Rumor detection driven by graph attention capsule network on dynamic propagation structures

Abstract

Rumor detection aims to judge the authenticity of posts on social media (such as Weibo and Twitter), which can effectively prevent the spread of rumors. While many recent rumor detection methods based on graph neural networks can be conducive to extracting the global features of rumors, each node of the rumor propagation structure learned from graph neural networks is considered to have multiple individual scalar features, which are insufficient for reflecting the deep-level rumor properties. To address the above challenge, we propose a novel model named graph attention capsule network on dynamic propagation structures (GACN) for rumor detection. Specifically, GACN consists of two components: a graph attention network enforced by capsule network that can encode static graphs into substructure classification capsules for mining the deep-level properties of rumor, and a dynamic network framework that can divide the rumor structure into multiple static graphs in chronological order for capturing the dynamic interactive features in the evolving process of the rumor propagation structure. Moreover, we use the capsule attention mechanism to combine the capsules generated from each substructure to focus more on informative substructures in rumor propagation. Extensive validation on two real-world datasets demonstrates the superiority of GACN over baselines.

Introduction

The rapid development of social media has changed the way people communicate with each other in daily life and has contributed to the proliferation of many rumors. Rumors quickly and widely spread, and their proliferation pollutes the social network ecology and affects users’ access to high-quality information. Selecting the COVID-19 epidemic in 2020 as an example, the rapid spread of much false information on social networks has caused public panic. Therefore, correctly identifying rumors has become an important research task for scholars and even the industry.

A rumor is defined as a story or statement in general circulation without confirmation or certainty of fact [1]. Consider Fig. 1 as an example, which shows a rumor event on Twitter with a source post and related comments. Previous methods mainly focus on the use of machine learning to detect rumors, such as Decision Tree [2], Random Forest [3], and Support Vector Machine(SVM) [4]. These methods are trained using extracted features that can effectively represent rumors, such as user features, text content, and propagation patterns [2, 4–7]. Such methods heavily rely on feature engineering, which is time-consuming and requires numerous human resources. Moreover, the handcrafted features are highly subjective and cannot capture deep-level features. In recent years, to extract higher-order features, many deep learning techniques have been widely applied in the field of rumor detection. Based on deep learning models, such as CNNs [8–11] and RNNs [12–14], researchers have proposed many models of rumor detection. However, these models fail to take into account the characteristics of the rumor propagation structure. Recent graph models such as GCN [15, 16], GAT [17], and GraphSage [18, 19] have successively emerged, attracting the attention of numerous researchers. Tian et al. [20] proposed a bidirectional graph convolutional network structure, in which the upwards and downwards propagation modes of social media texts were combined to effectively capture the global features of the rumor structure.

Fig. 1.

An example of rumor event on Twitter with a source post and related comments

Although graph neural networks have been widely employed in rumor detection [20–27], certain problems still need to be solved. When the rumor propagation structure is learned from the graph neural network to the graph embedding, the learning representation of each text node is considered to comprise multiple individual scalar features rather than an interdependent feature vector, which is not enough to express the deep-level properties. On the other hand, the current methods of rumor detection are mainly applied to a single graph structure and rumors are greatly affected by time, which cannot effectively capture the dynamic interaction information in the propagation process.

To address the above challenges, inspired by capsule network [28, 29], we propose a rumor detection model named graph attention capsule network on dynamic propagation structures(GACN). The model can effectively capture the deep-level properties of each graph node, and combined with the dynamic network framework, it can mine the dynamic interactive features among users in rumor propagation.

Our proposed method consists of two components: the graph attention capsule network and the dynamic network framework. In the graph attention capsule network, first, the graph attention network is applied to the graph-like propagation structure of rumors for aggregation calculation to obtain the globalized features of each graph node. Second, the capsule network is used to convert the scalar values on the graph node features into capsules using its unique dynamic routing mechanism [28] to deeply mine the properties of the texts. The model also incorporates the source post feature to enhance the feature representation of each graph node. The main task of the dynamic network framework is to divide the comments into a series of substructures in chronological order. We encode each of them by using the graph attention capsule network to capture the interaction features during propagation. Last, the capsule attention mechanism is designed to combine each structure to focus on more informative substructures in the propagation process.

The main contributions of this paper are summarized as follows:

• We propose a new model driven by the graph attention capsule network, GACN (Graph Attention Capsule Network on Dynamic Propagation Structures), to effectively mine the deep-level properties of rumors. To the best of our knowledge, this is the first application of capsule network for rumor detection.

• To capture the dynamic interactive features in the evolving process of the rumor propagation structure, we elaborately design a strategy that divides the dynamic propagation structure of rumor into multiple static graphs in chronological order.

• The GACN model is evaluated on two social network datasets, and the experimental results demonstrate that the proposed method has higher rumor detection performance than other advanced baselines.

The structure of the paper is described as follows. Section 2 introduces relevant and recently related work. Section 3 introduces the problem definition of rumor detection. Section 4 provides the experimental details of our proposed model. Section 5 describes the experimental settings. Section 6 reports and discusses the experimental results. We summarize the findings of the paper in Sect. 7.

Related work

The research on rumor detection is mainly divided into two aspects: (1) text content and user information, and (2) propagation structure. The comparison of previous works is summarized in Table 1.

Table 1.

Comparison of previous works

Papers	Text	User	Propagation structure
[30]	$✓$	$\times$	$\times$
[2]	$✓$	$✓$	$\times$
[12]	$✓$	$\times$	$\times$
[31]	$✓$	$\times$	$\times$
[4]	$\times$	$✓$	$\times$
[32]	$\times$	$✓$	$\times$
[33]	$✓$	$\times$	$✓$
[34]	$✓$	$\times$	$✓$
[20]	$✓$	$\times$	$✓$
[35]	$✓$	$\times$	$✓$

$✓$ and $\times$ mean that the method has or does not have this capability, respectively

Text content and user information

Previous studies on rumor detection extracted handcrafted features based on the text contents and then applied machine learning methods to classify rumors. Chua et al. [30] used a logistic regression classifier to identify rumors by analyzing six types of features such as comprehensibility, emotion, writing style, and theme of text content. Castillo et al. [2] investigated the information credibility based on handcrafted text features and utilized a decision tree model for the classification task of rumors. These methods are based on machine learning methods that require manual design and extraction of features, which is time-consuming and labor intensive. In recent years, the development of deep learning has provided many new methods for rumor detection. Ma et al. [12] exploited the characteristics of rumor temporal features to divide comments into subblocks of equal length in chronological order, which were input to an RNN for rumor detection. Liu et al. [31] divided source microblogs and related microblogs by cluster analysis and used convolutional neural network (CNN) to identify rumors.

Relying on textual information alone is not effective for rumor detection. In recent years, many studies have considered incorporating user information to assist text content for rumor detection. User-based methods are mainly employed for modeling user participation in social media, where the user’s characteristic information, such as description, gender, followers, friends, location, and verification type, is collected from the user’s profile. Yang et al. [4] extracted user characteristics for classification, such as gender, geographic location, and the number of followers. Castillo et al. [2] utilized user characteristics on Twitter to detect fake news, which includes the number of followers, number of friends, age of registration, etc. Liu et al. [32] combined RNN and CNN to capture users’ characteristics based on time series to improve the performance of rumor detection.

Propagation structure

Rumor detection methods based on propagation structure usually analyze the propagation paths or networks formed by retweets and comments of blog posts to identify rumors. Ma et al. [33] proposed a series of time series features based on the life cycle of rumors and applied these features for classification to improve the detection of rumors. Ma et al. [34] used recurrent neural networks to model the top-down propagation direction and the bottom-up diffusion direction of the propagation tree. However, these methods usually focus only on learning serialization features from a propagation perspective, disregarding the global forwarding relationships between posts on social networks. Certain recent studies modeled the propagation of information as a propagation graph and utilized graph neural networks to solve the problems of rumor detection. Bian et al. [20] exploited the graph convolutional network to mine the propagation structure characteristics of the propagation tree based on top-down and bottom-up directions. Yang et al. [35] proposed a rumor detection model based on a graph adversarial learning framework, in which an attacker dynamically adds intentional perturbations to the graph structure to deceive the detector and in which the detector will learn more unique structural features to resist these perturbations, thus improving the robustness and generalization of the model.

Although graph neural networks have achieved good performance for rumor detection [20–27], the learned representation of each text node is considered to comprise multiple individual scalar features rather than a feature vector with interdependencies, which is not sufficient to effectively represent the deep-level properties of rumors. Additionally, existing methods have difficulty capturing the dynamic interaction information during rumor propagation. Therefore, we propose GACN to better address these problems.

Problem Definition

Rumor detection is considered an event-level classification task. Let $c=\{x_1,x_2,...,x_n,S\}$ be an event, where $x_1$ is the source post, $x_j$ represents the $j-1-th$ comment, and $n-1$ comments are listed in chronological order. As time evolves, the propagation structure of rumors will constantly change, thus forming the propagation structure $S=\{S^{(1)},S^{(2)},...,S^{(T)}\}$ at different times, where T is the number of divisions and $S^{(i)}$ is the $i-th$ propagation substructure. The details of the delineation are described in the Method.

Each event $c\in C$ can be labeled with a category label $y\in Y$. The task of rumor detection is to learn the function f from the event set C to the label set Y. It is formulated as:

$$\begin{array}{c}\hfill f:C\to Y\end{array}$$ 1

Method

In this section, we introduce the overall framework of GACN and its detail of implementation. Figure 2 shows an overview of our framework, which will be described in the following sections. Table 2 summarizes some important notations used in this paper. We propose a Graph Attention Capsule Network on Dynamic Propagation Structures, named GACN. This model consists of two components: the graph attention capsule network which mines the deep-level properties of rumors and the dynamic network framework which captures the dynamic interactive features in the evolution process of the rumor propagation structure.

Fig. 2.

Illustration of our GACN model. It consists of two components: the dynamic network framework (left) and the graph attention capsule network (right)

Table 2.

List of notations

Notation	Definition
$c=\{x_1,x_2,...,x_n,S\}$	The event
$S=\{S^{(1)},S^{(2)},...,S^{(T)}\}$	The propagation structure
$x_1$	The source post
$x_j$	The $j-1-th$ comment
T	The number of divisions
C	The event set
Y	The label set
k	The number of categories
$S^{(t)}$	The $t-th$ propagation substructure
$V^{(t)}=\{x_1,x_2,...,x_{n^{(t)}}\}$	The nodes on $S^{(t)}$
$E^{(t)}$	The set of edges on $S^{(t)}$
$\mathbf{B}$	The affine transformation matrix
${{\mathit{h}}_i}^{(l)}$	The representation of the $i-th$ graph node after l graph attention layers
$\mathbf{H}\in {\mathbb{R}}^{N\times p\times d_m}$	The global features of nodes
$r\in {\mathbb{R}}^{d_r}$	The source post feature
${\mathbf{H}}^{{}^{\prime }}\in {\mathbb{R}}^{N\ast q\ast d_c}$	The primary capsules
$\mathbf{U}\in {\mathbb{R}}^{N\times q\times d_c}$	The normalized primary capsules
${\mathit{v}}_j$	The substructure classification capsule j
$\mathbf{I}\in {\mathbb{R}}^{k\ast f}$	The final classification capsules
${\tilde{T}}_i$	The indicator function of classification
$\lambda$	The scaling factor

Graph Attention Capsule Network

We design the graph attention capsule network to obtain the deep-level properties of each propagation structure inspired by capsule network [28]. The network consists of three parts: global features of nodes, source post encoding, and substructure classification capsules. We first describe how to generate the global features of nodes.

Global features of nodes

We construct graph propagation structure $<V,E>$ for each rumor c, depending on the response relationships between comments and between comments and source post. $V^{(t)}=\{x_1,x_2,...,x_{n^{(t)}}\}$ represents the nodes in the $t-th$ propagation substructure $S^{(t)}=<V^{(t)},E^{(t)}>$ , including $x_1$ being the node of the source post, $x_i$ being the node of the comments, and $E^{(t)}$ representing the set of edges that describe the response relationship between nodes. For each textual content, we encode them using the TF-IDF model [36].

First, the affine transformation matrix $\mathbf{B}$ transforms the initial feature $x_i$ into a hidden vector ${{\mathit{h}}_i}^{(0)}$, as shown in Eq.2. The GAT, proposed by Veličković et al. [17], is then applied to the hidden vectors to obtain the global features of each node. In updating the feature vectors of graph nodes, the graph attention network aggregates the neighbor information according to the weights to obtain the representation that contains the neighbor information. The detailed steps are presented as follows:

$$\begin{array}{cc}\hfill {{\mathit{h}}_i}^{(0)}=& \mathbf{B}{x}_i\hfill \end{array}$$ 2

$$\begin{array}{cc}\hfill {\alpha }_{\mathit{ij}}=& \frac{exp(LeakyReLU(a^T[\mathbf{W}{{\mathit{h}}_i}^{(l)}||\mathbf{W}{{\mathit{h}}_j}^{(l)}]))}{{\sum }_{k\in N_i}exp(LeakyReLU(a^T[\mathbf{W}{{\mathit{h}}_i}^{(l)}||\mathbf{W}{{\mathit{h}}_k}^{(l)}]))}\hfill \end{array}$$ 3

$$\begin{array}{cc}\hfill {{\mathit{h}}_i}^{(l+1)}=& \sigma ({\sum }_{j\in N_i}{{\alpha }_{\mathit{ij}}\mathbf{W}{\mathit{h}}_j}^{(l)})\hfill \end{array}$$ 4

The ${\alpha }_{\mathit{ij}}$ obtained by Eq. 3 represents the weight of importance when the features of the node j are aggregated to node i, where $N_i$ is the first-order neighbors of node i, both $\mathbf{W}$ and a are trainable parameters, ${{\mathit{h}}_i}^{(l)}$ is the representation of the i-th graph node after l graph attention layers are sequentially computed, and LeakyRelu is the activation function. By summing the vectors of neighbors according to the weights ${\alpha }_{\mathit{ij}}$, we can obtain the vector ${{\mathit{h}}_i}^{(l+1)}$ of node i at layer $l+1$ of the graph, as shown in Eq. 4. We concatenate the vectors ${\mathit{H}}_i$ obtained from the output of each graph attention layer for node i to obtain the global vector $\mathbf{H}\in {\mathbb{R}}^{N\times p\times d_m}$ on the substructure $S^{(t)}$. It is formulated as:

$$\begin{array}{cc}\hfill {{\mathit{H}}_i}^{{}_{}}=& concat([{{\mathit{h}}_i}^{(1)},{{\mathit{h}}_i}^{(2)},\cdots ,{{\mathit{h}}_i}^{(p)}])\hfill \end{array}$$ 5

$$\begin{array}{cc}\hfill \mathbf{H}=& concat([{\mathit{H}}_1,{\mathit{H}}_2,\cdots ,{\mathit{H}}_N])\hfill \end{array}$$ 6

where p is the number of graph network layers, N denotes the number of graph nodes, and $d_m$ is the dimension of the hidden vector after each graph attention layer is encoded.

Source post encoding

The source post contains rich information about a rumor, which is beneficial to strengthen the feature representation of graph nodes. In our proposed model, the transformer encoder [37] is used to encode the source post.

First, we use GloVe [38] to generate a word vector $\{w_r^1,w_r^2,...,w_r^{{}_{n^r}}\}$ for each word in the source post $x_1$, where $n^r$ refers to the number of words. Second, the self-attention mechanism is used to measure the importance of words. It is formulated as:

$$\begin{array}{cc}\hfill {\mathit{h}}_r=& \mathit{TransformerEncoder}(\{w_r^1,w_r^2,...,w_r^{{}_{n^r}}\})\hfill \end{array}$$ 7

$$\begin{array}{cc}\hfill r=& mean({{\mathit{h}}_r}^1,{{\mathit{h}}_r}^2,\cdots ,{{\mathit{h}}_r}^{n_r})\hfill \end{array}$$ 8

where ${\mathit{h}}_r$ is the result of the encoding by the encoder module in the transformer. Last, the final source post feature $r\in {\mathbb{R}}^{d_r}$ is obtained by averaging the hidden vectors of all words, where $d_r$ is the dimension of the source post feature.

Substructure classification capsules

After the aggregation calculation of each node through the graph attention network, the obtained vector $\mathbf{H}$ indicates that it has been able to capture the global features of the propagation structure. Considering that the source post of the rumor can highlight the typical features of the rumor, the model concatenates the source post feature with the global features of each node to obtain the representation $\mathbf{A}\in {\mathbb{R}}^{N\ast p\ast (d_m+d_r)}$ of each graph node which is enhanced. We use the one-dimensional convolution $conv1d(\bullet )$ by concatenating the features of different graph network layers at the same location to obtain the primary capsules ${\mathbf{H}}^{{}^{\prime }}\in {\mathbb{R}}^{N\ast q\ast d_c}$, where q is the number of primary capsules and $d_c$ is the dimension of primary capsules. It is formulated as:

$$\begin{array}{cc}\hfill \mathbf{A}=& \mathit{concat}(\mathbf{H},r)\hfill \end{array}$$ 9

$$\begin{array}{cc}\hfill {\mathbf{H}}^{{}^{\prime }}=& conv1d(\mathbf{A})\hfill \end{array}$$ 10

Substructure classification capsules are obtained by transforming primary capsules, which indicate the type of rumors. Each substructure classification capsule is a vector, and the scalar values in the vector represent the deep-level properties of the rumor.

Node normalization is performed to generate the attention value ${\alpha }_{\mathit{primary}}$ which is applied to the primary capsules. To obtain the normalized primary capsules $\mathbf{U}\in {\mathbb{R}}^{N\times q\times d_c}$, we employ two fully connected layers. It is formulated as:

$$\begin{array}{cc}\hfill \alpha =& F{C}_2(F{C}_1({\mathbf{H}}^{{}^{\prime }}))\hfill \end{array}$$ 11

$$\begin{array}{cc}\hfill \mathbf{U}=& {\alpha }_{\mathit{primary}}\ast {\mathbf{H}}^{{}^{\prime }}\hfill \end{array}$$ 12

The dynamic routing mechanism in the capsule network [28] is employed to transform primary capsules into substructure classification capsules. In the algorithm, $b_{\mathit{ij}}$ is initialized and the coupling coefficient weight $m_i$ is obtained, which represents the contribution of the normalized primary capsules i to the substructure classification capsules. It is formulated as:

$$\begin{array}{cc}\hfill b_{\mathit{ij}}=& b_{\mathit{ij}}+{\mathit{u}}_{j|i}\ast {\mathit{v}}_j\hfill \end{array}$$ 13

$$\begin{array}{cc}\hfill m_i=& \mathit{softmax}(b_i)\hfill \end{array}$$ 14

where $b_{\mathit{ij}}$ and ${\mathit{u}}_{j|i}$ denote the training parameters and prediction vectors, respectively, of the normalized primary capsule i to the substructure classification capsule j. The prediction vector ${\mathit{u}}_{j|i}$ is obtained by the weight $w_{\mathit{ij}}$ of the normalized primary capsules $\mathbf{U}$. The initialized capsule weight $m_{\mathit{ij}}$ is used to obtain the intermediate value ${\mathit{s}}_j$ of the substructure classification capsule j. ${\mathit{s}}_j$ is calculated by the activation function Squashing [28] to obtain the output ${\mathit{v}}_j$ of the substructure classification capsule j. The weight $m_{\mathit{ij}}$ is iteratively updated through the prediction vector ${\mathit{u}}_{j|i}$ and capsule output ${\mathit{v}}_j$. It is formulated as:

$$\begin{array}{cc}\hfill {\mathit{u}}_{j|i}=& w_{\mathit{ij}}\mathbf{U}\hfill \end{array}$$ 15

$$\begin{array}{cc}\hfill {\mathit{s}}_j=& \sum m_{\mathit{ij}}\ast {\mathit{u}}_{j|i}\hfill \end{array}$$ 16

$$\begin{array}{cc}\hfill {\mathit{v}}_j=& \frac{{∥{\mathit{s}}_j∥}^2}{1+{∥{\mathit{s}}_j∥}^2}.\frac{{\mathit{s}}_j}{{∥{\mathit{s}}_j∥}^2}\hfill \end{array}$$ 17

Dynamic Network Framework

Partition propagation structure

To capture the dynamic interaction characteristics in the evolving process of rumor propagation structure, we divide the structure according to the release time of each post. Exactly, all comments below each source post are divided by equal amounts. The propagation substructure starts with the number $S^{(1)}$ and then separately adds $⌈(n-1)/T⌉$ comments to form the next substructure, where $n-1$ is the number of comments and T is the number of partitions. The last substructure is formed when the number of comments increases to $T\times ⌈(n-1)/T⌉$. The propagation structure S representing the event c is described as:

$$\begin{array}{c}\hfill S=\{S^{(1)},S^{(2)},\cdots ,S^{(T)}\}\end{array}$$ 18

Capsule attention mechanism

To effectively capture the dynamic propagation characteristics of rumors, after the capsule network obtains the classification capsule vectors ${\mathit{G}}^{(i)}=[{\mathit{v}}_1,{\mathit{v}}_2,\cdots ,{\mathit{v}}_k]$ of the substructure $S^{(i)}$, where k is the number of rumor classes, we use the self-attention mechanism to measure the importance of the classification capsules of each substructure as shown in Fig. 3.

Fig. 3.

Illustration of capsule attention mechanism

The capsules belonging to the same category in all structures are formed into a matrix as the common values of $\mathit{Q}$, $\mathit{K}$, and $\mathit{V}$, where $\mathit{Q}$, $\mathit{K}$, and $\mathit{V}$ are the query vector, key vector and value vector, respectively. Therefore, the attentional substructure classification capsules ${\mathit{h}}_{G^{(i)}}$ are calculated according to Eq. 19, where $d_K$ is used to keep the gradient stable. The final classification capsules $\mathbf{I}\in {\mathbb{R}}^{k\ast f}$ are obtained by averaging over all substructure vectors ${\mathit{h}}_{G^{(i)}}$, where k is the number of categories and f is the dimension of the final classification capsules. It is formulated as:

$$\begin{array}{cc}\hfill \mathit{Attention}(\mathit{Q},\mathit{K},\mathit{V})=& \mathit{softmax}(\frac{(\mathit{Q}{\mathit{K}}^T)}{\sqrt{d_K}})\mathit{V}\hfill \end{array}$$ 19

$$\begin{array}{cc}\hfill \mathbf{I}=& \frac{1}{T}\sum _{i=1}^T{\mathit{h}}_{G^{(i)}}\hfill \end{array}$$ 20

where T is the number of partitions and $\mathit{softmax}(\bullet )$ is the activation function.

Prediction and classification

In this paper, the margin loss function [28] is used as the loss function of our proposed model. It can be expressed as Eq. 21:

$$\begin{array}{c}\hfill L\mathrm{os}{\mathrm{s}}_c=\sum _i\left\{{\tilde{T}}_{i}max{(0,m^{+}-||{\mathbf{I}}_i||)}^2+\lambda (1-{\tilde{T}}_i)min{(0,||{\mathbf{I}}_i||-m^{-})}^2\right\}\end{array}$$ 21

where i is the type of rumor, $||{\mathbf{I}}_i||$ is the output probability of final classification capsule i , ${\tilde{T}}_i$ is the indicator function of classification (the existence of class i is 1, and the nonexistence is 0), and $m^{+}$ is the upper bound, penalizing false positives, i.e., predicting the presence of class i but its true absence. $m^{-}$ is the lower bound, penalizing false negatives, i.e., predicting the absence of class i but its true presence, and $\lambda$ is the scaling factor, adjusting the weight of both. The overall algorithm description of our GACN is shown in Algorithm 1.

Experiment

In this section, we first introduce the two mainstream datasets used in the experiment, including Twitter15 [39] and Twitter16 [33], and then describe the baseline models selected in this article that contrast with the proposed method. Next, the experimental evaluation indicators are described. Finally, we describe the parameter settings of our proposed model.

Dataset

This paper will evaluate our proposed method on two publicly available datasets, including Twitter15 [39] and Twitter16 [33] . The statistics of the datasets are shown in Table 3.

Table 3.

Statistics of the datasets

Statistic	Twitter15	Twitter16
# of posts	331612	204820
# of True rumors	374	205
# of False rumors	370	205
# of Unverified rumors	374	203
# of Nonrumors	372	205
# of events	1490	818
Avg. time length/event	1,337 Hours	848 Hours
Avg. # of posts/event	223	251
Max # of posts/event	1768	2765
Min # of posts/event	55	81

Twitter15 and Twitter16 were created by Ma et al. [33, 39], who collected rumor information from the Twitter website, a famous international social networking platform at different times. The authors collect 1490 and 818 rumors that are marked into four categories: true rumor (TR), false rumor (FR), unverified rumor (UR), and nonrumor (NR). The method of dividing the Twitter15 and Twitter16 datasets refers to existing research [34], and the experiment is carried out using a fivefold cross-validation method.

Baselines

In this paper, certain state-of-the-art methods for rumor detection are selected as the baseline models to compare with our proposed model. These models are presented as follows:

• DTC [2]: A rumor detection model based on global handcrafted features to build a decision tree classifier to obtain information credibility.

• SVM-RBF [4]: A support vector machine classifier based on RBF kernel which uses statistical features manually constructed from blog content.

• SVM-TS [33]: A linear support vector machine classifier based on temporal context features.

• SVM-TK [39]: An SVM classifier with a propagation tree kernel on the basis of the propagation structures of rumors.

• GRU-RNN [12]: An RNN-based model that captures contextual information from continuous representations of relevant posts over time.

• RvNN [34]: A model based on RNN models to model the propagation direction and the diffusion direction, respectively, to learn the feature vector representation of the propagation tree.

• GLAN [21]: A model that combines global and local features to build heterogeneous graphs and extract features.

• GCAN [23]: A GCN-based model that can describe the rumor propagation mode and use the dual co-attention mechanism to capture the relationship among source post, user characteristics and propagation path.

• Bi-GCN [20]: A graph convolution neural network model based on the propagation direction and diffusion direction of the propagation tree.

• P-BiGAT [22]: A bidirectional graph attention networks based on the propagation tree and diffusion tree through the tweet comment and reposting relationship.

Evaluation metrics

Rumor detection investigated in this paper is essentially a classification problem, so we choose classification-based evaluation metrics to evaluate the performance. The accuracy (Acc) and the F1-value(F1) of each category are chosen as the evaluation metrics in the paper, and the calculation formulas are as:

$$\begin{array}{cc}\hfill Acc=& \frac{TP+\mathit{FN}}{TP+FP+TN+FN}\hfill \end{array}$$ 22

$$\begin{array}{cc}\hfill F1=& \frac{2\times TP}{2\times TP+FP+FN}\hfill \end{array}$$ 23

where TP (true positive) denotes the number of cases in which the true category is positive, and the predicted category is positive, FP (false positive) denotes the number of cases in which the true category is negative and the predicted category is positive, FN (false negative) denotes the number of cases in which the true category is positive and the predicted category is negative, and TN (true negative) denotes the number of cases in which the true category is negative and the predicted category is negative.

Experimental settings

Our experiments are implemented with PyTorch. The optimizer is Adam [40] with a learning rate of 0.001. Our model uses TF-IDF to initialize the text nodes, and its dimension is 5000. We adopt Glove with a dimension of 200 to encode the source post. The model is trained by using 3 layers of graph attention network layers and the hidden vector dimension between each layer is 64. The rate of dropout is 0.5. The experiments are set up with an early stopping strategy, which is to terminate the training when the accuracy of the validation set no longer decreases within 10 iterations. A 5-fold cross-validation method is applied to evaluate the experimental effects, and the results are averaged as the metrics of the model. The hyperparameters involved in the experiment are listed in Table 4.

Table 4.

Hyperparameters involved in GACN

Parameter	Value
Optimizer	Adam
Learning rate	0.001
The dimension of TF-IDF	5000
The dimension of GloVe	200
The number of graph attention layers	3
The hidden vector dimension between each layer	64
The rate of dropout	0.5
The number of cross-validation	5

Experimental results

In this section, we validate our proposed model in three aspects: rumor detection results, ablation study, and visualization.

Rumor detection results

Table 5 and Table 6 record the detection effects of the state-of-the-art models on Twitter15 and Twitter16. Among them, we rerun the open-source code provided by Bian et al. [20] and Lu et al. [23] to obtain the experimental results of Bi-GCN and GACN.

Table 5.

Rumor detection results on Twitter15 (%)

Model	Acc	F1
		NR	FR	TR	UR
DTC	45.4	73.3	35.5	31.7	41.5
SVM-RBF	31.8	22.5	8.2	45.5	21.8
SVM-TS	54.4	79.6	47.2	40.4	48.3
SVM-TK	66.7	61.9	66.9	77.2	64.5
GRU-RNN	64.1	68.4	63.4	68.8	57.1
RvNN	72.3	68.2	75.8	82.1	65.4
GCAN	83.1	79.0	84.2	88.4	80.8
GLAN	85.4	79.6	82.2	91.4	82.3
Bi-GCN	83.2	79.5	83.3	90.2	78.9
P-BiGAT	87.2	82.1	84.8	94.4	88.2
GACN	88.9	91.0	92.4	87.5	84.5

The values in bold indicate the maximum value under different indicators

Table 6.

Rumor detection results on Twitter16 (%)

Model	Acc	F1
		NR	FR	TR	UR
DTC	46.5	64.3	39.3	41.9	40.3
SVM-RBF	55.3	67.0	8.5	11.7	36.1
SVM-TS	57.4	75.5	42.0	57.1	52.6
SVM-TK	66.2	64.3	62.3	78.3	65.5
GRU-RNN	63.6	61.7	71.5	57.7	52.7
RvNN	73.7	66.2	74.3	83.5	70.8
GCAN	85.9	76.1	85.0	92.6	85.5
GLAN	87.4	85.1	87.7	91.3	85.8
Bi-GCN	86.8	78.0	90.1	93.4	85.7
P-BiGAT	89.6	81.5	93.4	97.9	83.4
GACN	90.0	96.4	88.9	90.0	84.6

The values in bold indicate the maximum value under different indicators

From the results in Table 5 and Table 6, we can determine that our proposed GACN model outperforms the state-of-the-art baselines on both Twitter15 and Twitter16. GACN improves 1.9% in accuracy compared with the optimal baseline model on Twitter15, while improving 0.4% on Twitter16. The results indicate that our proposed model has much better detection performance.

First, as shown in Table 5 and Table 6, all models based on deep learning (GRU-RNN, RvNN, GLAN, GCAN, Bi-GCN, P-BiGAT, and GACN) are superior to most of traditional models based on handcrafted features. This result confirms that deep learning methods are more accurate than traditional methods in extracting the deeper features of rumors.

Second, compared with RvNN, GCAN, Bi-GCN, P-BiGAT, and GACN are slightly better in all metrics. The main reason is that RvNN is a tree-based model that cannot capture long-distance dependencies in sequences. The graph-based models can solve this problem by capturing global characteristics in rumors, which improves the detection of rumors.

Last, in the graph-based models, the accuracy of GACN is higher than that of other graph-based models, which is attributed to the notion that these models only handle a single static graph, and cannot capture the dynamic interaction characteristics of rumors in the propagation process. On the other hand, these models can only extract the scalar features of graph nodes, which is not enough to effectively mine the deep-level properties of rumors.

Ablation study

To highlight the experimental effects of our proposed model, we conduct ablation analysis with the following models. The experimental results are shown in Table 7.

Table 7.

Effect of different components in GACN (%)

Model	Twitter15					Twitter16
	Acc	F1				Acc	F1
		NR	FR	TR	UR		NR	FR	TR	UR
w/o Dynamic	88.5	82.9	87.9	95.0	88.7	88.2	77.5	91.4	96.3	87.5
w/o Root	87.5	92.3	89.0	85.3	83.5	88.8	98.8	87.8	88.9	79.5
w/o Capsule	87.2	91.6	87.7	84.7	84.7	87.6	91.4	93.5	87.5	78.6
w/o Capsule &w/o Dynamic	85.4	80.3	86.9	92.7	81.9	87.0	78.1	88.9	95.1	85.7
GACN	88.9	91.0	92.4	87.5	84.5	90.0	96.4	88.9	90.0	84.6

The values in bold indicate the maximum value under different indicators

• w/o Dynamic: This is a static graph capsule network model, not including dynamic network framework.

• w/o Root: This model only considers the rumor propagation structure and does not consider the source post.

• w/o Capsule: This model replaces the capsule network after the graph network model with a fully connected layer and applies cross-entropy as the loss function.

• w/o Capsule &w/o Dynamic: The model does not take into account the capsule network and dynamic network framework.

The results in Table 7 show that our proposed model has the highest accuracy on Twitter15 and Twitter16, while the w/o Capsule &w/o Dynamic achieves poor detection performance. The accuracy of GACN, w/o Root, and w/o Dynamic outperform the w/o Capsule and w/o Capsule &w/o Dynamic without the capsule network, respectively, which confirms that the capsule network can better excavate the deep-level properties of rumors. Second, compared with w/o Root, our proposed model achieves better results, indicating that the information of the source post feature has an important role in improving the performance of rumor detection. Table 7 shows that the GACN and w/o Capsule models outperform the corresponding w/o Dynamic and w/o Capsule &w/o Dynamic without a dynamic network framework in terms of accuracy metrics, which further demonstrates the effectiveness of the dynamic propagation structure. The results suggest the necessity of capturing the dynamic interactive features in the evolving process of the rumor propagation structure. In summary, the dynamic propagation structure of rumors and the capsule network have a certain auxiliary effect for rumor detection.

Visualization

GACN mines the deep-level properties of the rumor by using the capsule network. To clarify the practical effect of the properties in each capsule, we use Tsne [41] to extract the values of each channel in the final classification capsules for dimensionality reduction and then present them in the form of visualization in Table 8. For Table 8, the categories of rumors are labeled with 0, 1, 2, and 3, representing nonrumor, false rumor, true rumor, and unverified rumor, and the corresponding points in the figures are colored red, green, yellow, and blue, respectively. In each row of the table, we compare two categories, three categories, and four categories of rumors. Selecting the first Row 0_1 as an example, we compare nonrumor and false rumors. Considering the size limitation of the paper, we choose channels that can highlight the properties of rumors for analysis.

Table 8.

Visualization of channels in classification capsules

Table 8 shows that when the two categories are compared, the vectors of each channel can distinguish specific categories after dimensionality reduction. For example, Channel3 can well distinguish 1 from 2, but it is difficult to distinguish 1 from 3. In contrast, Channel1 can easily distinguish 1 and 3, but not 1 and 2. This result indicates that the properties captured by Channel1 may be the factor determining the difference between 1 and 2, as well as Channel3. Channel2 can almost completely distinguish 0 from 2 and 2 from 3, which also explains why the types of rumors represented by 0, 2, and 3 can be completely divided when comparing the three categories of rumors 0_2_3. In the four classification rows, none of the individual channels can effectively classify each category, so it is necessary to integrate all channels to obtain their respective properties for classification. Compared with scalar-based deep learning models, using the capsule network can better integrate the properties captured by each channel to improve the accuracy of rumor detection.

Next, we use Tsne to reduce the dimensionality of each classification capsule, and the obtained results are shown in Table 9. Almost every classification capsule can roughly distinguish different types of rumors, indicating that each classification capsule focuses on the properties of rumors in different categories. Compared with the scalar-based neural network, the graph structure of rumors can be represented as multiple graph embeddings, each of which contains rich properties, so the use of capsule network can fully extract the features of rumors.

Table 9.

Visualization of classification capsules

Conclusion

In this paper, we propose a Graph Attention Capsule Network on Dynamic Propagation Structures, named GACN. The method divides the propagation structure by using the dynamic network framework to capture the dynamic interaction characteristics in the evolving process of rumor propagation. The graph attention capsule network is then applied to transform the divided static graph structures into capsules to extract deep-level properties. To the best of our knowledge, this is the first model that applies capsule network for rumor detection. Through experiments on two mainstream datasets, compared with the state-of-the-art baselines, the extensive results show that GACN achieves improvements of up to 1.9% and 0.4%, respectively. In future work, we will explore the specific meanings on which each channel in the capsule focuses to visually explain the improvement in rumor detection.

Data availability

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

Declarations

Conflict of interest

The authors declare that they have no competing interests.

Consent to participate

All authors contributed to this work.

Consent for Publication

All authors have checked the manuscript and have agreed to the submission.

Ethics approval

All authors read and approved the final version of the manuscript.