2021_SIGIR_Social Recommendation with Implicit Social Influence

[论文阅读笔记]2021_SIGIR_Social Recommendation with Implicit Social Influence

论文下载地址： https://doi.org/10.1145/3404835.3463043
发表期刊：SIGIR
Publish time: 2021
作者及单位:

• Changhao Song12, Bo Wang12, Qinxue Jiang3, Yehua Zhang1, Ruifang He12, Yuexian Hou1
  1College of Intelligence and Computing, Tianjin University, Tianjin, China
  2State Key Laboratory of Communication Content Cognition, People’s Daily Online, Beijing, China
  3School of Engineering, Newcastle University, Newcastle, UK

数据集：

• Yelp:用户可以在那里交朋友并对餐馆评分 http://www.yelp.com/

代码：

其他人写的文章

• Social Recommendation with Implicit Social Influence(几乎翻译了全文)

简要概括创新点：

• 本文提出了 DiffNetLG (Diffusion neural Network with Local and Global implicit influence) 其实就是DiffNet和DiffNet++的改进版本，命名也沿用了这个命名序列
  • a model that unifies the modeling of explicit and implicit social influence for social recommendation. (这个模型统一了显性和隐性社交影响来建模社交推荐)
  • The model combines the social network and interest network. (该模型结合了社交网络和兴趣网络)
  • In combined network, local implicit influence is involved by predicting the unobserved social relationship, (在组合网络中，局部隐性影响是通过预测未观察到的社交 关系来实现的)
  • and global implicit influence is modeled by defining the global popularity of each item. (全局隐性影响是通过定义每个项目的全局流行度来建模的)
  • Finally, on combined network, explicit influence and two implicit social influences are jointly modeled with a graph convolution network and achieve improved embedding representations of users and items for social recommendation. (最后，在组合网络上，将显式影响和两种隐式社交影响联合建模在图卷积网络上，实现改进了用户和项目的嵌入表示)

Abstract

• (1) Social influence is essential to social recommendation. Current influence-based social recommendation focuses on the explicit influence on observed social links. (社交影响对社交推荐至关重要。目前基于影响的社交推荐关注在对观察到的社交联系的显式影响)
• (2) However, in real cases, implicit social influence can also impact users’ preference in an unobserved way. (然而，在实际情况下，隐性的社交影响也会以一种未被观察到的方式影响用户的偏好)
• (3) In this work, we concern two kinds of implicit influence: Local Implicit Influence of persons on unobserved interpersonal relations, and Global Implicit Influence of items broadcasted to users. We improve the state-of-the-art GNN-based social recommendation methods by modeling two kinds of implicit influences separately. (在这项工作中，我们关注两种隐性影响：未观察到的人际关系的局部隐性影响，以及项目传播给用户的全局隐性影响。我们通过分别建模两种隐性影响，改进了最先进的基于GNN的社交推荐方法)
  • Local implicit influence is involved by predicting unobserved social relationships. (局部隐性影响是通过预测未观察到的社交关系来实现的)
  • Global implicit influence is involved by defining global popularity of each item and personalize the impact of the popularity on each user. (全局隐性影响是通过定义每个项目的全局受欢迎程度和个性化项目对每个用户的受欢迎程度影响来实现的)
  • In a GCN network, explicit and implicit influence are integrated to learn the social embedding of users and items in social recommendation. (在GCN网络中，整合显式和隐式影响，学习用户和项目在社交推荐中的社交嵌入)
  • Experimental results on Yelp initially demonstrate the effectiveness of proposed model. (在Yelp上的实验结果初步证明了该模型的有效性)

CCS CONCEPTS

Information systems → Recommender systems.

KEYWORDS

• Social recommendation;
• graph neural network;
• implicit influence

1 INTRODUCTION

• (1) Social recommendation utilizes the social resources, e.g. interpersonal relations and influence, as extra information to improve the performance of recommendation [4, 8, 19]. (社交推荐利用社交资源，如人际关系和影响，作为额外的信息来提高推荐的表现)

• (2) Social theory of homogenization supposes that people with social connections will influence each other, leading to similar interests [1, 2, 11]. This theory inspires the research of influence-based social recommendation. (社会同质化理论认为，有社会联系的人会相互影响，导致相似的兴趣。这个理论引起了基于影响的社交推荐的研究)

  • In this direction, social recommendation systems use users’ social matrix as side information to enhance each user’s embedding learning , or to standardize the user’s embedding learning by social neighbors [5, 7, 8, 15]. (在这个方向上，社交推荐系统使用用户的社交矩阵作为附信息来增强每个用户的嵌入学习，或者通过社交邻居来标准化用户的嵌入学习)
  • These approaches consider the influence of first-order neighbors of each user, which alleviates the data sparseness problem of collaborative filtering model. (这些方法考虑了每个用户的一阶邻居的影响，缓解了协同过滤模型的数据稀疏性问题)

• (3) However, in social network, users can be affected not only by first-order neighbors, but also by higher-order neighbors. (然而，在社交网络中，用户不仅会受到一阶邻居的影响，还会受到高阶邻居的影响)

• (4) Recently, influence of high-order neighbors are studied [22, 23]. (近年来，人们研究了高阶邻居的影响 high-order高阶邻居(高阶关系)2020年，2021年论文的聚焦点 )

  • For example, DiffNet[23] proposes a diffusion network model with hierarchical influence propagation to simulate the high-order recursive social diffusion in social recommendation. (例如，DiffNet提出了一种具有分层影响传播的扩散网络模型来模拟社交推荐中的高阶递归社交扩散)
  • DiffNet++[22] improves the DiffNet by connecting user-user social network and user-item interest network according to common users. (DiffNet++通过根据连接用户社交网络和用户-项目兴趣网络来改进DiffNet)
  • In this way, higher-order social influence and interest diffusion can be jointly modeled and further improve the performance of recommendation. (这样，就可以联合建模更高阶的社交影响和兴趣扩散，并进一步提高推荐的性能)

• (5) Given an observed social network, current social recommendation methods have modeled the high-order explicit influence between users, but ignore the implicit influence. (给定一个观察到的社交网络，目前的社会推荐方法已经模拟了用户之间的高阶显式影响，但忽略了隐式影响)

• (6) Recent works propose models of implicit influence [12, 25, 27], different from which,

  • We define implicit influence as the influence whose diffusion route is not observed in given social network. (我们将隐式影响定义为在给定的社交网络中没有观察到扩散路径的影响)
  • Furthermore, we distinguish two kinds of implicit influence: local implicit influence and global implicit influence. (此外，我们区分了两种隐性影响：局部隐性影响和全局隐性影响)
  • Local implicit influence occurs between two people with unobserved social relationship. (局部隐性影响发生在两个未被观察到的社交关系的人之间)
    • For example, they have unknown offline relationship instead of observable online connection, or they are friends in a social media not involved in current data. (例如，他们有未知的离线关系，而不是观察到的在线联系，或者他们是不包含在当前数据的社交媒体上的朋友)
  • Global implicit influence is broadcasted social influence without depending on interpersonal relationship. (全局隐式影响是通过不依赖于人际关系而传播社交影响的)
    • For example, the influence of popular items appear in media advertising. (例如，流行物品的影响发生在媒体广告中)

• (7) In this paper, we propose DiffNetLG (Diffusion neural Network with Local and Global implicit influence) 其实就是DiffNet和DiffNet++的改进版本，命名也沿用了这个命名序列 :

  • a model that unifies the modeling of explicit and implicit social influence for social recommendation. (这个模型统一了显性和隐性社交影响来建模社交推荐)
  • The model combines the social network and interest network. (该模型结合了社交网络和兴趣网络)
  • In combined network, local implicit influence is involved by predicting the unobserved social relationship, (在组合网络中，局部隐性影响是通过预测未观察到的社交 关系来实现的)
  • and global implicit influence is modeled by defining the global popularity of each item. (全局隐性影响是通过定义每个项目的全局流行度来建模的)
  • Finally, on combined network, explicit influence and two implicit social influences are jointly modeled with a graph convolution network and achieve improved embedding representations of users and items for social recommendation. (最后，在组合网络上，将显式影响和两种隐式社交影响联合建模在图卷积网络上，实现改进了用户和项目的嵌入表示)

• (8) In summary, our major contributions are as follows:

  • (1) We propose to model implicit social influence in social recommendation. Local and global implicit social influence are defined and modeled respectively without the need for extra information in addition to observed social network. (我们提出在社交推荐中建模隐性的社交影响。局部和全局隐性社交影响分别被定义及建模，除了观察到的社交网络外，不需要额外的信息。)
  • (2) Improving state-of-the-art graph convolution network models of social recommendation, we design an unified model connecting social network and interest network, in which implicit and explicit influence are integrated to learn the embedding of users and items. (改进了最先进的社交推荐图卷积网络模型，设计了一个连接社交网络和兴趣网络的统一模型，其中集成隐性和显性影响来学习用户和项目的嵌入)
  • (3) Extensive experimental results on a real dataset demonstrate the effectiveness of proposed model. There are more than 4% on HR metric and 6% on NDCG metric improvements on the Top-10 recommendation compared to the best-performing baselines. (在真实数据集上的大量实验结果证明了所提模型的有效性。与表现最好的基线相比，在Top-10推荐上，HR指标提高了超过4%，NDCG指标提高了6%)

2 RELATED WORK

• (1) Social influence is essential to the research of social recommendation [4, 8, 15, 29]. According to the social impact theory, when
  information spreads in social networks, users in the network will be affected by their social relations, leading to similar preferences
  among social neighbors [1,2,6,16]. (社交影响对社会推荐的研究至关重要，根据社交影响理论，当信息在社交网络中传播时，网络中的用户就会受到社交关系的影响，导致社交邻居之间产生相似的偏好)

• (2) In early studies, social influence is often represented by social regularization in social recommendation [7, 15]. (在早期的研究中，社交影响往往以社会推荐中的社交正规化为代表。)

  • For example, TrustSVD [5] takes social neighbors’ preference as auxiliary feedback on current users, and adds the trust influence of social neighbors on the basis of SVD++[10] model. (TrustSVD将社交邻居的偏好作为对当前用户的辅助反馈，并在SVD++模型的基础上增加了社交邻居的信任影响)
  • Similarly, SR[14] learns users’ social matrix by introducing factor vectors, (SR通过引入因子向量来学习用户的社交矩阵)
  • SocialMF[7] believes that users’ representations are influenced by their friends, (SocialMF认为用户的表示受朋友的影响)
  • and STE[13] combines users’ personal interests with that of their friends. (STE结合用户的个人兴趣与朋友的兴趣)

• (3) Besides regularization, social influence of neighbors can also be represented in social embedding of users and items, especially using graph neural networks. （除了正则化外，邻居的社交影响也可以在用户和项目的社交嵌入中表示，特别是使用图神经网络）

  • For example, GCN[9] based methods [20, 21, 26, 28] are proved to be more effective than regularization. (例如，基于GCN的方法被证明比正则化更有效)
  • Among these methods, earlier studies focus on modeling influence of first-order neighbors, e.g., GraphRec[3]. (在这些方法中，早期的研究集中在一阶邻居的建模影响上，如GraphRec)
  • Recent works explore higher-order influence, e.g., (2020年，2021年，前沿就是high-order高阶关系+超图。本文就是顺着这个前沿往前探索) (最近的研究探索了高阶影响)
    • PinSage[26] learns nodes embedding by combining random walk and graph convolution, (PinSage通过结合随机游走和图卷积来学习节点嵌入)
    • NGCF[21] determines the association between message propagation and the central node, and (NGCF确定了消息传播与中心节点之间的关联)
    • DiffNet[23] simulates user preferences based on user social relationships and historical behavior. (iffNet根据用户的社交关系和历史行为模拟用户偏好)

• (4) Besides explicit influence, different implicit influence is also studied. (除了显式影响外，还研究了不同的隐式影响) 阐述隐式影响的发展历程。本文的创新就是在前人 DiffNet的基础上，author加上了自己的implict influence，而implicit influence也是站在前人的肩膀上继续推进而来的

  • [12] introduces implicit influence in social regularization. (在社交正规化中引入了隐式影响)
  • SoInp[25] models the implicit influence from the perspective of information propagation which is inferred from ratings on the same items. (SoInp从信息传播的角度建模其中的隐式影响，这是从对同一项目的评分中推断出来的)
  • [27] captures the implicit users through meta-path based embedding in heterogeneous network. (通过在异构网络中元路径的嵌入来捕获隐式用户)

• (5) Although GNN-based social recommendation has well modeled the explicit social influence, the implicit influence on unobserved social links is still an open problem. In this work, we improve the state-of-the-art GNN-based social recommendation by modeling implicit social influence from both local and global perspectives (虽然基于GNN的社交推荐已经很好地模拟了显式的社交影响，但对未观察到的社交联系的隐性影响仍然是一个问题。在这项工作中，我们通过从局部和全局的角度建模隐式的社交影响，改进了最先进的基于GNN的社交推荐。)

3 METHODOLOGY

3.1 Problem Statement and overall framework

• (1) In social recommendation, we have users set $U(|U|=M)$ and items set $V(|V|=N)$
• (2) The social network of users is defined as a directed graph $G_S=<U,S>$,
  • where $S\in {\mathcal{R}}^{M\times M}$ is a matrix representing social relations between users
• (3) The user interest network is defined as an undirected bipartite graph $G_I=<U\cup V,R>$,
  • where $R\in {\mathcal{R}}^{M\times M}$ is a matrix representing users’ real-valued preferences to items
• (4) In addition, each user $a$ is associated with a real-valued attribute vector, denoted as $x_a$ in an user attribute matrix $X\in {\mathcal{R}}^{d_1\times M}$
• (5) Each item $i$ is also associated with an attribute vector $y_i$ in item attribute matrix $Y\in {\mathcal{R}}^{d_2\times N}$
• (6) The task of social recommendation in this work is to predict users’ unknown real-valued preferences to items in $R\in {\mathcal{R}}^{M\times N}$ according to given $G_S,G_I,X$ and $Y$

• (7) We propose DiffNetLG model as shown in Fig.1.
• DiffNetLG has three parts:

  • the fusion layer, (融合层)

  • the social and interest influence diffusion layers (社交和兴趣影响扩散层) and

  • the rating predicting layer. (评分预测层)
    (1)融合层

  • By taking inputs, the fusion layer fuses features and free embeddings of users and items. (通过获取输入，融合层融合了用户和项目的特征和自由嵌入向量)
    (2)社交和兴趣影响扩散层

  • In the social and interest influence diffusion layers, we use GCN to jointly model explicit and implicit influence. (在社交和兴趣影响扩散层中，我们使用GCN来联合建模显式和隐式影响)

    • Explicit influence is modeled by observed links in social and interest networks. (显性影响是通过在社交和兴趣网络中观察到的链接来建模的)
    • For implicit influence, we model local implicit influence by predicting unobserved user-user social links which are added as observed links for the next iteration in GCN learning, (对于隐式影响，我们通过预测未观察到的用户与用户之间的社交联系来建模局部隐性影响，这些联系在GCN学习的下一次迭代中被添加为观察到的联系)
    • we model global implicit influence by calculating the popularity of each item on all users and combine it with items’ explicit influence on users. (我们通过计算每个项目对所有用户的流行程度来建模全局隐式影响，并将其与项目对用户的显式影响相结合)

    (2)融合层

  • Finally, with trained embedding of users of items, the rating predicting layer predicts the preference score of each unobserved user-item pair. (最后，通过训练项目的用户嵌入，评分预测层预测每个未观察到的用户-项目对的偏好得分)

3.2 Explicit Influence Modeling

• (1) In DiffNetLG, observed links in social and interest network are modeled with the edges in a graph convolution network. The explicit influence diffusion on observed links are modeled with iterative representation learning of user and item embedding in the graph. (在DiffNetLG中，社交和兴趣网络中观察到的链接用图卷积网络中的边来建模。对观察到的显性影响进行扩散是通过对用户和项目在图中嵌入的迭代表示学习来建模的。)

• (2) In initial step of learning, for each user $a$, a free embedding vector $p_a$ and the relevant feature vector $x_a$ are fused. (在学习的初始阶段，对于每个用户$a$，融合一个自由嵌入向量$p_a$和相关的特征向量$x_a$)

  • The fused vector $u_a^0$ is taken as the initial vector of $a$. (以融合向量$u_a^0$作为$a$的初始向量)
  • Similarly, for each item $i$, the free embedding vector $q_i$ and the relevant feature vector $y_i$ are fused to be the initial vector $v_i^0$. (同样，对于每一个项目，将自由嵌入向量 $q_i$和相关的特征向量 $y_i$ 融合为初始向量$v_i^0$）

• (3) By inputting initial potential vectors of users and items, hierarchical convolution modeling is recursively performed for the dynamic propagation of users’ and items’ potential preferences in the network. (通过输入用户和项目的初始潜在向量，递归地对用户和项目的潜在偏好在网络中的动态传播进行分层卷积建模)

• (4) We learn the embedding of each review word and get the feature vector of each user/item by averaging learned word vectors of the user/item. (我们学习每个评论词的嵌入，并通过平均用户/项目的学习词向量，得到每个用户/项目的特征向量)

• (5) This iteration step starts at $k=0$ and ends when the recursion reaches a predefined depth $K$. In our model, for best effect, we set $K=2$ (此迭代步骤从=0开始，当递归达到预定义的深度层时结束。在我们的模型中，为了达到最佳效果，我们设置了=2。)

• (6) For each item $i$, given its $k$-th layer embedding $v_i^k$, its update embedding for the $(k+1)$-th layer can be modeled as: (对于每个项目，给定其第层嵌入$v_i^k$ ，其对（+1）层的更新嵌入可以建模为：
  

  • where $u_a^k$ is the $k$-th layer embedding vector of user $a$, (其中$u_a^k$是用户的第层嵌入向量)

  • ${\eta }_{ia}^{k+1}$ represents the aggregated weights where $R_i$ is the set of users have rated item $i$. We use an average pooling that performs a mean operation of all interacted users’ latent embedding at the $k$-th layer. (${\eta }_{ia}^{k+1}$表示聚合权重, 其中$R_i$是对项目有评分的用户集。我们使用一个平均池化，它对所有的交互用户在第层的潜在嵌入执行一个平均操作)

• (7) For each user $a$, $u_a^k$represents his/her $k$-th potential embedding.

  • The $k+1$-th update embedding of users are influenced by two aspects:
    • social network influence and
    • interest network influence.
  • Let ${\tilde{p}}_a^{k+1}$ represents the explicit influence of neighbor users on the $(k+1)$-th layer,
  • ${\tilde{p}}_{a-E}^{k+1}$ represents the explicit influence of neighbor items on the $(k+1)$-th layer.
  • Explicit influences are modeled as:
    
    • where ${\alpha }_{ab}^{k+1}$ represents the influence weight of user $b$ on user $a$ at the $(k+1)$-th layer in social network,
    • ${\beta }_{ai}^{k+1}$ represents the influence weight of item $i$ on user $a$ at the $(k+1)$-th layer in interest network.
    • $S_a$ and $R_a$i s the users set and items set that rated and followed by user $a$, respectively.
    • Like ${\eta }_{ia}^{k+1}$, ${\alpha }_{ab}^{k+1}$ and ${\beta }_{ai}^{k+1}$ use an average pooling to aggregate the influence of users and items on $a$.

3.3 Implicit Influence Modeling

In this work, local and global implicit influence are separately modeled and integrated into the embedding learning of users and items. (在本工作中，局部和全局隐式影响分别被建模和集成到用户和项目的嵌入学习中。)

3.3.1 Local Implicit Influence.

• (1) Local implicit influence occurs on unobserved interpersonal links. (局部隐式影响发生在未被观察到的人际联系上)

  • To involve implicit influence in DiffNetLG, we adopt the techniques of link prediction to predict unobserved interpersonal links. (为了在DiffNetLG中包含隐式影响，我们采用链接预测技术来预测未观察到的人际联系)
  • It is noted that, in a network, the performance of nodes embedding learning and that of link prediction are closely depending on each other. (值得注意的是，在网络中，节点嵌入学习和链路预测的性能是密切依赖的)
  • Therefore, in our GCN learning, the predicted interpersonal links on $K$-th layer are added to next training process as observed links, so that the learning of nodes embedding and link prediction can benefit each other.(因此，在我们的GCN学习中，将层预测的人际链接作为观察链接添加到下一个训练过程中，使节点嵌入学习和链接预测相互受益)

• (2) In our algorithm, the probability of unobserved links are measured by the similarity between the embedding vectors of a pair of user nodes. (在我们的算法中，未被观察到的链接出现的可能性那个是通过一对用户节点的嵌入向量之间的相似性来衡量的)

  • Specifically, we measure the similarity between the embedding vectors into the proximity of two vectors in Euclidean space. (具体地说，我们测量了在欧几里得空间中嵌入向量接近的两个向量之间的相似性 相似性度量的选取，很重要 )
  • For example, the probability of existing an unobserved link between two unconnected users $u_i$ and $u_j$ in social network is:
    
    • where, $u_i^K$, $u_j^K\in {\mathcal{R}}^D$ is the ($K$-th) embedding vector of node $u_i$ and $u_j$, and $D$ is the dimension of the vectors. We set a threshold (0.9) of calculated probability to identify unobserved links.

3.3.2 Global Implicit Influence.

• (1) Global implicit influence is assumed as broadcasted influence of each item to all users. (全局隐式影响被假设为每个项目对所有用户的传播影响)

• (2) In this work, global implicit influence of each item is calculated as a popularity value, which is updated in each iteration of GCN learning and concatenated with item embedding. (在本工作中，每个项目的全局隐式影响被作为一个受欢迎程度值被计算，它在GCN学习的每次迭代中进行更新，并与项目嵌入连接起来)

• (3) The popularity $po{p}_i$ of an item $i$ is quantified by a smoothed ratio of linked users of $i$ to the linked users of all items:$po{p}_i=(|R_i|+1)/({\sum }_{j\in V}|R_j|+|V|)$, (项目的受欢迎程度 通过的链接用户与所有项目的链接用户的平滑比例 来量化)

  • where $R_i$ is the set of the users linked to $i$ and
  • $V$ is the set of all items.

• (4) In order to personalize the global implicit influence of item $i$ to each user, cosine similarity between the embedding of $i$ and each user is calculated after influence iteration of each layer. (为了个性化项目对每个用户的全局隐式影响，在每一层的影响迭代后，计算的嵌入与每个用户之间的余弦相似性)

  • Therefore, the global implicit influence weight of item $i$ to user $a$ on $(k+1)$-th layer is : ${\tau }_{ai}^{k+1}=po{p}_i\times cos(u_a^k,v_i^k)$
  • Then the implicit influence of items on $a$ on $(k+1)$-th layer can be formalized as:
    

• (5) For each user, the explicit influence in Eq.(2) and the global implicit influence in Eq.(4) are combined with a trade-off parameter $\tilde{\lambda }$,

  • and the aggregated influence of user $a$’s neighbor items on $(k+1)$-th layer can finally be modeled as: (用户的邻居项目对第(+1）层的聚合影响最终可以建模为：)
    

3.4 Fusion Approach and Model Training

• (1) In GCN training, given the $k$-th layer embedding $v_i^k$ of an item $i$, the update embedding $v_i^{k+1}+$ of the $(k+1)$-th layer is: $v_i^{k+1}={\tilde{v}}_i^{k+1}+v_i^k$,

  • where ${\tilde{v}}_i^{k+1}$ aggregates neighbor users’ embedding by Eq.(1) (通过公式(1)聚合邻居用户的嵌入)

• (2) Given $k$-th layer embedding $u_a^k$ of an user $a$, the update embed-ding $u_a^{k+1}$ of the $(k+1)$-th layer is influenced by both social and interest network: $u_a^{k+1}=u_a^k+{\tilde{p}}_a^{k+1}+{\tilde{q}}_a^{k+1}$ (给定用户的第层嵌入$u_a^k$,（+1层的更新嵌入同时受到社交和兴趣网络的影响

  • where ${\tilde{p}}_a^{k+1}$ aggregates influence of $a$’s neighbor users’ by Eq.(2).
  • ${\tilde{q}}_a^{k+1}$ aggregates influence of items on $a$ by Eq.(5).

• (3) After the iterative diffusion process with $K$ times, we obtain the embedding set of $u$ and $i$ with $u_a^k$ and $v_i^k$ for $k=[0,1,2...,K]$. (经过次的迭代扩散过程，我们得到了在$k=[0,1,2...,K]$时，和的嵌入集$u_a^k$ and $v_i^k$)

  • Then, for each user $a$, the final embedding is denoted as $u_a^f=[u_a^0\parallel u_a^1\parallel ...\parallel u_a^K]$ that concatenates each layer’s embedding. (对于每个用户，最终的嵌入表示为, (连接每一层的嵌入))
  • Similarly, each item $i$’s final embedding is: $v_i^f=[v_i^0\parallel v_i^1\parallel ...\parallel v_i^K]$ (同样，每个项目的最终嵌入是)
  • After that, the predicted rating is modeled as the inner product between the final user and item embeddings: ${\hat{r}}_{ai}={(u_a^f)}^T{v}_i^f$. (然后，预测的评分被建模为最终用户和项目嵌入之间的内积)

• (4) With learned embedding of users and items, a pair-wise ranking based loss function is used to optimize social recommendation: (通过学习用户和项目的嵌入，使用基于成对排名的损失函数来优化社交推荐)
  

  • where $R^{+}$ is the set of positive samples (observed user-item pairs)(正样本集（观察到的用户项目对),
  • and $R^{-}$ is the set of negative samples (unobserved user- item pairs that randomly sampled from $R$). (负样本集(从R中随机抽样的未观察到的用户项目对)
  • $\sigma (x)$ is sigmoid function, $\theta =[{\Theta }_1,{\Theta }_2]$.
    • with ${\Theta }_1=[P,Q]$,
    • and the parameter set in the fusion layer, i.e, ${\Theta }_2=[F,{[W^K]}_{k=0}^{K-1}]$,
    • $\lambda$ is a regularization parameter that controls the complexity of user and item free embedding matrices. (是一个正则化参数，它控制用户和项目自由嵌入矩阵的复杂性。)
    • All the parameters in the above loss function are differentiable. (上述损失函数中的所有参数都是可微的)

4 EXPERIMENTS

4.1 Dataset

We conducted experiments on widely used Yelp1dataset, where users make friends and review restaurants. We randomly select 10%, 10% and 80% of the data for testing, validation and training, respectively. The count of users, items, links and ratings is 17K, 38K, 143K, 204K, respectively. The link density is 0.048%. (我们在广泛使用的Yelp数据集上进行了实验，用户可以在那里交朋友并对餐馆评分。我们分别随机选择10%、10%和80%的数据用于测试、验证和训练。用户、项目、链接和评分数分别为17K、38K、143K、204K。链路密度为0.048%。)

4.2 Baselines.

• (1) We compared our model with three sets of baselines, including
  • classical CF models (BPR[18], FM[17]) without social information,
  • social recommendation models (SocialMF[7], TrustSVD[4], ContextMF[8], CNSR[24]) modeling first-order social influence
  • and the state-of-the-art GNN-based social recommendation models (GraphRec[3], PinSage[26], NGCF[21], DiffNet[23], DiffNet++[22]) modeling high-order social influence.

(我们将我们的模型与三组基线进行了比较，包括没有社交信息的经典CF模型(BPR[18]，FM[17])、社交推荐模型(社会MF[7]、TrustSVD[4]、上下文MF[8]，CNSR[24])建模一阶社交影响和最先进的基于GNN的社交推荐模型(SocialMF[3]，PinSage[26]，NGCF[21]，DiffNet[23]，DiffNet++[22])建模高阶社交影响。

• (2) For our proposed model, besides the main DiffNetLG model involving both local and global influence, we also investigate the
  performance of two variants named DiffNetL and DiffNetG, which only involves local and global implicit, respectively. (对于我们提出的模型，除了局部和全局影响的主要DiffNetLG模型外，我们还研究了两个变体DiffNetL和DiffNetG的性能，它们分别只涉及局部和全局隐式)

4.3 Evaluation Metrics. Recommending Top-N items for each user,

• (1) we used two popular ranking based metrics:
  • Hit Ratio (HR) (点击率)
  • and Normalized Discounted Cumulative Gain (NDCG). (标准化折扣累积增益(NDCG))
  • HR measures the percentage of hit items in Top-N list and (HR衡量的是前N项列表中点击项目的百分比)
  • NDCG puts more emphasis on top ranked items. (NDCG更强调排名靠前的项目)
• (2)We ranked all the items to calculate the values of metrics and randomly selected 1,000 unrated items that a user has not interacted with as negative samples of this user. (我们对所有项目进行排序以计算指标值，并随机选择1000个用户未交互的未评级项目作为该用户的负样本)
• (3) We mixed these pseudo negative samples and corresponding positive samples (in the test set) to select Top-N candidate items. (我们将这些负样本和相应的正样本（在测试集中）混合，以选择Top-N个候选项目)
• (4)We repeated this procedure 10 times and report the average ranking results. (我们重复这个过程10次，并报告平均排名结果。)

4.4 Results.

• (1) Recommendation results are shown in Table 1 and Table 2 with various embedding size $D$ and Top-N values, respectively. In the results, BPR and FM only use observed user-item rating matrix and mostly suffers from data sparsity. SocialMF, TrustSVD, ContextMF and CNSR mitigate this problem by using first-order neighbor users as auxiliary information. GraphRec achieves further improvement by combining interest neighbors. Beyond first-order influence, GCN-based PinSage, NGCF and Diffnet show advantage of modeling higher-order user-item graph or social structure. Latest DiffNet++ integrates the higher-order user-item graph and social structure and achieves the state-of-the-art performance. (结果表明，BPR和FM只使用观察到的用户项目评分矩阵，数据稀疏性较大。SocialMF、TrustSVD、ContextMF和CNSR通过使用一阶邻居用户作为辅助信息来缓解这个问题。GraphRec通过结合兴趣邻居实现了进一步的改进。除了一阶影响外，基于GCN的PinSage、NGCF和Diffnet还显示出建模高阶用户项目图或社交结构的优势。最新的DiffNet++集成了高阶用户项目图和社交结构，实现了最先进的性能)

• (2) Introducing implicit influence into Diffnet, our models exceed all baselines in most cases, which verifies the general advantage
  of modeling implicit influence. Furthermore, DiffNetLG with both local and global implicit influence exceeds DiffNetL and DiffNetG
  involving only one implicit influence, which demonstrates the necessary of modeling both implicit influence. In addition, compared
  with Diffnet++ using attention mechanism, DiffNetLG has higher convergence speed and less time cost. (在Diffnet中引入隐式影响，我们的模型在大多数情况下超过了所有基线，这验证了建模隐式影响的优势。此外，具有局部和全局隐影响的DiffNetLG超过了只涉及一个隐式影响的DiffNetL和DiffNetG，这表明了两种隐影响建模的必要性。此外，与使用注意力机制的Diffnet++相比，DiffNetLG具有更高的收敛速度和更短的时间。

5 CONCLUSIONS

• (1) For social recommendation, we propose to model two kinds of implicit influence on users’ preference, besides explicit social influence. (对于社交推荐，我们提出除了显式的社交影响外，还有两种对用户偏好的隐式影响进行建模)
• (2) The local implicit influence is modeled by predicting unobserved links (局部隐式影响通过预测未观察到的链接来建模)
  • and global implicit influence is modeled by personalized popularity of items. (全局隐式影响通过对项目的个性化流行度来建模)
• (3) Explicit and implicit influence are recursively updated through an unified GCN network and achieve optimized social embedding of users and items. (显式和隐式影响通过统一的GCN网络进行递归更新，来优化用户和项目的社交嵌入)
• (4) In initial experimental results on Yelp, the proposed model exceeds the state-of-the-art baselines.

ACKNOWLEDGMENTS

REFERENCES