Evaluation	In this section, we describe a dataset, baselines, experimental setting, and experimental results. In the experiments, we seek to answer the following research questions: RQ1: What is the performance of our model and baselines? RQ2: How beneficial is each submodule of our model? RQ3: How effective is our attention mechanisms? RQ4: What is sensitivity of our model with regard to hyperparameters?

Table TABREF66 presents characteristics of baselines and our model, showing what information each model utilizes. Note that even though CMN and NAIS both utilize co-occurrence context, CMN only utilizes user co-occurrence context whereas NAIS looks into URL co-occurrence context.

Evaluation ::: RQ1: Performance of Our Model and Baselines	Table TABREF70 presents performance of our model and baselines. According to the results and information described in Table TABREF66, we had the following observations. First, deep learning-based approaches usually obtained better performance than traditional models (e.g., MF and GAU). This observation makes sense because (1) traditional models failed to capture the important non-linear relationship between users and fact-checking URLs; (2) Most deep-learning based baseline models employ attention mechanism which helps better understand the semantic relation between user and URL; and (3) training tricks such as drop out and batch normalization also contribute to a better quality of training. In particular, $NAIS_{concat}$ achieves better performance than $NAIS_{prod}$ which supports the reason (1). The second observation is that models with text review achieve better results compared with collaborative filtering-based methods. It is not surprising since that textual content contains rich information which could be auxiliary information to implicit feedback data and thus improve the recommendation accuracy. However, we observed that text-based recommendation approaches usually have a high complexity. Third, social context and co-occurrence context play important roles in improving recommendation results.

Evaluation ::: Baselines	To measure relative effectiveness of our model, we compare our model against eight state-of-the-art baselines including the traditional collaborative filtering method, neural network-based models, and context-aware approaches. MF  is a standard collaborative filtering technique. It factorizes an interaction matrix $X \in \mathbb {R}^{M \times N}$ into two matrices $U \in \mathbb {R}^{M \times d}$ and $X \in \mathbb {R}^{d \times N}$. $U$ contains each user's latent representation, and $X$ contains each URL's latent representation. GAU  is a framework specifically designed for fact-checking URL recommendation utilizing rich side information such as a user' social network, tweets, and referred fact-checking pages. It is the most relevant and domain-specific baseline. NeuMF  is a neural network based item recommendation algorithm. We adopted a composite version of MF jointly coupled with a MLP. CMN  combines a global latent factor model with an augmented memory network to capture personalized neighbor-based structure in a non-linear fashion.

NAIS  is an item-based collaborative filtering architecture that integrates attention mechanism to distinguish the contribution of previously consumed items. The authors proposed two versions of NAIS: (1) $NAIS_{concat}$ which concatenates two vectors to learn the attention weight; and (2) $NAIS_{prod}$ which feeds the element-wise product of the two vectors to the attention network. Therefore, we also build two versions of NAIS, and compare them with our model. DeepCoNN  was originally proposed for an item rating prediction task which jointly model user and item based on their textual reviews. The prior work shows that it significantly outperforms other topic modeling based methods.We re-implemented the baseline and adapted it for our recommendation task with implicit feedback. NARRE  is a deep neural network based framework for a item rating prediction task. It employs the attention mechanism to distinguish the importance of each review. We re-implemented the framework for our implicit feedback situation. NGCF  is a new recommendation framework based on graph neural network, explicitly encoding the collaborative signal in the form of high-order connectivity in user-item bipartite graph by performing embedding propagation.

Evaluation ::: Hyper-parameter Settings	We implement our framework by using Pytorch framework, initialize weight parameters by Xavier initialization , and optimize the model with Adam optimizer . The mini-batch size is set to 128. Empirically, in CSAN, we select 10 neighbors for each stream. In HGAN, we choose 8 user neighbors and 8 URL neighbors for each central node at a single layer, and the default number of graph attention layers is set to 2. If the object (i.e.g, user neighbor or URL neighbor) is not sufficient enough, we pad the sequence with zeros vectors. In the proposed AMRAN model, all hyperparameters are tuned by using the grid-search on the validation set, which is formed by holding out one interaction of each user from the training data like the prior work .

Conclusion	In this paper, we proposed a novel framework, which effectively recommends relevant fact-checking URLs to fact-checkers. The proposed framework inspired by recent advancements in graph neural network and attention mechanism leveraged user-URL specific context information to capture deep semantic and complex structure between target user and target URL. We compared the performance of our model, AMRAN, with eight state-of-the-art baselines. Experimental results showed that our model achieved up to 5.3% improvement against the best baseline. Both submodules of AMRAN positively contributed to the recommendation results. This work was supported in part by NSF grant CNS-1755536, AWS Cloud Credits for Research, and Google Cloud. Any opinions, findings and conclusions or recommendations expressed in this material are the author(s) and do not necessarily reflect those of the sponsors.

Evaluation ::: Case Study: Visualization of Relevance Propagation	Attention mechanism not only improve recommendation performance of our model, but also provide explainability of our model. As a case study, we specifically chose an example to demonstrate relevance propagation. In particular, we randomly sampled a user 7849 as the example as shown in Figure FIGREF80. The user 7849 has 3 co-occurrenced users, 3 following users, and posted 4 URLs. Note that we omit less important 2nd-degree neighbors for simplicity. The most relevant neighbors and the propagation paths are highlighted automatically via the attention mechanism. In general, based on the user's historical context URLs, we observe that the topic that user 7849 would like to participate in debunking is fauxtography. However, in this very particular case, the most influential context neighbors of the user are user 25 (co-occurrence user) and user 4759 (social context) given URL 1623. Both of the context neighbors share the similar taste with user 7849 on the favorite website (Politifact.com).

Related Works ::: Advancements in Recommender System	Traditionally, recommendation algorithms can be divided into two categories: collaborative filtering  and content-based filtering. However, in the past few years, the recommendation has become a more integrated task due to the success of the deep neural network. Neural Networks (NNs) proves to be effective to capture underlying nonlinear relations . Another advantage is that the NNs enhanced the model's capability of extracting knowledge from multimodal data , , , which serves as auxiliary information and provide solutions to address the data sparsity problem. More recently, researchers introduced attention mechanism into recommender systems, which has achieved great success in various fields , . Researchers developed multiple variants of attention mechanism to improve both the recommendation precision and model interpretability , , , . In this paper, we also propose two novel designs of attention mechanism. Following , , we further explore multi-relational context of given user-URL pair, aiming at discriminating the most important elements towards URL-dependent user preference.

Proposed Framework	We propose a novel framework called Attributed Multi-Relational Attention Network (AMRAN), to understand the influence of the multi-relational context to target user's fact-checking behavior. In this section, we elaborate our proposed AMRAN with using notations described in Table TABREF15. At the high level, AMRAN is composed of two modules as shown in Figure FIGREF16: (i) a convolutional spatial attention network (CSAN) and (ii) a heterogeneous graph attention network (HGAN). CSAN jointly models the influence of multi-relational context on target user-URL pair (Section 4.1). It enriches the neighborhood diversity, and expands the scope of information reception. HGAN leverages both global node connectivity and local node attributes, in order to incorporate the effect of information propagation and encode user's dynamic preference in depth (Section 4.2). At the final step, the model produces recommendations by combining wide context-aware target user embedding and URL embedding, multi-relational context user embedding and context URL embedding, and deep context-aware user embedding and URL embedding (Section 4.3).

Evaluation ::: Evaluation Protocol	We adopt the leave-one-out evaluation protocol to evaluate the performance of our model and baselines. The leave-one-out evaluation protocol has been widely used in top-K recommendation tasks. In particular, we held the latest interaction of each user as the test set and used the remaining interactions for training. Each testing instance was paired with 99 randomly sampled negative instances. Each recommendation model ranks the 100 instances according to its predicted results. The ranked list is judged by Hit Ratio (HR)  and Normalized Discount Cumulative Gain (NDCG)  at the position 10. HR@10 is a recall-based metric, measuring the percentage of the testing item being correctly recommended in the top-10 position. NDCG@10 is a ranked evaluation metric which considers the position of the correct hit in the ranked result. Since both modules in our framework introduce randomness, we repeat each experiment 5 times with different weight initialization and randomly selecting neighbors. We report the average score of the best performance in each training process for both metrics to ensure the robustness of our framework.

NAIS significantly outperforms CMN and becomes the strongest baseline model. It indicates that URL-URL co-occurrence relationship is more important than user-user co-occurrence relationship since semantic representation of each user is much complex than semantic representation of a fact-checking URL. Overall, our AMRAN outperforms all baselines, achieving 0.657 HR@10 and 0.410 NDCG@10. It improves HR@10 by 5.3% and NDCG@10 by 3% over the best baseline (i.e., $NAIS_{concat}$).

Evaluation ::: RQ3: Effectiveness of our Attention Mechanisms	We proposed two attention mechanisms: (1) spatial attention block in CSAN; and (2) graph attention mechanism in HGAN described in Section SECREF4. In this experiment, we are interested in studying the impact of the attention mechanisms. In particular, we run each submodule of AMRAN (i.e., CSAN or HGAN) with/without a corresponding attention mechanism. Table TABREF74 shows performance of these models. In both submodules, our proposed attention mechanisms positively improved the performance of these submodules, confirming the positive impact toward correctly recommending fact-checking URLs.

The similarity between the target user's node representation $h^{(l)}_u$ and all of its selected neighbors are defined as: where $h^{(l)}_i$ is the representation of user $i$ at layer $l$, and $\mathcal {N}^{\phi _t}_i$ denotes the node type-based neighbor. We adopt $f(h^{(l)}_i,h^{(l)}_j)=cosine(h^{(l)}_i,h^{(l)}_j)$ as similarity function. Intuitively, $\alpha ^{\phi }_{ij}$ measures the importance of neighbor $j$ towards central node $i$. Meanwhile, we obtain the edge weight $A_{ij}$ as well. After this, we aggregate the type-based neighborhood node representation and generate the embedding of neighborhood as the average of different types of nodes: To model the information propagation and capture higher-order relations, we stack the HGAL multiple times. In addition, we introduce the residual connection  to help train a HGAN with many layers. where $\sigma $ denotes the sigmoid function.

We define edges based on users' reference of URL (user-URL edges), user co-occurrence relation (user-user edges), and URL co-occurrence (URL-URL edges). We then introduce an adjacency matrix $A$ of $\mathcal {G}$ based on the importance of each edge. In particular, to compute the weight of user-user edges and URL-URL edges, we adopt a matrix named Shifted Positive Point-wise Mutual Information (SPPMI) , a popular measure for word associations, to utilize the co-concurrence context information. In word embedding scenario, each cell within the matrix measures the relation of corresponding word-context pair. The factorization of such matrix is proved to be equivalent to skip-gram model with negative sampling (SGNS). The Point-wise Mutual Information (PMI) between node $i$ and node $j$ is computed as $PMI(i,j) = log \frac{P(i,j)}{P(i)P(j)}$ where $P(i,j) = \frac{\# (i,j)}{|D|}$ and $P(i) = \frac{\# (i)}{|D|}$.

Attributed Multi-Relational Attention Network for Fact-checking URL Recommendation	To combat fake news, researchers mostly focused on detecting fake news and journalists built and maintained fact-checking sites (e.g., this http URL and this http URL). However, fake news dissemination has been greatly promoted via social media sites, and these fact-checking sites have not been fully utilized. To overcome these problems and complement existing methods against fake news, in this paper we propose a deep-learning based fact-checking URL recommender system to mitigate impact of fake news in social media sites such as Twitter and Facebook. In particular, our proposed framework consists of a multi-relational attentive module and a heterogeneous graph attention network to learn complex/semantic relationship between user-URL pairs, user-user pairs, and URL-URL pairs. Extensive experiments on a real-world dataset show that our proposed framework outperforms eight state-of-the-art recommendation models, achieving at least 3~5.3% improvement.

Evaluation ::: RQ4: Hyperparameter Sensitivity	Now, we turn to analyze how our model is sensitive to hyperparameter values, and which hyperparameter value produces the best recommendation result. Recall that we utilize the context information to generate comprehensive embedding of given user and URL. In CSAN, we employ four streams to capture fine-grained context characteristics and share the embedding weight matrix with the target user and target URL representations. In the first experiment, we vary the number of neighbors associated with each steam in CSAN to show how CSAN's performance is changed. Figure FIGREF76 shows that both $HR@10$ and $NDCG@10$ have similar trends, and selecting 10 neighbors at each stream produced the best result. Next, we measure how performance of HGAN is changed when varying the number of HGALs and a size of selected neighbor nodes at each layer. Figure FIGREF77 demonstrates the necessity of employing 2 HGALs, which consistently outperforms the one HGAL. The best performance was achieved when a size of selected neighbor nodes was set to 8.

Proposed Framework ::: Convolutional Spatial Attention Network (CSAN)	The left bounding box in Figure FIGREF16 illustrates the structure of CSAN module. To provide a broad scope of knowledge for generating wide context-aware target user embedding and URL embedding, we adopt a multi-branch setting in CSAN. The two parallel branch models multi-relational context for target user and target URL respectively. Each branch contains two identical streams. We select $b_h$ context neighbors for each stream (e.g., historical context URL neighbors and co-occurrenced context URL neighbors of target URL, social context user neighbors and co-occurenced user neighbors of target user). These streams are employed to learn the most discriminative features from multi-relational neighbors of target user and target URL. Then we employ a gated fusion layer to capture the optimal global level representation of target user-URL pair. Note that we enable the embedding sharing within each branch as users/URLs share the same feature set.

Evaluation ::: Dataset	We evaluate our proposed model on a Twitter dataset obtained from the authors of . The interaction behavior collected in the dataset is consistent with our definition in SECREF3. As they did for their study, we only kept users who have at least three interactions (i.e., posting at least three fact-checking messages containing fact-checking URLs). We conducted additional preprocessing step by removing users whose posts are non-English, or their tweets were inaccessible, because some of our baselines require a fact-checker's tweets. Our final dataset consists of 11,576 users (i.e, fact-checkers), 4,732 fact-checking URLs and 63,429 interactions. The dataset also contains each user's social network information. Note that each user's social relationship is restricted within available users in the dataset. And we further take available feature values of both user and URL into consideration. For instance, a category of referred fact-checking article and the name of corresponding fact-checking website reveals linguistic characteristics such as writing style and topical interest of each URL; while the number of followers and number of followees of each user indicates the credibility and influence of the fact-checker. Statistics of the final dataset is presented in Table TABREF65.

To motivate these fact-checkers further quickly engage with fake news posters and intelligently consume increased volume of fact-checking articles, in this paper we propose a novel personalized fact-checking URL recommender system. According to , co-occurrence matrix within the given context provides information of semantic similarity between two objects. Therefore, in our proposed deep-learning based recommender system, we employ two extended matrices: user-user co-occurrence matrix, and URL-URL co-occurrence matrix to facilitate our recommendation. In addition, users tend to form relationships with like-minded people . Therefore, we incorporate each user's social context to capture the semantic relation to enhance the recommendation performance. Our main contributions are summarized as follows: We propose a new framework for personalized fact-checking URL recommendation, which relies on multi-relational context neighbors. We propose two attention mechanisms which allow for learning deep semantic representation of both a target user and a target URL at different granularity. Experimental results show that our proposed model outperforms eight state-of-the-art baselines, covering various types of recommendation approaches. Ablation study confirm the effectiveness of each component in our proposed framework.

Problem Formulation ::: Example	Figure FIGREF12 illustrates the multi-relational context. In Figure FIGREF12, $c_1$, $c_2$, $c_3$ represents fact-checking URLs and $u_1$, $u_2$, $u_3$ are users who involve sharing these URLs. For example, $(u_1 \rightarrow u_2)$ indicates the social relationship between $u_1$ and $u_2$. Intuitively, we care more about the influence of $u_2$ on $u_1$. $(u_1 \rightarrow c_1 \leftarrow u_2)$ means $u_1$ and $u_2$ are co-occurrenced user neighbors. Similarly, we name $c_1$ and $c_2$ as co-occurrenced URL neighbors of $u_3$, and $c_2$ is historical context URL neighbor given target $u_3$-$c_3$ pair.

Problem Formulation ::: Definition 3 (Multi-relational Context)	Given target user $i$, we define his following fact-checkers and co-occurrenced fact-checkers as his social context user neighbors and co-occurrenced context user neighbors, respectively. Similarly, we name the other URLs posted by target user $i$ and co-occurrenced URLs of target URL $j$ as historical context URL neighbors and co-occurrenced context URL neighbors, respectively. In general, we call all the context neighbors as multi-relational context of given target user-URL pair.

Problem Formulation ::: Definition 2 (Heterogeneous Network) @!START@@!END@	Formally, consider a heterogeneous graph $\mathcal {G}=(\mathcal {V},\mathcal {E})$, where $\mathcal {V} (|V|= m + n)$ and $E$ denote the node set and edge set, respectively. The heterogeneity represents by the node type mapping function: $\phi : \mathcal {V} \rightarrow \mathcal {A}$ and edge type projection function: $\psi : \mathcal {E} \rightarrow \mathcal {R}$, where $\mathcal {A}$ and $\mathcal {R}$ denote the sets of predefined node types and edge types, and $|\mathcal {A}| + |\mathcal {R}| > 2$. Note that we does not consider self-loop in our graph construction.

Problem Formulation ::: Definition 1 (Fact-checking URL Recommendation Task)	Let $\mathcal {U} = \lbrace u_1,u_2,...,u_n\rbrace $ denotes a set of fact-checkers on social media, and use $\mathcal {C} = \lbrace c_1,c_2,...,c_m\rbrace $ to index fact-checking URLs. We construct user-URL interaction matrix $Y = \lbrace y_{ij} | u\in \mathcal {U}, v \in \mathcal {C} \rbrace $ according to users' fact-checking behavior, where each value of 1 for $y_{ij}$ indicates the existence of implicit interaction between target user $i$ and target URL $j$. Each user $u_i$ and each URL $c_j$ associate with a set of attributes. The goal of the recommendation task is to recommend top-N URLs from the URL set $\mathcal {C}$ to each user. We also construct the entire dataset as a heterogeneous graph, which is a special kind of information network that consists of either multiple types of objects or different types of links, or both.

Moreover, we take advantage of advancements in graph neural networks and attention mechanisms, and solve the aforementioned research problems.

Problem Formulation	We formally introduce definitions before describing our proposed framework. We define fact-checking behavior as a user (i.e., fact-checker) embeds a fact-checking URL in his reply in order to debunk fake news. We regard each fact-checking behavior as an implicit interaction between target user $i$ and target URL $j$.

Related Works ::: Graph Convolutional Networks	With the surge of Graph-based Neural Network, GCN-based approaches have shown strong effectiveness on various tasks, , , including recommender system. The core idea is to iteratively aggregate attributed node vectors around each node, and messages propagates by stacking multiple layers. However, the original design of GCN is not suitable for our scenario because of the following reasons: First, existing GCN works ,  do not distinguish different types of nodes, whereas in our case, it does not make sense to aggregate user and URL nodes together. And the aggregation function proposed in most GCN works treats all its adjacency nodes with the same importance. It is inappropriate in real-world applications and probably tends to neglect necessary information.  breaks this schema by using a multi-head attention mechanism to replace the convolution-like operator, yet it requires significant extra computation and memory. Compared to the previous works, in this paper, we focus on a novel application and investigate both co-occurrence context and social context related influences for fact-checking URL recommendation. We also incorporate sets of auxiliary attributes, which enable more comprehensive learning of the compatibility between given pairs of user and URL.

In literature, researchers focused on four topics regarding fake news: characterization (i.e., types of fake news), motivation, circulation, and countermeasures , . A large body of work has been done on fake news identification , , ,  by exploiting multiple content-related and social-related components. However, we notice that the fake news still has been widely spread even after early detection . Therefore, we propose to study a complementary approach to mitigate the spread and impact of fake news. Recently, community and journalists started building and maintaining fact-checking websites (e.g., Snopes.com). Social media users called fact-checkers also started using these fact-checking pages as factual evidences to debunk fake news by replying to fake news posters. Figure FIGREF1 demonstrates a real-world example of a fact-checker's fact-checking behavior on Twitter by debunking another user's false claim with a Snopes page URL as an evidence to support the factual correction. In , researchers found that these fact-checkers actively debunked fake news mostly within one day, and their replies were exposed to hundreds of millions users.

Related Works ::: Fake News and Misinformation	Fake news has attracted considerable attention since it is related to our daily life and has become a serious problem related to multiple areas such as politics  and finance . Social media sites have become one of popular mediums to propagate fake news and misinformation. The dominant line of work in this topic is fake news detection  which was mostly formulated as a binary classification problem. Researchers began to incorporate social context and other features for identifying fake news at an early stage and preventing it from diffusion on the social network , . Some other researchers focus on investigating the propagation patterns of fake news in social network , .  also studied fake news intervention. Unlike most previous works, we follow the direction of  and propose to build a personalized recommender system for promoting the fact-checking article circulation to debunk fake news.

Related Works	In this section, we briefly review related works and position our work within the following areas: (1) fake news and misinformation; (2) advancements in recommender systems; and (3) graph convolutional networks.

Proposed Framework ::: Convolutional Spatial Attention Network (CSAN) ::: Attribute Embedding Layer	We then project them into the same latent space via a set of attribute-specific transformation matrices $W_1, W_2, ..., W_{s+t}$ to project all the attributes into a $w$-dimensional space. The attributes of each neighbor then are stacked as a matrix in shape of $s \times w$ for users and $t \times w$ for URLs. However, we treat the target user-URL pair differently. After projecting attributes by the same attribute-specific transformation matrix as their relational neighbors, instead of stacking them as a matrix, we concatenate the attribute embedding vectors together and feed it through a linear projection to generate $u^{\prime }_i \in \mathbb {R}^d$ and $c^{\prime }_j \in \mathbb {R}^d$ for future reference.

Proposed Framework ::: Convolutional Spatial Attention Network (CSAN) ::: Raw Attribute Input	User and URL associate with different feature sets. Therefore, CSAN starts from embedding the input attribute set of each context neighbor. We use $s$ and $t$ to denote the number of features related to user and URL, respectively. Note that the dimension of initial embedding for each attribute could be different since they may carry with different information volume. We use one-hot encoding for categorical feature inputs, and apply direct lookup on these features. However, the same solution performs poorly when it comes continuous attributes such as the post frequency of an URL. Empirically, we found that an available solution is to bucketize these features into small intervals. Specifically, we map these continuous attributes in range $[0,1), [1,2),..., [2^k, 2^{k+1})$ into $0,1,..., k$ in this work.

Proposed Framework ::: Heterogeneous Graph Attention Network (HGAN) ::: Heterogeneous Graph Network	We try to capture different semantic relation behind various types of nodes and edges. For every single layer, if the central node is user node, its neighborhood contains its co-occurrenced users and posted URLs. If the central node type is URL, its neighborhood nodes consist of users who posted it and its co-occurrenced URLs. We adopt similar embedding approach as we did in CSAN for the initial representation of each node, but we concatenate all the features into a long vector $x_i$ for each node instead of stacking them as a matrix. Considering the different types of the node associated with the varied feature set, we use a set of node type-specific transformation matrices to project different types of node representation into the same feature space before aggregation as follows: Let $H^{(0)} \in \mathbb {R}^{(m+n) \times d}$ be the embedding matrix of all the attributed nodes, where $m+n$ is the total number of nodes and d is the dimension of latent embedding space; each row $h_i^{(0)}$ stands for the initial embedding vector of node $i$.

Proposed Framework ::: Convolutional Spatial Attention Network (CSAN) ::: Spatial Attention Block	To prevent some unknown misalignment and conduct better comparison among the neighborhood features, we proposed a schema for jointly learning the layer-wise and channel-wise attention. In particular, for each stream, we pile the neighbors' representation matrices together to obtain a 3-dimensional tensor $M$. Intuitively, the design helps improve the alignment quality of neighbor's features. Then, inspired by , , we employ a spatial attention block in each stream for jointly learning channel-level and layer-level soft attention. See figure FIGREF21 for a high-level illustration of our spatial attention block. All the streams adopt identical spatial attention blocks, and each block attends the input attribute representations independently. In the figure, we use the historical context URL stream for illustration. The output of spatial attention block is an attention weight map $S \in \mathbb {R}^{t \times w \times b}$ which is in the same shape with the input tensor $M$. Intuitively, the layer-wise attention and channel-wise attention are dedicated to selecting the most discriminative features and the most important neighbors, respectively.

Proposed Framework ::: Heterogeneous Graph Attention Network (HGAN) ::: Heterogeneous Attention Layer (HGAL)	Given the node's initial representation defined as above, we then pass messages to aggregate the neighborhood nodes' information and combine it with the target user's interests. A popular propagation strategy in existing GCN works is the normalized Laplacian matrix . Even though it proves to be effective, it is not trainable and it assigns every adjacent node with the same weight. Following previous work , we propose to incorporate a hierarchical attention mechanism to learn the weight of each adjacent node adaptively. Since the distribution of the number of neighbors of each node disperses greatly, sub-sampling becomes an essential procedure in our task to avoid an explosion of computation cost after multiple hops stacked. We adopt Weighted Random Selection (WRS)  to select a fixed number of nodes for both node types in each graph attention layer. Figure FIGREF40 shows a graphical illustration of one HGAL. Assume that the central node is a user node. We separately calculate the attention weights between the user node and its user node neighbors, or between the user node and its URL node neighbors.

In addition, we vary the number of negative samples, and a size of latent semantic space for the target user and target URL (i.e., an embedding vector size of the target user and target URL). Figure FIGREF78 shows high dimensional latent semantic space produces high performance of AMRAN. 64 dimensional embeddings produced the best results. We also observe that one negative sample would not be enough to produce good results in especially when an embedding vector size is small. The top performance is achieved when one positive instance paired with 3 or 4 negative instances.

Evaluation ::: RQ2: Effectiveness of our submodules	In this experiment, we are interested in measuring effectiveness of our submodules of AMRAN: CSAN and HGAN. Table TABREF71 the experimental result. CSAN achieves 0.642 HR@10 and 0.387 HR@10, whereas HGAN achieves 0.653 HR@10 and 0.403 NDCG@10. Both of the submodules outperform all the baselines in HR@10. HGAN outperforms all the baselines, and CSAN is competitive over the baselines. This experimental result confirms that both CSAN and HGAN positively contributed to the performance of our AMRAN.

We conduct the grid search over a latent dimension size from {8,16,32,64}, a regularization term from {0.1, 0.01, 0.001, 0.0001, 0.00001}, a learning rate from {0.0001, 0.0003, 0.001, 0.01, 0.05, 0.1}, and SPPMI shifted constant value $s$ from {1, 2, 5, 10}. The number of negative samples w.r.t each positive interaction is set to 4. We adopt the same latent dimension size for all sub-modules. For a fair comparison, we also thoroughly optimize the baselines' hyperparameters by using the validation set.

Proposed Framework ::: Training	We adopt the cross-entropy loss function during the training process. We follow a uniform sampling strategy to obtain negative samples $(i,j) \in Y^{-}$ from unobserved interactions. Since the entire architecture is differentiable, we use back propagation to achieve end-to-end training.

Proposed Framework ::: Interaction Layer	The interaction layer is tailored for recommendation tasks. Recall that we obtained wide context-based user embedding $u^{\prime }_i$ and URL embedding $c^{\prime }_j$, context representations $p_i$, $p_j$ and deep context-based user embedding $h^{(l)}_i$ and URL embedding $h^{(l)}_j$ in the previous sections. Then we formulate the final URL-dependent user representation by using a fully connected layer as: where $W_o$ and $b_o$ are a linear transformation weight matrix and bias term, respectively. $\oplus $ denotes vector concatenation. Note that the fully-connected layer can be replaced by other techniques (e.g. CNN). Finally, we feed it through a softmax function to calculate the probability that user interested in the given URL.

$W_g^{(l)}$ and $b_g^{(l-1)}$ are the shared weight matrix and bias term at layer $l$, respectively. The node representation at $l$-th layer provides knowledge of $l$ degrees away.

$TF_{ij}$ further normalizes it by the maximum number of post times of any URL by user $i$. The $IDF_i$ is associated with the user's previous behavior as $m$ denotes the total number of URLs and $m_i$ is the number of URLs posted by user $i$. Formally, the weight of the edge between node $i$ and node $j$ is defined as:

Thus, they are highly complementary to each other in functionality; and we adopt a factorized manner for optimization and computational efficiency as: where $L \in \mathbb {R}^{t \times w \times 1}$ and $C \in \mathbb {R}^{1 \times 1 \times b}$ denote the layer-wise feature map and channel-wise feature map, respectively. $S$ is the result of tensor multiplication.

$|D|$ denotes the total number of observed word-context pairs within a predefined sliding window. $P(i,j)$ is the joint probability that word $i$ and word $j$ appear together within the window size. Furthermore, we introduce the SPPMI matrix as an extension based on PMI value: where $k$ is a hyperparameter, which represents the number of negative samples. Conceptually, a positive PMI value implies a semantically correlated word-context pair, Therefore, SPPMI, which only takes the positive value of PMI shifted by a global constant, reflects a closer semantic relation between word-context pairs. Inspired by this concept/idea, we use $|D|$ to denote the number of times of user (URL) co-occurrence and generate the user co-occurrence matrix in shape of $n \times n$ and URL co-occurrence matrix of $m \times m$. Note that we do not discriminate between the target node and context node. Similarly, we learn from the TF-IDF concept and redefine it on recommendation task with implicit feedback  as: where $\# (i,j)$ represents the number of times URL $j$ be posted by user $i$.

Moreover, we found that URL 2525 appeared in 2nd-degree neighborhood of the user 7849, and was originated from the same website (Snopes.com) with URL 1623.

Proposed Framework ::: Heterogeneous Graph Attention Network (HGAN)	Following recent success in Graph Convolutional Network (GCN) , , , , . We propose a heterogeneous graph attention network (HGAN) which is tailored for recommendation task. In particular, our proposed module adopts a parallel attention structure for the user neighbor and the URL neighbor of the central node, respectively. Considering a heterogeneous graph $\mathcal {G}=(\mathcal {V},\mathcal {E})$, the nodes represent objects in this network which can be either user or URL. The edges denote the relation between connected nodes. The node attributes pass along the edges during the propagation. We try to leverage between the local node attributes and global network structure. Our novelty lies in two aspects: (i) we differentiate the contribution of URL node and user node, respectively; and (ii) we consider both similarities of node and the influence of different relation types. While the CSAN obtains information from multi-relational immediate neighbors, which expand the scope of knowledge for target user and target URL representations, HGAN aims at learning deeper semantic representations of target user and target URL.

Proposed Framework ::: Convolutional Spatial Attention Network (CSAN) ::: Gated Branch Fusion Layer	We apply another CNN layer of $3 \times 3$ filter after the attended user representation of each stream for feature extraction and dimension : which produces the multi-relational context representation vectors: $o_{i_h}, o_{i_c}, o_{u_f}$ and $o_{u_c}$ for each stream, respectively. We employ a gated mechanism to assigns different weights to relation-specific neighborhood representation as: where scalars $g_u$ and $g_v$ are learned automatically to control the importance of the two streams within each branch.

Proposed Framework ::: Convolutional Spatial Attention Network (CSAN) ::: Spatial Attention Block ::: Channel-wise Attention	The design of channel-wise attention is very similar to layer-wise attention, which aims to acquire a global view of discriminative users. Formally, the global average pooling is defined as: where $t$ and $w$ are shared height and width of all channels. Similarly, we employ two convolution layers after the pooling operation. Note that each convolution layer was followed by batch normalization operation. Furthermore, as other work of modern CNN structure , we append a ReLU activation function to assure $L>0, C>0$. We further introduce one more convolution layer of $1 \times 1 \times b$ filter for enhancing the fusion of the layer-wise attention and channel-wise attention. The output tensor then is fed through a sigmoid function for normalization and generate the final attention weight tensor of spatial attention block. Formally, the output of the spatial attention module is the element-wise product of initial feature tensor $M$ and generated attention weights $S$: Intuitively, the attended feature map learned fine-grained important elements via high alignment and compatible attentions.

Proposed Framework ::: Convolutional Spatial Attention Network (CSAN) ::: Spatial Attention Block ::: Layer-wise Attention	Conceptually, the layer-wise attention learns globally important elements in the feature. We apply a cross-channel average pooling operation onto the input tensor, following by 2 convolution layers of $3 \times 3$ and $1 \times 1$ filter, respectively. Specifically, cross-channel average pooling operation is defined as: where $b$ is the number of selected neighbors.

Introduction	While social media sites provide users with the revolutionized communication medium by bringing the communication efficiency to a new level, they can be easily misused for widely spreading misinformation and fake news. Fake news and misinformation have been a long-standing issue for various purposes such as political propaganda  and financial propaganda . To fight against fake news, traditional publishers employed human editors to manually and carefully check the content of news articles to maintain their reputation. However, social media provided a new way to spread news, which lead to broader information sources and expanded audience (i.e., anyone can be a media and create news). In particular, users share news articles with their own opinion or read articles shared by their friends from whatever the source of news is with mostly blind trust  or with their own ideologies , . Although social media posts usually have a very short life cycle, the unprecedented amount of fake news may lead to a catastrophic impact on both individuals and society. Besides from misleading users with false information , widely propagated fake news could even cause trust crisis of entire news ecosystem , even further affecting both the cyberspace and physical space.

Question: What is the model accuracy?
Answer: Overall, our AMRAN outperforms all baselines, achieving 0.657 HR@10 and 0.410 NDCG@10.