  hashtag，0   if the rumorMidoes not have  a  hashtag.MentionMi2=1if  rumorMimentions  uservj，0  if  rumorMidoes not  mention uservj.HyperlinksMi3=1if  rumorMihas hyperlinks，0  if  rumorMidoes not have  hyperlinks.With pictures or videosMi4=1if  rumorMihas pictures  or videos，0  if  rumorMidoes not  have   pictures  or videos.LengthMi5=lengthi−minlength/maxlength−minlengthNote 1: lengthi denotes the length of disinformation Mi, and maxlength and minlength denote the maximum and minimum values among all lengthi, respectivelyNote 2: Mi5 denotes the relative length of disinformation Mi among all disinformationPopularityForwarding numberMi6=retweeti−minretweet/maxretweet−minretweetNote 1: retweeti denotes the forwarding number of disinformation Mi, and maxretweet and minretweet denote the maximum and minimum values among all retweeti, respectivelyNote 2: Mi6 denotes the relative forwarding number of disinformation Mi among all disinformationComment numberMi7=commenti−mincomment/maxcomment−mincommentNote 1: commenti denotes the comment number of disinformation Mi, and maxcomment and mincomment denote the maximum and minimum values among all commenti, respectivelyNote 2: Mi7 denotes the relative comment number of disinformation Mi among all disinformationLike numberMi8=likei−minlike/maxlike−minlikeNote 1: likei denotes the like number of disinformation Mi, and maxlike and minlike denote the maximum and minimum values among all disinformation likei, respectivelyNote 2: Mi8 denotes the relative like number of disinformation Mi among all disinformationSemantic featuresAmbiguityMi9=1if  rumorMihas  amphibolous  words,0  if  rumorMidoes not  have  amphibolous  words. Note: constructing an amphibolous dictionary to check whether disinformation contains amphibolous wordsInductivityMi10=1if  rumorMihas  inductivity words,0  if  rumorMidoes not have  inductivity  words. Note: constructing an inductivity dictionary to check whether disinformation contains inductivity wordsEmotional intensityMi11=∑1nemotionn/nNote 1: emotioni denotes the emotional intensity of words in disinformationNote 2: Mi11 denotes the emotional intensity of disinformation MiNote 3: the emotional intensity of a word is determined by using an emotional dictionaryThe susceptibility of users to disinformation features is calculated as the mean value of the corresponding features of all Weibo posts forwarded by them, which is then normalized. The calculation formula is as follows:(6)YGjp=∑p=1mMjp/m−min∑p=1mMjp/mmax∑p=1mMjp/m−min∑p=1mMjp/m,where Mip denotes the value of the p-th attribute of each microblog forwarded by user Vi and max∑p=1mMjp/m and min∑p=1mMjp/m denote the maximum and minimum susceptibility of users to the p attribute, respectively, p = 1, 2, …, 10.


## 3.2. Predict the Probabilityp_persuadeik of User vi Being Persuaded to Forward Disinformation Mk

Becausep_persuadeik is determined by the power of all friends to persuade a user to forward disinformation, we first calculate the probability p_persuadeik that user vi is persuaded by each friend to forward disinformation Mk.According to the analysis in the previous section, the features that influence whether uservi forwards disinformation mk published by friend vj comprise mainly four aspects: the social influence intensity Iij of user vj on user vi, the entity similarity Sij between user vi and user vj, the structural equivalence Eij between user vi and user vj, and the susceptibility Fik of user vi to disinformation mk. Therefore, the calculation formula of p_persuadeijk is as follows:(7)ppersuadeijk=Ppersuadeijk=1=PRetweetijk=1|Iij,Sij,Eij,Fik,where Retweetijk=1 indicates that user vi forwards disinformation mk published by friend vj and persuadeijk=1 indicates that user vj persuades user vi to forward disinformation mk.We predictpijk using the random forest algorithm. To improve the prediction accuracy of pijk, we predict p_persuadeijk using the bagging method and M-estimation. In particular, we extract training samples using the bootstrap method from the original sample set and obtain 50 training sets after 50 rounds of extraction. Then, we train 50 decision trees from these sample data and calculate p_persuadeijk as the average value of the probability estimation of the 50 decision trees. The training process and prediction process are shown in Figures 4 and 5, respectively.Figure 4
Construction of the training data algorithm.Figure 5
Prediction process.Then, we calculate the probabilityp_persuadeijk of user vi being persuaded to forward disinformation Mk. The calculation formula of p_persuadeik is as follows:(8)ppersuadeik=Ppersuadeik=1=1−∏vj∈V1−ppersuadeik,where persuadeik=1 indicates that user vi is persuaded to forward disinformation Mk.


## 3.3. Predict the Probabilityp_retweetik of User vi Forwarding Disinformation Mk

We denote the unobserved variable that affects uservi forwarding disinformation Mk by Hik and combine it with the probability p_persuadeik of user vi being persuaded to forward disinformation Mk. Then, according to the Bayesian probability formula, the calculation formula of p_retweetik is as follows:(9)pRetweetik=PRetweetik=1|ppersuadeik,Hik=PRetweetik=1Pppersuadeik,Hik|Retweetik=1∑r=0,1PRetweetik=rPppersuadeik,Hik|Retweetik=r.For the naive Bayesian estimation, we assume thatHik and p_persuadeik are independent. Then,(10)pRetweetik=PRetweetik=1Pppersuadeik|Retweetik=1PHik|Retweetq=1∑r=0,1PRetweetik=rPppersuadeik|Retweetik=rPHik|Retweetik=r.In the naive Bayes algorithm, a common approach is to make the probability density of each input variable obey the exponential distribution [64]. Then, we can describe the probability density function of PRetweetik=r as follows: fRetweetik=λRetweetike−λRetweetikx,x≥0, where λRetweetik is the parameter of the probability density function, r=0,1. Then, we can estimate PRetweetik=r as fRetweetik.We can estimate Pp_persuadeik|Retweetik=r and PHq||Retweetik=r in the same manner. Therefore, to compute p_retweetik, we need to learn the following vector of parameters from TRAIN:(11)θ=p1,λppersuadeik|1,λHik|1,p0,λppersuadeik|0,λHik|0,where p1 and p0 are the estimates of prior probability PRetweetik=1 and PRetweetik=0, respectively, and λp_persuadeik|1, λHik|1, λp_persuadeik|0, and λHik|0 are the density parameters for friends persuading users and unobserved power H given disinformation forward decision a, respectively, where a = 0 or 1.Simultaneously, the confounding features are indispensable in a prediction. The problem is how to learn the parameterθ in the case of missing training data.To overcome this obstacle, we combine bootstrap sampling and EM algorithm to learn parameterθ. The bootstrap method is mainly used for sampling training data, whereas the EM algorithm is used for learning the parameters of unobserved variables.The EM algorithm is the most common implicit variable estimation method. It is an iterative process from the initial parameter estimation. Each iteration of EM is composed of Steps E and M. In Step E, the maximum likelihood estimation value is calculated using the existing estimation value of the unobserved variable, whereas in Step M, the value of the parameter is calculated by maximizing the maximum likelihood value obtained in Step E. Additionally, the parameter estimates found in Step M are used in the next Step E calculation and they are conducted alternately.In our study, the specific steps for learning parameters are shown in Figure6.Figure 6
The learning parameter process of the DFP method.As mentioned above, we consider three cases when setting the initial value of the unobserved variable parameters. Therefore, we perform cyclic training for the three cases in the iteration of Steps E and M. The training algorithm for parameterθ is shown in Figure 7.Figure 7
Parameter training algorithm.We can predict the probability of disinformation forwarding after training the parameters. Given parameter estimationθ^, for user vi and disinformation mk,(12)p_retweetik=PRetweetik=1|p_persuadeik,Hik=PRetweetik=1Pppersuadeik|Retweetik=1PHik|Retweetik=1∑r=0,1PRetweetik=rPPsdik|Retweetik=rPHik|Retweetik=r=p^1λ^ppersuadeik|1exp−λ^ppersuadeik|1ppersuadeikλ^Hik|1exp−λ^Hik|1Hik∑r=0,1p^rλ^ppersuadeik|rexp−λ^ppersuadeik|rppersuadeikλ^Hik|rexp−λ^Hik|rHik,where the probability density function of Hik is(13)fHik|θ^=fHik|Rik=1,θ^PRik=1|θ^+fHik|Rik=0,θ^PRik=0|θ^.Therefore, we can use the expected value based onHik to approximately calculate the disinformation forwarding probability. As shown in Figure 8, the forwarding probability inference algorithm generates Hik samples repeatedly and calculates the disinformation forwarding probability using the sample data and equation (12) until it converges. The output of this algorithm is the expected value of the disinformation forwarding probability based on Hq.Figure 8
Inferencing retweet probability.


## 4. Empirical Evaluation and Results

We evaluate our proposed method on real-world social network data to demonstrate its superior prediction performance over several existing methods and then empirically analyze its important properties. In this section, we describe the data and benchmark methods, detail our evaluation design, and report important evaluation results.


### 4.1. Dataset

The data we used in this study comes from the microblog, which is the largest social media platform in China. We are provided with real data by the microblog data center as a result of our cooperation with them. We obtain a total of nine disinformation-mongering tweets that were widely spread on social media between April 2018 and August 2018, which covered common disinformation topics, such as personal safety, health and wellness, death anxiety, and geomantic superstitions. Additionally, 38,079 users participated in disinformation forwarding. It is noted that all the disinformation-mongering tweets in our experiments are identified as disinformation by Weibo platform. The information on the spread of these disinformation is shown in Table5.Table 5
Disinformation information distribution.
Blog IDTime of postingNumber of forwardingNumber of commentsNumber of likesThemeM12018.04.24718576339Personal safetyM22018.04.26581227104Health preservationM32018.05.1450927871Death anxietyM42018.05.233089825008785Death anxietyM52018.06.24759168282Political public opinionM62018.06.241840830678EducationM72018.08.1672504761275Fengshui superstitionM82018.08.1960029728Death anxietyM92018.08.1911172612208Fengshui superstition


### 4.2. Benchmark Methods

Compared to current research on prediction of user information forwarding behavior, our proposed method systematically investigates the features affecting user disinformation forwarding and takes unobserved features into considerations. Therefore, to demonstrate the superiority of our proposed method, we design the following two groups of experiments to evaluate the features.The objective of the first group of experiments is to compare the effects of features used in the proposed method and features used in current methods on the prediction accuracy of user disinformation forwarding. Both the experimental group and control group use the same prediction algorithm, but the experimental group and control group use different features that influence disinformation forwarding. Because there is little research on features that influence disinformation forwarding in existing systems, we not only compare the common features that influence disinformation forwarding but also the common features that affect the behavior of social network users. Specially, in the first group of experiments, we do not take the unobserved features into consideration.The objective of the second group of experiments is to evaluate the effects of unobserved features used in the proposed method on the prediction accuracy of user disinformation forwarding. Both the experimental group and control group utilize observed features used in the proposed method, but the experimental group uses our proposed prediction algorithm with considering the unobserved features, whereas the control group uses the regular classification prediction algorithms without considering the unobserved features.Tables6 and 7 summarize the methods compared in the evaluations.Table 6
The comparison between features used in the proposed method and features used in current methods.
Features of disinformation forwarding (abbreviated)Calculation method of features of disinformation forwardingPrediction algorithmFeatures proposed in our method (PF)Generated from social persuasion and user susceptibility to disinformationPM, NB, RF, ADB, LR, KNN, SVMSocial influence features (SI)Generated from social influencePM, NB, RF, ADB, LR, KNN, SVMSocial persuasion features 1 (SP1)Generated from social persuasion; calculates structural equivalence with only considering one kind of structural equivalence; calculates entity similarity with only considering profile similarityPM, NB, RF, ADB, LR, KNN, SVMSocial persuasion features 2 (SP2)Generated from social persuasion; calculates social persuasion structural equivalence with considering social network topology and profile similarity; calculates entity similarity with considering profile similarity, behavior similarity, and comprehensive similarityPM, NB, RF, ADB, LR, KNN, SVMPM: proposed method (without considering unobserved features); NB: naive Bayes; RF: Random Forest; ADB: AdaBoost; LR: logistic regression; KNN: K-nearest neighbor; SVM: support vector machine.Table 7
The comparison between proposed method and other regular classifiers.
Prediction algorithm name (abbreviated)Calculation method of features of disinformation forwardingProposed method (PM)Generated from social persuasion, user susceptibility to disinformation, and unobserved featuresNaive Bayes (NB)Generated from social persuasion and user susceptibility to disinformationRandom Forest (RF)Generated from social persuasion and user susceptibility to disinformationAdaBoost (ADB)Generated from social persuasion and user susceptibility to disinformationLogistic regression (LR)Generated from social persuasion and user susceptibility to disinformationK-nearest neighbor (KNN)Generated from social persuasion and user susceptibility to disinformationSupport vector machine (SVM)Generated from social persuasion and user susceptibility to disinformationTable 8
Test training dataset division.
GroupRetweet data (1)Unretweet data (0)SumTraining data148050148050296100Testing data370123701274024Sum185062185062370124


### 4.3. Evaluation Design

Our experiments are conducted using the following steps:Step 1: divide the training set and testing set.We obtain a total of 37,014 records of data. The ratio of records for which the user forwarded the disinformation, marked as 1, to data for which the user do not forward the disinformation, marked as 0, is 1 : 1. We randomly divide the data into a training set and testing set according to the ratio 4 : 1. The data after division are shown in Table8.Step 2: calculate the features that influence disinformation forwarding.We calculate the features that influence disinformation forwarding used by each experimental group and control group. In the analysis of social network topology, we divided the social network users collected into 28 communities using the Louvain algorithm and then further analyzed the topology of the internal community and individual users.Step 3: predict the disinformation forwarding probability of users.We predicted the probability of each user forwarding each disinformation by inputting the calculated features that influenced disinformation forwarding into the classifier used by each experimental group and control group.We performed the above steps ten times, and each time we randomly divided the training set and testing set to ensure the stability of the evaluation results.


### 4.4. Prediction Results and Evaluation Analysis

#### 4.4.1. Evaluation Index

To solve the binary classification problem, the machine learning models usually predict the probability valueP (Y|X) for modeling, where X is the sample and Y is the category to which it belongs. Additionally, PY=1|X denotes the probability that Y belongs to category 1 when sample X appears. We set a threshold value and hypothesize it as k, and it is classified as category 1 if PY=1|X>k; otherwise, it is classified as category 0. For example, the default threshold of a neural network and logistic regression is 0.5. It can be seen that the threshold selection quality directly determines the generalization ability of the machine learning model, and the ROC curve can indicate the influence of threshold change on the classifier.We calculate the true positive rate (TPR) as the vertical axis and false positive rate (FPR) as the horizontal axis:(14)TPR=TPTP+FN,FPR=FPTN+FP.The area under the ROC curve (AUC) is used to determine the comparison between two machine learning models.


#### 4.4.2. Evaluation Results

First, we tested the influence of our proposed disinformation forwarding features on the prediction accuracy of disinformation forwarding compared with other commonly used disinformation forwarding features. Figure9 shows the ROC curves of features generated from different methods. Figure 10 shows the AUCs of our proposed features that influence disinformation forwarding and other commonly used disinformation forwarding features in the classification prediction algorithm. Cross-validation AUC values are shown in Table 9.Figure 9
ROC curves of features generated from different methods: (a) PF, SP1, and SI; (b) PF, SP2, and SI.
(a)(b)Figure 10
Average AUCs of each algorithm for different features.Table 9
Cross-validation AUC values.
No.GroupPMNBRFADBLRKNNSVM1PF0.96660.90340.94540.94630.93920.95320.9082SI0.58740.56390.56050.55890.56120.56030.5578SP10.82070.74730.80000.75450.74330.77700.7464SP20.94670.89400.91060.91260.89850.91100.88992PF0.96660.91130.94460.94870.94070.95430.9139SI0.58290.55850.56350.56050.55790.51850.5620SP10.82150.74300.81090.75390.73740.76530.7493SP20.94580.89660.91360.90810.89680.89240.89233PF0.96660.90890.94530.94520.93770.93130.9095SI0.58020.55930.55940.55920.55380.51970.5602SP10.82100.74070.80490.75700.73450.81090.7486SP20.94210.89740.91290.91060.90360.91000.88684PF0.96480.90710.94480.94620.93860.94890.9105SI0.57870.56240.55930.55660.55440.56090.5583SP10.82340.74800.80430.75660.73710.81380.7589SP20.94510.89460.91250.91140.89580.90530.88955PF0.96730.90640.94740.94800.94240.95430.9157SI0.58000.56030.55810.55950.55500.52170.5603SP10.81940.73840.80220.75640.74090.80830.7675SP20.94210.89800.91000.91050.89860.90570.89026PF0.96400.91070.94540.94680.93870.95000.9121SI0.57860.55640.56080.55700.55860.50960.5604SP10.81810.74390.80640.75090.74150.79620.7584SP20.94680.89350.91090.91190.89730.90260.88657PF0.96720.90990.94230.94560.94240.94140.9135SI0.58230.56230.55800.56060.55830.55810.5595SP10.81450.73890.80770.75460.74120.77150.7522SP20.94100.89320.91210.91260.89630.89300.88988PF0.96510.90880.94220.94530.93970.94980.9145SI0.58770.55980.55570.55930.55620.55840.5586SP10.83010.74110.80990.76060.73800.80930.7654SP20.94720.89440.91170.91260.89760.90500.88399PF0.96750.90860.94690.94770.94220.95390.9135SI0.57720.55610.56040.56030.55990.51930.5611SP10.82270.74060.80240.75560.73630.80060.7577SP20.95160.89600.91230.91310.89420.89230.891310PF0.96910.90660.94580.94800.94220.95370.9044SI0.58290.56460.55840.55790.55500.51250.5608SP10.81620.74370.80880.75510.74010.80400.7465SP20.94450.89960.91570.91030.89480.88090.8905AvgPF0.96650.90820.94500.94680.94040.94910.9116SI0.58180.56040.55940.55900.55700.53390.5599SP10.82080.74260.80570.75550.73900.79570.7551SP20.94530.89570.91220.91140.89730.89980.8891Proposed features (PF) refer to features proposed in our method. Social influence features (SI) refer to features related to social influence. Both social persuasion features 1 (SP1) and social persuasion features 2 (SP2) refer to features related to social persuasion, which include social influence, structural equivalence, and entity similarity. The primary difference between SP2 and SP1 is that the structural equivalence and entity similarity are calculated in different ways. SP1 calculates structural equivalence with only considering one kind of structural equivalence and calculates entity similarity with only considering profile similarity. SP2 calculates structural equivalence with considering social network topology and profile similarity and calculates entity similarity with considering profile similarity, behavior similarity, and comprehensive similarity.From Figures9 and 11, the following results can be concluded:(1)
Regardless of the classifier, the best performance results come from our proposed features (PF), compared with other features used in control groups. This demonstrates that our proposed features, which consider both social persuasion of publishers and the susceptibility of users, can greatly improve the prediction accuracy of classifiers.(2)
Regardless of the classifier, the worst performance results come from features related to social influence (SI). By using features related to social persuasiveness for the prediction of individual disinformation forwarding (SP1), the prediction accuracy of classifiers can be significantly improved: when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of SP1 increases by 29.9%, 18.02%, 24.63%, 19.65%, 18.2%, 26.18%, and 19.52%, respectively, compared with SI. This demonstrates that social persuasion of publishers, rather than social influence of publishers, should be taken into consideration when predicting individual disinformation forwarding.(3)
Our proposed method utilizes a new method to calculate structural equivalence by considering more topology information of SNS. We compare the effects of structural equivalence features calculated by our proposed method (SP2) with those calculated by common calculation methods (SP1) on the prediction accuracy of user disinformation forwarding. The results show that when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of SP2 increases by 12.45%, 15.31%, 10.65%, 15.59%, 15.83%, 10.41%, and 13.4%, respectively, compared with SP1. This demonstrates that structural equivalence features calculated by our proposed method is more reasonable.(4)
Our proposed method takes the susceptibility of users to disinformation. We compare the effects of features considering the susceptibility of users to disinformation (PF) with those without considering the susceptibility of users to disinformation (SP2) on the prediction accuracy of user disinformation forwarding. The results show that when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of PF increases by 2.12%, 1.25%, 3.28%, 3.54%, 4.31%, 4.93%, and 2.25%, respectively, compared with SP2. This demonstrates that the susceptibility of users to disinformation should be taken into consideration, when predicting individual disinformation forwarding.Figure 11
AUC value of each algorithm.We further evaluate the prediction accuracy of our proposed method considering the unobserved features by comparing it with other classification methods. Table10 and Figure 11 show the AUC values of each classification method. Figure 12 shows the ROC curves of each classification method.Table 10
AUC values for the proposed method and benchmark methods.
No.PMNBRFADBLRKNNSVM10.96590.90660.94480.94790.94060.95420.913020.96600.90800.94470.94820.93860.95350.904430.96610.90990.94450.94910.94050.95350.914940.96500.91020.94530.94990.94330.93480.912650.96630.90650.94620.94900.94060.95450.916760.96740.90610.94420.94580.93730.94730.909970.96460.91180.94790.94980.94400.95610.914180.96250.91010.94290.94870.94070.95170.909690.96450.91170.94830.94980.94200.95540.9110100.96550.90630.94620.94690.93710.95140.9119Av.0.96540.90870.94550.94850.94050.95120.9118Std.0.00130.00220.00160.00130.00220.00600.0032Figure 12
ROC curves of each prediction classifier.According to Table10 and Figures 11 and 12, the prediction accuracy of our proposed method is the highest, compared with other common classification methods including NB, SVM, LR, RF, ADB, and KNN. This demonstrates that unobserved features should be taken into consideration when predicting the individual disinformation forwarding behavior.In summary, the experiment results demonstrate that our proposed features can greatly improve the prediction accuracy of classifiers. The experiment results also demonstrate that our proposed method considering unobserved features exhibits superior performance than common classification methods.


## 4.1. Dataset

The data we used in this study comes from the microblog, which is the largest social media platform in China. We are provided with real data by the microblog data center as a result of our cooperation with them. We obtain a total of nine disinformation-mongering tweets that were widely spread on social media between April 2018 and August 2018, which covered common disinformation topics, such as personal safety, health and wellness, death anxiety, and geomantic superstitions. Additionally, 38,079 users participated in disinformation forwarding. It is noted that all the disinformation-mongering tweets in our experiments are identified as disinformation by Weibo platform. The information on the spread of these disinformation is shown in Table5.Table 5
Disinformation information distribution.
Blog IDTime of postingNumber of forwardingNumber of commentsNumber of likesThemeM12018.04.24718576339Personal safetyM22018.04.26581227104Health preservationM32018.05.1450927871Death anxietyM42018.05.233089825008785Death anxietyM52018.06.24759168282Political public opinionM62018.06.241840830678EducationM72018.08.1672504761275Fengshui superstitionM82018.08.1960029728Death anxietyM92018.08.1911172612208Fengshui superstition


## 4.2. Benchmark Methods

Compared to current research on prediction of user information forwarding behavior, our proposed method systematically investigates the features affecting user disinformation forwarding and takes unobserved features into considerations. Therefore, to demonstrate the superiority of our proposed method, we design the following two groups of experiments to evaluate the features.The objective of the first group of experiments is to compare the effects of features used in the proposed method and features used in current methods on the prediction accuracy of user disinformation forwarding. Both the experimental group and control group use the same prediction algorithm, but the experimental group and control group use different features that influence disinformation forwarding. Because there is little research on features that influence disinformation forwarding in existing systems, we not only compare the common features that influence disinformation forwarding but also the common features that affect the behavior of social network users. Specially, in the first group of experiments, we do not take the unobserved features into consideration.The objective of the second group of experiments is to evaluate the effects of unobserved features used in the proposed method on the prediction accuracy of user disinformation forwarding. Both the experimental group and control group utilize observed features used in the proposed method, but the experimental group uses our proposed prediction algorithm with considering the unobserved features, whereas the control group uses the regular classification prediction algorithms without considering the unobserved features.Tables6 and 7 summarize the methods compared in the evaluations.Table 6
The comparison between features used in the proposed method and features used in current methods.
Features of disinformation forwarding (abbreviated)Calculation method of features of disinformation forwardingPrediction algorithmFeatures proposed in our method (PF)Generated from social persuasion and user susceptibility to disinformationPM, NB, RF, ADB, LR, KNN, SVMSocial influence features (SI)Generated from social influencePM, NB, RF, ADB, LR, KNN, SVMSocial persuasion features 1 (SP1)Generated from social persuasion; calculates structural equivalence with only considering one kind of structural equivalence; calculates entity similarity with only considering profile similarityPM, NB, RF, ADB, LR, KNN, SVMSocial persuasion features 2 (SP2)Generated from social persuasion; calculates social persuasion structural equivalence with considering social network topology and profile similarity; calculates entity similarity with considering profile similarity, behavior similarity, and comprehensive similarityPM, NB, RF, ADB, LR, KNN, SVMPM: proposed method (without considering unobserved features); NB: naive Bayes; RF: Random Forest; ADB: AdaBoost; LR: logistic regression; KNN: K-nearest neighbor; SVM: support vector machine.Table 7
The comparison between proposed method and other regular classifiers.
Prediction algorithm name (abbreviated)Calculation method of features of disinformation forwardingProposed method (PM)Generated from social persuasion, user susceptibility to disinformation, and unobserved featuresNaive Bayes (NB)Generated from social persuasion and user susceptibility to disinformationRandom Forest (RF)Generated from social persuasion and user susceptibility to disinformationAdaBoost (ADB)Generated from social persuasion and user susceptibility to disinformationLogistic regression (LR)Generated from social persuasion and user susceptibility to disinformationK-nearest neighbor (KNN)Generated from social persuasion and user susceptibility to disinformationSupport vector machine (SVM)Generated from social persuasion and user susceptibility to disinformationTable 8
Test training dataset division.
GroupRetweet data (1)Unretweet data (0)SumTraining data148050148050296100Testing data370123701274024Sum185062185062370124


## 4.3. Evaluation Design

Our experiments are conducted using the following steps:Step 1: divide the training set and testing set.We obtain a total of 37,014 records of data. The ratio of records for which the user forwarded the disinformation, marked as 1, to data for which the user do not forward the disinformation, marked as 0, is 1 : 1. We randomly divide the data into a training set and testing set according to the ratio 4 : 1. The data after division are shown in Table8.Step 2: calculate the features that influence disinformation forwarding.We calculate the features that influence disinformation forwarding used by each experimental group and control group. In the analysis of social network topology, we divided the social network users collected into 28 communities using the Louvain algorithm and then further analyzed the topology of the internal community and individual users.Step 3: predict the disinformation forwarding probability of users.We predicted the probability of each user forwarding each disinformation by inputting the calculated features that influenced disinformation forwarding into the classifier used by each experimental group and control group.We performed the above steps ten times, and each time we randomly divided the training set and testing set to ensure the stability of the evaluation results.


## 4.4. Prediction Results and Evaluation Analysis

### 4.4.1. Evaluation Index

To solve the binary classification problem, the machine learning models usually predict the probability valueP (Y|X) for modeling, where X is the sample and Y is the category to which it belongs. Additionally, PY=1|X denotes the probability that Y belongs to category 1 when sample X appears. We set a threshold value and hypothesize it as k, and it is classified as category 1 if PY=1|X>k; otherwise, it is classified as category 0. For example, the default threshold of a neural network and logistic regression is 0.5. It can be seen that the threshold selection quality directly determines the generalization ability of the machine learning model, and the ROC curve can indicate the influence of threshold change on the classifier.We calculate the true positive rate (TPR) as the vertical axis and false positive rate (FPR) as the horizontal axis:(14)TPR=TPTP+FN,FPR=FPTN+FP.The area under the ROC curve (AUC) is used to determine the comparison between two machine learning models.


### 4.4.2. Evaluation Results

First, we tested the influence of our proposed disinformation forwarding features on the prediction accuracy of disinformation forwarding compared with other commonly used disinformation forwarding features. Figure9 shows the ROC curves of features generated from different methods. Figure 10 shows the AUCs of our proposed features that influence disinformation forwarding and other commonly used disinformation forwarding features in the classification prediction algorithm. Cross-validation AUC values are shown in Table 9.Figure 9
ROC curves of features generated from different methods: (a) PF, SP1, and SI; (b) PF, SP2, and SI.
(a)(b)Figure 10
Average AUCs of each algorithm for different features.Table 9
Cross-validation AUC values.
No.GroupPMNBRFADBLRKNNSVM1PF0.96660.90340.94540.94630.93920.95320.9082SI0.58740.56390.56050.55890.56120.56030.5578SP10.82070.74730.80000.75450.74330.77700.7464SP20.94670.89400.91060.91260.89850.91100.88992PF0.96660.91130.94460.94870.94070.95430.9139SI0.58290.55850.56350.56050.55790.51850.5620SP10.82150.74300.81090.75390.73740.76530.7493SP20.94580.89660.91360.90810.89680.89240.89233PF0.96660.90890.94530.94520.93770.93130.9095SI0.58020.55930.55940.55920.55380.51970.5602SP10.82100.74070.80490.75700.73450.81090.7486SP20.94210.89740.91290.91060.90360.91000.88684PF0.96480.90710.94480.94620.93860.94890.9105SI0.57870.56240.55930.55660.55440.56090.5583SP10.82340.74800.80430.75660.73710.81380.7589SP20.94510.89460.91250.91140.89580.90530.88955PF0.96730.90640.94740.94800.94240.95430.9157SI0.58000.56030.55810.55950.55500.52170.5603SP10.81940.73840.80220.75640.74090.80830.7675SP20.94210.89800.91000.91050.89860.90570.89026PF0.96400.91070.94540.94680.93870.95000.9121SI0.57860.55640.56080.55700.55860.50960.5604SP10.81810.74390.80640.75090.74150.79620.7584SP20.94680.89350.91090.91190.89730.90260.88657PF0.96720.90990.94230.94560.94240.94140.9135SI0.58230.56230.55800.56060.55830.55810.5595SP10.81450.73890.80770.75460.74120.77150.7522SP20.94100.89320.91210.91260.89630.89300.88988PF0.96510.90880.94220.94530.93970.94980.9145SI0.58770.55980.55570.55930.55620.55840.5586SP10.83010.74110.80990.76060.73800.80930.7654SP20.94720.89440.91170.91260.89760.90500.88399PF0.96750.90860.94690.94770.94220.95390.9135SI0.57720.55610.56040.56030.55990.51930.5611SP10.82270.74060.80240.75560.73630.80060.7577SP20.95160.89600.91230.91310.89420.89230.891310PF0.96910.90660.94580.94800.94220.95370.9044SI0.58290.56460.55840.55790.55500.51250.5608SP10.81620.74370.80880.75510.74010.80400.7465SP20.94450.89960.91570.91030.89480.88090.8905AvgPF0.96650.90820.94500.94680.94040.94910.9116SI0.58180.56040.55940.55900.55700.53390.5599SP10.82080.74260.80570.75550.73900.79570.7551SP20.94530.89570.91220.91140.89730.89980.8891Proposed features (PF) refer to features proposed in our method. Social influence features (SI) refer to features related to social influence. Both social persuasion features 1 (SP1) and social persuasion features 2 (SP2) refer to features related to social persuasion, which include social influence, structural equivalence, and entity similarity. The primary difference between SP2 and SP1 is that the structural equivalence and entity similarity are calculated in different ways. SP1 calculates structural equivalence with only considering one kind of structural equivalence and calculates entity similarity with only considering profile similarity. SP2 calculates structural equivalence with considering social network topology and profile similarity and calculates entity similarity with considering profile similarity, behavior similarity, and comprehensive similarity.From Figures9 and 11, the following results can be concluded:(1)
Regardless of the classifier, the best performance results come from our proposed features (PF), compared with other features used in control groups. This demonstrates that our proposed features, which consider both social persuasion of publishers and the susceptibility of users, can greatly improve the prediction accuracy of classifiers.(2)
Regardless of the classifier, the worst performance results come from features related to social influence (SI). By using features related to social persuasiveness for the prediction of individual disinformation forwarding (SP1), the prediction accuracy of classifiers can be significantly improved: when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of SP1 increases by 29.9%, 18.02%, 24.63%, 19.65%, 18.2%, 26.18%, and 19.52%, respectively, compared with SI. This demonstrates that social persuasion of publishers, rather than social influence of publishers, should be taken into consideration when predicting individual disinformation forwarding.(3)
Our proposed method utilizes a new method to calculate structural equivalence by considering more topology information of SNS. We compare the effects of structural equivalence features calculated by our proposed method (SP2) with those calculated by common calculation methods (SP1) on the prediction accuracy of user disinformation forwarding. The results show that when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of SP2 increases by 12.45%, 15.31%, 10.65%, 15.59%, 15.83%, 10.41%, and 13.4%, respectively, compared with SP1. This demonstrates that structural equivalence features calculated by our proposed method is more reasonable.(4)
Our proposed method takes the susceptibility of users to disinformation. We compare the effects of features considering the susceptibility of users to disinformation (PF) with those without considering the susceptibility of users to disinformation (SP2) on the prediction accuracy of user disinformation forwarding. The results show that when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of PF increases by 2.12%, 1.25%, 3.28%, 3.54%, 4.31%, 4.93%, and 2.25%, respectively, compared with SP2. This demonstrates that the susceptibility of users to disinformation should be taken into consideration, when predicting individual disinformation forwarding.Figure 11
AUC value of each algorithm.We further evaluate the prediction accuracy of our proposed method considering the unobserved features by comparing it with other classification methods. Table10 and Figure 11 show the AUC values of each classification method. Figure 12 shows the ROC curves of each classification method.Table 10
AUC values for the proposed method and benchmark methods.
No.PMNBRFADBLRKNNSVM10.96590.90660.94480.94790.94060.95420.913020.96600.90800.94470.94820.93860.95350.904430.96610.90990.94450.94910.94050.95350.914940.96500.91020.94530.94990.94330.93480.912650.96630.90650.94620.94900.94060.95450.916760.96740.90610.94420.94580.93730.94730.909970.96460.91180.94790.94980.94400.95610.914180.96250.91010.94290.94870.94070.95170.909690.96450.91170.94830.94980.94200.95540.9110100.96550.90630.94620.94690.93710.95140.9119Av.0.96540.90870.94550.94850.94050.95120.9118Std.0.00130.00220.00160.00130.00220.00600.0032Figure 12
ROC curves of each prediction classifier.According to Table10 and Figures 11 and 12, the prediction accuracy of our proposed method is the highest, compared with other common classification methods including NB, SVM, LR, RF, ADB, and KNN. This demonstrates that unobserved features should be taken into consideration when predicting the individual disinformation forwarding behavior.In summary, the experiment results demonstrate that our proposed features can greatly improve the prediction accuracy of classifiers. The experiment results also demonstrate that our proposed method considering unobserved features exhibits superior performance than common classification methods.


## 4.4.1. Evaluation Index

To solve the binary classification problem, the machine learning models usually predict the probability valueP (Y|X) for modeling, where X is the sample and Y is the category to which it belongs. Additionally, PY=1|X denotes the probability that Y belongs to category 1 when sample X appears. We set a threshold value and hypothesize it as k, and it is classified as category 1 if PY=1|X>k; otherwise, it is classified as category 0. For example, the default threshold of a neural network and logistic regression is 0.5. It can be seen that the threshold selection quality directly determines the generalization ability of the machine learning model, and the ROC curve can indicate the influence of threshold change on the classifier.We calculate the true positive rate (TPR) as the vertical axis and false positive rate (FPR) as the horizontal axis:(14)TPR=TPTP+FN,FPR=FPTN+FP.The area under the ROC curve (AUC) is used to determine the comparison between two machine learning models.


## 4.4.2. Evaluation Results

First, we tested the influence of our proposed disinformation forwarding features on the prediction accuracy of disinformation forwarding compared with other commonly used disinformation forwarding features. Figure9 shows the ROC curves of features generated from different methods. Figure 10 shows the AUCs of our proposed features that influence disinformation forwarding and other commonly used disinformation forwarding features in the classification prediction algorithm. Cross-validation AUC values are shown in Table 9.Figure 9
ROC curves of features generated from different methods: (a) PF, SP1, and SI; (b) PF, SP2, and SI.
(a)(b)Figure 10
Average AUCs of each algorithm for different features.Table 9
Cross-validation AUC values.
No.GroupPMNBRFADBLRKNNSVM1PF0.96660.90340.94540.94630.93920.95320.9082SI0.58740.56390.56050.55890.56120.56030.5578SP10.82070.74730.80000.75450.74330.77700.7464SP20.94670.89400.91060.91260.89850.91100.88992PF0.96660.91130.94460.94870.94070.95430.9139SI0.58290.55850.56350.56050.55790.51850.5620SP10.82150.74300.81090.75390.73740.76530.7493SP20.94580.89660.91360.90810.89680.89240.89233PF0.96660.90890.94530.94520.93770.93130.9095SI0.58020.55930.55940.55920.55380.51970.5602SP10.82100.74070.80490.75700.73450.81090.7486SP20.94210.89740.91290.91060.90360.91000.88684PF0.96480.90710.94480.94620.93860.94890.9105SI0.57870.56240.55930.55660.55440.56090.5583SP10.82340.74800.80430.75660.73710.81380.7589SP20.94510.89460.91250.91140.89580.90530.88955PF0.96730.90640.94740.94800.94240.95430.9157SI0.58000.56030.55810.55950.55500.52170.5603SP10.81940.73840.80220.75640.74090.80830.7675SP20.94210.89800.91000.91050.89860.90570.89026PF0.96400.91070.94540.94680.93870.95000.9121SI0.57860.55640.56080.55700.55860.50960.5604SP10.81810.74390.80640.75090.74150.79620.7584SP20.94680.89350.91090.91190.89730.90260.88657PF0.96720.90990.94230.94560.94240.94140.9135SI0.58230.56230.55800.56060.55830.55810.5595SP10.81450.73890.80770.75460.74120.77150.7522SP20.94100.89320.91210.91260.89630.89300.88988PF0.96510.90880.94220.94530.93970.94980.9145SI0.58770.55980.55570.55930.55620.55840.5586SP10.83010.74110.80990.76060.73800.80930.7654SP20.94720.89440.91170.91260.89760.90500.88399PF0.96750.90860.94690.94770.94220.95390.9135SI0.57720.55610.56040.56030.55990.51930.5611SP10.82270.74060.80240.75560.73630.80060.7577SP20.95160.89600.91230.91310.89420.89230.891310PF0.96910.90660.94580.94800.94220.95370.9044SI0.58290.56460.55840.55790.55500.51250.5608SP10.81620.74370.80880.75510.74010.80400.7465SP20.94450.89960.91570.91030.89480.88090.8905AvgPF0.96650.90820.94500.94680.94040.94910.9116SI0.58180.56040.55940.55900.55700.53390.5599SP10.82080.74260.80570.75550.73900.79570.7551SP20.94530.89570.91220.91140.89730.89980.8891Proposed features (PF) refer to features proposed in our method. Social influence features (SI) refer to features related to social influence. Both social persuasion features 1 (SP1) and social persuasion features 2 (SP2) refer to features related to social persuasion, which include social influence, structural equivalence, and entity similarity. The primary difference between SP2 and SP1 is that the structural equivalence and entity similarity are calculated in different ways. SP1 calculates structural equivalence with only considering one kind of structural equivalence and calculates entity similarity with only considering profile similarity. SP2 calculates structural equivalence with considering social network topology and profile similarity and calculates entity similarity with considering profile similarity, behavior similarity, and comprehensive similarity.From Figures9 and 11, the following results can be concluded:(1)
Regardless of the classifier, the best performance results come from our proposed features (PF), compared with other features used in control groups. This demonstrates that our proposed features, which consider both social persuasion of publishers and the susceptibility of users, can greatly improve the prediction accuracy of classifiers.(2)
Regardless of the classifier, the worst performance results come from features related to social influence (SI). By using features related to social persuasiveness for the prediction of individual disinformation forwarding (SP1), the prediction accuracy of classifiers can be significantly improved: when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of SP1 increases by 29.9%, 18.02%, 24.63%, 19.65%, 18.2%, 26.18%, and 19.52%, respectively, compared with SI. This demonstrates that social persuasion of publishers, rather than social influence of publishers, should be taken into consideration when predicting individual disinformation forwarding.(3)
Our proposed method utilizes a new method to calculate structural equivalence by considering more topology information of SNS. We compare the effects of structural equivalence features calculated by our proposed method (SP2) with those calculated by common calculation methods (SP1) on the prediction accuracy of user disinformation forwarding. The results show that when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of SP2 increases by 12.45%, 15.31%, 10.65%, 15.59%, 15.83%, 10.41%, and 13.4%, respectively, compared with SP1. This demonstrates that structural equivalence features calculated by our proposed method is more reasonable.(4)
Our proposed method takes the susceptibility of users to disinformation. We compare the effects of features considering the susceptibility of users to disinformation (PF) with those without considering the susceptibility of users to disinformation (SP2) on the prediction accuracy of user disinformation forwarding. The results show that when using the PM, NB, RF, ADB, LR, KNN, and SVM classifiers, the AUC value of PF increases by 2.12%, 1.25%, 3.28%, 3.54%, 4.31%, 4.93%, and 2.25%, respectively, compared with SP2. This demonstrates that the susceptibility of users to disinformation should be taken into consideration, when predicting individual disinformation forwarding.Figure 11
AUC value of each algorithm.We further evaluate the prediction accuracy of our proposed method considering the unobserved features by comparing it with other classification methods. Table10 and Figure 11 show the AUC values of each classification method. Figure 12 shows the ROC curves of each classification method.Table 10
AUC values for the proposed method and benchmark methods.
No.PMNBRFADBLRKNNSVM10.96590.90660.94480.94790.94060.95420.913020.96600.90800.94470.94820.93860.95350.904430.96610.90990.94450.94910.94050.95350.914940.96500.91020.94530.94990.94330.93480.912650.96630.90650.94620.94900.94060.95450.916760.96740.90610.94420.94580.93730.94730.909970.96460.91180.94790.94980.94400.95610.914180.96250.91010.94290.94870.94070.95170.909690.96450.91170.94830.94980.94200.95540.9110100.96550.90630.94620.94690.93710.95140.9119Av.0.96540.90870.94550.94850.94050.95120.9118Std.0.00130.00220.00160.00130.00220.00600.0032Figure 12
ROC curves of each prediction classifier.According to Table10 and Figures 11 and 12, the prediction accuracy of our proposed method is the highest, compared with other common classification methods including NB, SVM, LR, RF, ADB, and KNN. This demonstrates that unobserved features should be taken into consideration when predicting the individual disinformation forwarding behavior.In summary, the experiment results demonstrate that our proposed features can greatly improve the prediction accuracy of classifiers. The experiment results also demonstrate that our proposed method considering unobserved features exhibits superior performance than common classification methods.


## 5. Discussion and Conclusion

We propose a novel method to predict the disinformation forwarding probability of users on social networks and verify it using real data. Our proposed method makes two important contributions. First, we study disinformation forwarding behavior from the perspective of social network behavior spread and then identify and calculate the key features that affect the disinformation forwarding behavior of social network users. Second, we develop an algorithm that combines Random Forest and EM to predict the probability of social network users forwarding disinformation based on the key features. The greatest advantage of this algorithm is that it can take into account the influence of unobserved features on the behavior of social network users, which was not available in previous studies on disinformation forwarding behavior.The results demonstrate the following three important points: (1) social persuasion of publishers, rather than social influence of publishers, should be taken into consideration when predicting individual disinformation forwarding; (2) when predicting individual disinformation forwarding, the susceptibility of users to disinformation and the unobserved features should be taken into consideration; (3) structural equivalence features should be calculated by considering more topology information of SNS.Our study also has some implications in practice. First, the government can monitor the development of public opinion more efficiently using our proposed method, which can locate users who may believe and forward disinformation and refute them in a targeted manner. For example, during the outbreak of COVID-19, a large number of disinformation spreads easily on social networks and made people anxious. With the support of our method, the government could have determined the people who easily believe disinformation related to the pandemic scenario before they forward the disinformation and performed a targeted refutation of disinformation, which could have effectively curbed the spread of disinformation and helped to stabilize the hearts of people. Second, enterprises can eliminate the negative impact of disinformation on their brand image using our proposed method. For instance, disinformation that is not conducive to the image of an enterprise is often spread on social networks when an enterprise encounters some major crisis. With the support of our method, enterprises could identify people who easily believe this disinformation in a timely manner and perform targeted disinformation refutation to eliminate the negative impact of disinformation on the enterprises and help the enterprises survive the public opinion crisis.Our study could be extended in several directions. First, although our proposed method considers the features that affect the disinformation forwarding of social network users more comprehensively than existing methods, there may also be more precise methods to calculate these features. The experimental results of this study prove that the original method for calculating structural equivalence between users can be further improved. Future research should explore more accurate methods to calculate the influencing features and evaluate their effectiveness accordingly. Second, our proposed method estimates the influence of unobserved features using the EM algorithm, but in fact, besides the EM algorithm, there also exists more than one algorithm that can estimate the influence of unobserved features. Future research should compare these algorithms and evaluate their effectiveness accordingly. Third, interactions between the influencing features, such as social influence and entity similarity, have interactive effects on the adoption decision [34, 46]. Therefore, it is of great importance to investigate how to extend our approach by combining the features.



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*Source: 9216063-2022-03-02.xml*