2019_WWW_Graph Neural Networks for Social Recommendation

[论文阅读笔记]2019_WWW_Graph Neural Networks for Social Recommendation

论文下载地址： https://doi.org/10.1145/3308558.3313488
发表期刊：WWW
Publish time: 2019
作者及单位:

• Wenqi Fan Department of Computer Science City University of Hong Kong [email protected]
• Yao Ma Data Science and Engineering Lab Michigan State University [email protected]
• Qing Li Department of Computing The Hong Kong Polytechnic University [email protected]
• Yuan He JD.com [email protected]
• Eric Zhao JD.com [email protected]
• Jiliang Tang Data Science and Engineering Lab Michigan State University [email protected]
• Dawei Yin JD.com [email protected]

数据集： 正文中的介绍

• Ciao http://www.ciao.co.uk
• Epioions http://www.cse.msu.edu/∼tangjili/index.html
  www.epinions.com
  代码：
• https://github.com/wenqifan03/GraphRec-WWW19 （文中作者给的）

其他：

其他人写的文章

• Graph Neural Networks for Social Recommendation 论文解读

简要概括创新点：

• (1) we present a novel graph neural network framework (GraphRec) for social recommendations. (我们提出了一种新的用于社会推荐的图神经网络框架 (GraphRec) 。)
• (2)In particular, we provide a principled approach to jointly capture interactions and opinions in the user-item graph and propose the framework GraphRec, which coherently models two graphs and heterogeneous strengths. (特别是，我们提供了一种原则性的方法来联合捕获用户项图中的交互 和 观点，并提出了框架GraphRec，该框架对 两个图 和 异构力量(强度) 进行了一致建模。)
• (3)User-Modeling we first use two types of aggregation to learn factors from two graphs, as shown in the left part in Figure 2. (我们首先使用两种类型的聚合来从两个图中学习因子，如图2左侧所示。)
  • The first aggregation, denoted as item aggregation, is utilized to learn item-space user latent factor $h_i^I\in R^d$ from the user-item graph. (第一个聚合表示为项目聚合，用于从用户项目图中学习项目空间用户潜在因子$h_i^I\in R^d$)
  • The second aggregation is social aggregation where social-space user latent factor $h_i^S\in R^d$ is learned from the social graph. (第二种聚合是社会聚合，其中社会空间用户潜在因子 $h_i^S\in R^d$是从社交图中学习)
    • 加了注意力机制—we perform an attention mechanism with a two-layer neural network to extract these users that are important to influence $u_i$
  • Then, these two factors are combined together to form the final user latent factors $h_i$. (然后，这两个因素结合在一起，形成最终的用户潜在因素)
• (4) Item-Modeling Therefore, interactions and opinions in the user-item graph should be jointly captured to further learn item latent factors. (因此，应该共同捕获用户项目图中的交互和意见，以进一步了解项目潜在因素。)
  • 加了注意力机制---- In addition, we introduce an attention mechanism to differentiate the importance weight ${\mu }_{jt}$ of users with a two-layer neural attention network, taking $f_{jt}$ and $q_j$ as the input,

ABSTRACT

• (1) In recent years, Graph Neural Networks (GNNs), which can naturally integrate node information and topological structure, have been demonstrated to be powerful in learning on graph data. These advantages of GNNs provide great potential to advance social recommendation since data in social recommender systems can be represented as user-user social graph and user-item graph; and learning latent factors of users and items is the key. (近年来，图形神经网络（GNNs）在图形数据的学习中表现出了强大的能力，它可以自然地集成节点信息和拓扑结构。由于社交推荐系统中的数据可以表示为用户-用户-社交图和用户-项目图，GNNs的这些优点为推进社交推荐提供了巨大的潜力；而了解用户和项目的潜在因素是关键。)
• (2) However, building social recommender systems based on GNNs faces challenges. For example, (然而，构建基于GNNs的社会推荐系统面临着挑战。例如)
  • the user-item graph encodes both interactions and their associated opinions; (用户项目图对交互及其相关意见进行编码；)
  • social relations have heterogeneous strengths; (社会关系具有异质性优势；)
  • users involve in two graphs (e.g., the user-user social graph and the user-item graph). (用户参与两个图（例如，用户社交图和用户项目图）。)
• (3) To address the three aforementioned challenges simultaneously, in this paper, we present a novel graph neural network framework (GraphRec) for social recommendations. (我们提出了一种新的用于社会推荐的图神经网络框架 (GraphRec) 。)
• (4) In particular, we provide a principled approach to jointly capture interactions and opinions in the user-item graph and propose the framework GraphRec, which coherently models two graphs and heterogeneous strengths. (特别是，我们提供了一种原则性的方法来联合捕获用户项图中的交互和观点，并提出了框架GraphRec，该框架对两个图和==异构力量(强度)==进行了一致建模。)
• (5) Extensive experiments on two real-world datasets demonstrate the effectiveness of the proposed framework GraphRec. Our code is available at https://github.com/wenqifan03/GraphRec-WWW19

CCS CONCEPTS

• Information systems → Social recommendation; • Computing methodologies → Neural networks; Artificial intelligence.

KEYWORDS

Social Recommendation; Graph Neural Networks; Recommender Systems; Social Network; Neural Networks

1 INTRODUCTION

• (1) The exploitation of social relations for recommender systems has attracted increasing attention in recent years [18, 28, 30]. These social recommender systems have been developed based on the phenomenon that users usually acquire and disseminate information through those around them, such as classmates, friends, or colleagues, implying that the underlying social relations of users can play a significant role in helping them filter information [23]. Hence, social relations have been proven to be helpful in boosting the recommendation performance [8, 29]. (近年来，利用社会关系构建推荐系统越来越受到关注[18,28,30]。这些社会推荐系统是基于这样一种现象而开发的，即用户通常通过周围的人（如同学、朋友或同事）获取和传播信息，这意味着用户的潜在社会关系可以在帮助他们过滤信息方面发挥重要作用[23]。因此，社会关系已被证明有助于提高推荐绩效[8,29]。)

• (2) Recent years have witnessed great developments in deep neural network techniques for graph data [15]. These deep neural network architectures are known as Graph Neural Networks (GNNs) [5, 10, 19], which have been proposed to learn meaningful representations for graph data. (近年来，图形数据的深层神经网络技术取得了巨大发展[15]。这些深层神经网络结构被称为图形神经网络（GNN）[5,10,19]，它被用来学习图形数据的有意义表示。)

  • Their main idea is how to iteratively aggregate feature information from local graph neighborhoods using neural networks. Meanwhile, node information can be propagated through a graph after transformation and aggregation. Hence, GNNs naturally integrate the node information as well as the topological structure and have been demonstrated to be powerful in representation learning [5, 7, 15]. (他们的主要思想是如何使用神经网络从局部图邻域迭代聚合特征信息。同时，节点信息经过变换和聚合后可以通过图传播。因此，GNN自然地集成了节点信息和拓扑结构，并已被证明在表征学习中非常强大[5,7,15]。)
  • On the other hand, data in social recommendation can be represented as graph data with two graphs. As demonstrated in Figure 1, these two graphs include a social graph denoting the relationships between users, and a user-item graph denoting interactions between users and items. Users are simultaneously involved in both graphs, who can bridge them. (另一方面，社会推荐中的数据可以用两个图表示为图数据。如图1所示，这两个图包括一个表示用户之间关系的社交图，以及一个表示用户和项目之间交互的用户项目图。用户同时参与这两个图形，他们可以将它们连接起来。)
  • Moreover, the natural way of social recommendation is to incorporate the social network information into user and item latent factors learning [37]. Learning representations of items and users is the key to build social recommender systems. Thus, given their advantages, GNNs provide unprecedented opportunities to advance social recommendation. (此外，社交推荐的自然方式是将社交网络信息纳入用户和项目潜在因素学习[37]。学习项目和用户的表示是构建社会推荐系统的关键。因此，考虑到GNN的优势，它为推动社会推荐提供了前所未有的机会。)

• (3) Meanwhile, building social recommender systems based on GNNs faces challenges. The social graph and the user-item graph in a social recommender system provide information about users from different perspectives. It is important to aggregate information from both graphs to learn better user representations. Thus, the first challenge is how to inherently combine these two graphs. Moreover, the user-item graph not only contains interactions between users and items but also includes users’ opinions on items. For example, as shown in Figure 1, the user interacts with the items of “trousers" and “laptop"; and the user likes “trousers" while disliking “laptop". Therefore, the second challenge is how to capture interactions and opinions between users and items jointly. In addition, the low cost of link formation in online worlds can result in networks with varied tie strengths (e.g., strong and weak ties are mixed together) [36]. Users are likely to share more similar tastes with strong ties than weak ties. Considering social relations equally could lead to degradation in recommendation performance. Hence, the third challenge is how to distinguish social relations with heterogeneous strengths. (同时，构建基于GNNs的社会推荐系统也面临着挑战。社交推荐系统中的社交图和用户项图从不同的角度提供用户信息。重要的是要从两个图中收集信息，以了解更好的用户表示。因此，第一个挑战是如何内在地结合这两个图形。此外，用户项目图不仅包含用户和项目之间的交互，还包含用户对项目的意见。例如，如图1所示，用户与“裤子”和“笔记本电脑”项目互动；用户喜欢“裤子”而不喜欢“笔记本电脑”。因此，第二个挑战是如何联合捕获用户和项目之间的互动和意见。此外，网络世界中链接形成的低成本可能导致网络具有不同的联系强度（例如，强弱关系混合在一起）[36]。与弱领带相比，强领带的用户可能更倾向于分享相似的口味。平等考虑社会关系可能会导致推荐绩效下降。因此，第三个挑战是如何区分具有异质优势的社会关系。)

• (4) In this paper, we aim to build social recommender systems based on graph neural networks.

• Specially, we propose a novel graph neural network GraphRec for social recommendations, which can address three aforementioned challenges simultaneously. Our major contributions are summarized as follows:

  • We propose a novel graph neural network GraphRec, which can model graph data in social recommendations coherently; (特别地，我们提出了一种新的用于社会推荐的图神经网络GraphRec，它可以同时解决上述三个挑战。我们的主要贡献总结如下：)
  • We provide a principled approach to jointly capture interactions and opinions in the user-item graph; (我们提供了一种原则性的方法来共同捕获用户项目图中的交互和观点；)
  • We introduce a method to consider heterogeneous strengths of social relations mathematically; and (在数学上引入了一种考虑社会关系异质性的方法；和)
  • We demonstrate the effectiveness of the proposed framework on various real-world datasets. (我们在各种真实数据集上展示了所提出的框架的有效性。)

• (5) The remainder of this paper is organized as follows. We introduce the proposed framework in Section 2. In Section 3, we conduct experiments on two real-world datasets to illustrate the effectiveness of the proposed method. In Section 4, we review work related to our framework. Finally, we conclude our work with future directions in Section 5. (本文的其余部分组织如下。我们将在第2节介绍拟议的框架。在第3节中，我们在两个真实数据集上进行了实验，以说明所提方法的有效性。在第4节中，我们回顾了与我们的框架相关的工作。最后，我们在第5节总结了我们的工作和未来的方向。)

2 THE PROPOSED FRAMEWORK

• In this section, we will first introduce the definitions and notations used in this paper, next give an overview about the proposed framework, then detail each model component and finally discuss how to learn the model parameters. (在本节中，我们将首先介绍本文中使用的定义和符号，然后概述所提出的框架，然后详细介绍每个模型组件，最后讨论如何学习模型参数。)
  

2.1 Definitions and Notations

• (1) Let $U=\{u_1,u_2,...,u_n\}$ and $V=\{v_1,v_2,...,v_m\}$ be the sets of users and items respectively,
  • where $n$ is the number of users, and $m$ is the number of items. (其中n是用户数，m是项目数)
  • We assume that $R\in R^{n\times m}$is the user-item rating matrix, which is also called the user-item graph.
  • If $u_i$ gives a rating to $v_j$, $r_{ij}$ is the rating score, otherwise we employ 0 to represent the unknown rating from $u_i$ to $v_j$, i.e., $r_{ij}$ = 0.
  • The observed rating score $r_{ij}$ can be seen as user $u_i$’s opinion on the item $v_j$.
  • Let $O=\{<u_i,v_j>|r_{ij}\ne 0\}$ be the set of known ratings
  • and$T=\{<u_i,v_j>|r_{ij}=0\}$ be the set of unknown ratings.
  • Let $N(i)$ be the set of users whom $u_i$ directly connected with, (直接与之连接的一组用户，)
  • $C(i)$ be the set of items which $u_i$ have interacted with,
  • and $B(j)$ be the set of users who have interacted with $v_j$.
  • In addition, users can establish social relations to each other.
  • We use $T\in R^{n\times n}$ to denote the user-user social graph,
  • where $T_{ij}=1$ if $u_j$ has a relation touiand zero otherwise.
  • Given the user-item graph R and social graph $T$, we aim to predict the missing rating value in $R$.
  • Following [11], we use an embedding vector $p_i\in R^d$ to denote a user $u_i$ and an embedding vector $q_j\in R^d$ to represent an item $v_j$, where $d$ is the length of embedding vector.
  • More details will be provided about these embedding vectors in the following subsections. The mathematical notations used in this paper are summarized in Table 1.
    

2.2 An Overview of the Proposed Framework

• (1) The architecture of the proposed model is shown in Figure 2. (提出的模型的架构如图2所示)
  • The model consists of three components: user modeling, item modeling, and rating prediction. (该模型由三部分组成：用户建模、项目建模和评分预测)
  • The first component is user modeling, which is to learn latent factors of users. As data in social recommender systems includes two different graphs, i.e., a social graph and a user-item graph, we are provided with a great opportunity to learn user representations from different perspectives. Therefore, two aggregations are introduced to respectively process these two different graphs. (第一部分是用户建模，即了解用户的潜在因素。由于社交推荐系统中的数据包括两个不同的图，即社交图和用户项图，我们有机会从不同的角度学习用户表示。因此，引入了两个聚合来分别处理这两个不同的图。)
    • One is item aggregation, which can be utilized to understand users via interactions between users and items in the user-item graph (or item-space). (一种是项目聚合，它可以通过用户和用户项目图（或项目空间）中的项目之间的交互来理解用户。)
    • The other is social aggregation, the relationship between users in the social graph, which can help model users from the social perspective (or social-space). Then, it is intuitive to obtain user latent factors by combining information from both item space and social space. (另一种是社交聚合，即社交图中用户之间的关系，它可以帮助用户从社交角度（或社交空间）建模。然后，结合项目空间和社交空间的信息，直观地获取用户潜在因素。)
  • The second component is item modeling, which is to learn latent factors of items. In order to consider both interactions and opinions in the user-item graph, we introduce user aggregation, which is to aggregate users’ opinions in item modeling. (第二部分是项目建模，即学习项目的潜在因素。为了考虑用户项目图中的交互和意见，我们引入用户聚合，这是在项目建模中聚集用户的意见。)
  • The third component is to learn model parameters via prediction by integrating user and item modeling components. Next, we will detail each model component. (第三个组件是通过集成用户和项目建模组件，通过预测来学习模型参数。接下来，我们将详细介绍每个模型组件。)

2.3 User Modeling

• (1) User modeling aims to learn user latent factors, denoted as $h_i\in R^d$ for user $u_i$. The challenge is how to inherently combine the user- item graph and social graph.
• To address this challenge, we first use two types of aggregation to learn factors from two graphs, as shown in the left part in Figure 2. (我们首先使用两种类型的聚合来从两个图中学习因子，如图2左侧所示。)
  • The first aggregation, denoted as item aggregation, is utilized to learn item-space user latent factor $h_i^I\in R^d$ from the user-item graph. (第一个聚合表示为项目聚合，用于从用户项目图中学习项目空间用户潜在因子$h_i^I\in R^d$)
  • The second aggregation is social aggregation where social-space user latent factor $h_i^S\in R^d$ is learned from the social graph. (第二种聚合是社会聚合，其中社会空间用户潜在因子 $h_i^S\in R^d$是从社交图中学习)
  • Then, these two factors are combined together to form the final user latent factors $h_i$. (然后，这两个因素结合在一起，形成最终的用户潜在因素)
  • Next, we will introduce item aggregation, social aggregation and how to combine user latent factors from both item-space and social-space. (接下来，我们将介绍项目聚合、社交聚合以及如何从项目空间和社交空间结合用户潜在因素。)

2.3.1 Item Aggregation.

• (1) As user-item graph contains not only interactions between users and items but also users’ opinions (or rating scores) on items, we provide a principled approach to jointly capture interactions and opinions in the user-item graph for learning item-space user latent factors $h_i^I$, which is used to model user latent factor via interactions in the user-item graph. (由于用户项目图不仅包含用户和项目之间的交互，还包含用户对项目的意见（或评分），因此我们提供了一种原则性的方法来联合捕获用户项目图中的交互和意见，以学习项目空间中的用户潜在因素$h_i^I$，通过用户项图中的交互作用来建模用户潜在因素。)

• (2)The purpose of item aggregation is to learn item-space user latent factor $h_i^I$ by considering items a user $u_i$ has interacted with and users’ opinions on these items. To mathematically represent this aggregation, we use the following function as: (项目聚合的目的是学习项目空间用户潜在因子$h_i^I$通过将项目视为用户$u_i$已经与这些项目进行了互动，并听取了用户的意见。为了从数学上表示这种聚合，我们使用以下函数：)
  

  • where $C(i)$ is the set of items user $u_i$ has interacted with (or $u_i$’s neighbors in the user-item graph),
  • $x_{ia}$ is a representation vector to denote opinion-aware interaction between $u_i$ and an item $v_a$, (是表示$u_i$和$v_a$之间的观点感知交互的表示向量)
  • and $Aggr{e}_{items}$is the items aggregation function.
  • In addition, $\sigma$ denotes non-linear activation function (i.e., a rectified linear unit),
  • and $W$ and $b$ are the weight and bias of a neural network.
  • Next we will discuss how to define opinion-aware interaction representation xiaand the aggregation function $Aggr{e}_{items}$. (接下来，我们将讨论如何定义观点感知交互表示和聚合函数)

• (3) A user can express his/her opinions (or rating scores), denoted as $r$, to items during user-item interactions. These opinions on items can capture users’ preferences on items, which can help model item-space user latent factors. (在用户项目交互期间，用户可以对项目表达他/她的观点（或评分分数），表示为$r$。这些对项目的意见可以捕捉用户对项目的偏好，这有助于建模项目空间用户的潜在因素。)

• To model opinions, for each type of opinions $r$, we introduce an opinion embedding vector $e_r\in R^d$ that denotes each opinion $r$ as a dense vector representation.

• For example, in a 5-star rating system, for each $r\in \{1,2,3,4,5\}$, we introduce an embedding vector $e_r$.

• For an interaction between user $u_i$ and item $v_a$ with opinion $r$, we model opinion-aware interaction representation $x_{ia}$ as a combination of item embedding $q_a$ and opinion embedding $e_r$ via a Multi-Layer Perceptron (MLP).

• It can be denoted as $g_v$ to fuse the interaction information with the opinion information as shown in Figure 2. The MLP takes the concatenation of item embedding $q_a$ and its opinion embedding $e_r$ as input. The output of MLP is the opinion-aware presentation of the interaction between $u_i$ and $v_a$, $x_{ia}$, as follows:
  

  • where $\oplus$ denotes the concatenation operation between two vectors. (表示两个向量之间的串联操作。)

• (4) One popular aggregation function for $Aggr{e}_{items}$is the mean operator where we take the element-wise mean of the vectors in $\{x_{ia},\forall a\in C(i)\}$. This mean-based aggregator is a linear approximation of a localized spectral convolution [15], as the following function: (这个基于均值的聚合器是局部谱卷积的线性近似[15]，如下函数所示：)
  

  • where ${\alpha }_i$ is fixed to $\frac{1}{|C(i)|}$ for all items in the mean-based aggregator. (用于基于均值的聚合器中的所有项目。)
  • It assumes that all interactions contribute equally to understand the user $u_i$. (它假设所有的交互都能平等地理解用户$u_i$.)
  • However, this may not be optimal, due to the fact that the influence of interactions on users may vary dramatically. Hence, we should allow interactions to contribute differently to a user’s latent factor by assigning each interaction a weight. (然而，这可能不是最优的，因为交互对用户的影响可能会有很大的差异。因此，我们应该通过为每个交互分配权重，允许交互对用户的潜在因素做出不同的贡献。)

• (5) To alleviate the limitation of mean-based aggregator, inspired by attention mechanisms [3, 38], an intuitive solution is to tweak ${\alpha }_i$ to be aware of the target user $u_i$, i.e., assigning an individualized weight for each $(v_a,u_i)$ pair, (受注意机制[3,38]的启发，为了缓解基于均值的聚合器的局限性，一个直观的解决方案是调整${\alpha }_i$以了解目标用户$u_i$例如，为每个$(v_a，u_i)$分配一个个性化权重​)
  

  • where ${\alpha }_{ia}$ denotes the attention weight of the interaction with $v_a$ in contributing to user $u_i$’s item-space latent factor when characterizing user $u_i$’s preference from the interaction history $C(i)$. (其中${\alpha }_{ia}$表示在从交互历史$C（i）$描述用户$u_i$的偏好时，与$v_a$交互的注意权重对用户$u_i$的项目空间潜在因素起作用。)
  • Specially, we parameterize the item attention ${\alpha }_{ia}$ with a two-layer neural network, which we call as the attention network. The input to the attention network is the opinion-aware representation $x_{ia}$ of the interaction and the target user $u_i$’s embedding $p_i$. Formally, the attention network is defined as, (特别地，我们用两层神经网络将注意力${\alpha }_{ia}$参数化​，我们称之为注意力网络。注意力网络的输入是交互的观点感知表征$x_{ia}$和目标用户$u_i$u的嵌入$p_i$. 正式来说，注意力网络的定义是，)
    

• (6) The final attention weights are obtained by normalizing the above attentive scores using Softmax function, which can be interpreted as the contribution of the interaction to the item-space user latent factor of user $u_i$ as: (最后的注意权重是通过使用Softmax函数对上述注意分数进行归一化得到的，该函数可以解释为交互对用户$u_i$的项目空间用户潜在因子的贡献​：)
  

2.3.2 Social Aggregation.

• (1) Due to the social correlation theories [20, 21], a user’s preference is similar to or influenced by his/her directly connected social friends. We should incorporate social information to further model user latent factors. (根据社会关联理论[20,21]，用户的偏好与他/她直接联系的社会朋友相似或受其影响。我们应该结合社会信息来进一步模拟用户的潜在因素。)

  • Meanwhile, tie strengths between users can further influence users’ behaviors from the social graph. In other words, the learning of social-space user latent factors should consider heterogeneous strengths of social relations. (同时，用户之间的联系强度可以从社交图上进一步影响用户的行为。也就是说，学习社会空间的用户潜在因素应考虑社会关系的异质优势。)
  • Therefore, we introduce an attention mechanism to select social friends that are representative to characterize users social information and then aggregate their information. (因此，我们引入一种注意机制来选择具有代表性的社交朋友来描述用户的社交信息，然后聚合他们的信息。)

• (2) In order to represent user latent factors from this social perspective, we propose social-space user latent factors, which is to aggregate the item-space user latent factors of neighboring users from the social graph. (为了从这个社会角度来表示用户潜在因素，我们提出了社会空间用户潜在因素，即从社会图中聚合相邻用户的项目空间用户潜在因素。)

• Specially, the social-space user latent factor of $u_i$, $h_i^S$, is to aggregate the item-space user latent factors of users in $u_i$’s neighbors N(i), as the follows: (特别,$u_i$的社会空间用户潜在因素​, $h_i^S$, 是对$u_i$的邻居的项目空间用户潜在因素进行聚合），如下所示：)
  

  • where $Aggr{e}_{neigbhors}$ denotes the aggregation function on user’s neighbors (表示用户邻居的聚合函数)

• (3) One natural aggregation function for $Aggr{e}_{neigbhors}$ is also the mean operator which take the element-wise mean of the vectors in $\{h_o^I,\forall \in N(i)\}$, as the following function:
  

  • where ${\beta }_i$ is fixed to $\frac{1}{|N(i)|}$ for all neighbors for the mean-based aggregator. It assumes that all neighbors contribute equally to the representation of user ui. However, as mentioned before, strong and weak ties are mixed together in a social network, and users are likely to share more similar tastes with strong ties than weak ties. (用于基于均值的聚合器的所有邻居。它假设所有邻居对用户ui的表示都有同等的贡献。然而，正如前面提到的，在一个社交网络中，强弱关系是混合在一起的，用户可能会与强弱关系分享更多相似的口味。)
  • Thus, we perform an attention mechanism with a two-layer neural network to extract these users that are important to influence $u_i$, and model their tie strengths, by relating social attention ${\beta }_{io}$ with $h_o^I$ and the target user embedding $p_i$, as below, (因此，我们使用两层神经网络执行注意机制，以提取这些对$u_i$有重要影响的用户​ , 并通过关联社会注意力${\beta }_{io}$和$h_o^I$来模拟他们的联系强和以及目标用户嵌入$p_i$, 如下：)
    
    • where the ${\beta }_{io}$ can be seen as the strengths between users. (其中，${\beta }_{io}$可以被视为用户之间的力量。)

2.3.3 Learning User Latent Factor.

• In order to learn better user latent factors, item-space user latent factors and social-space user latent factors are needed to be considered together, since the social graph and the user-item graph provide information about users from different perspectives. (为了更好地了解用户潜在因素，需要同时考虑项目空间用户潜在因素和社会空间用户潜在因素，因为社会图和用户项目图从不同的角度提供用户信息。)
• We propose to combine these two latent factors to the final user latent factor via a standard MLP where the item-space user latent factor $h_i^I$ and the social-space user latent factor $h_i^S$ are concatenated before feeding into MLP. Formally, the user latent factor $h_i$ is defined as, (我们建议通过标准MLP将这两个潜在因素结合到最终用户潜在因素中，其中项目空间用户潜在因素$h_i^I$社会空间用户潜在因素​$h_i^S$在喂进MLP之前连接。形式上，用户潜在因素$h_i$定义为：，)
  
  • where $l$ is the index of a hidden layer. (其中ll是隐藏层的索引。)

2.4 Item Modeling

• As shown in the right part of Figure 2, item modeling is used to learn item latent factor, denoted as $z_j$, for the item $v_j$ by user aggregation. Items are associated with the user-item graph, which contains interactions as well as user’s opinions. Therefore, interactions and opinions in the user-item graph should be jointly captured to further learn item latent factors. (如图2右侧所示，项目建模用于学习项目潜在因素，表示为$z_j$, 关于$v_j$项​,通过用户聚合。项目与用户项目图相关联，该图包含交互以及用户的意见。因此，应该共同捕获用户项目图中的交互和意见，以进一步了解项目潜在因素。)

User Aggregation.

• (1) Likewise, we use a similar method as learning item-space user latent factors via item aggregation. For each item $v_j$, we need to aggregate information from the set of users who have interacted with $v_j$, denoted as $B(j)$. (同样，我们使用了一种类似于通过项目聚合学习项目空间用户潜在因素的方法。每项$v_j$, 我们需要从与$v_j$进行交互的用户集合中收集信息​, 表示为$B(j)$。)

• (2) Even for the same item, users might express different opinions during user-item interactions. These opinions from different users can capture the characteristics of the same item in different ways provided by users, which can help model item latent factors. (即使对于同一个项目，用户在与项目交互时也可能表达不同的意见。这些来自不同用户的意见可以以用户提供的不同方式捕捉同一项目的特征，这有助于对项目潜在因素进行建模。)

• For an interaction from $u_t$ to $v_j$ with opinion $r$, we introduce an opinionaware interaction user representation $f_{jt}$, which is obtained from the basic user embedding $p_t$ and opinion embedding $e_r$ via a MLP, denoted as $g_u$. $g_u$ is to fuse the interaction information with the opinion information, as shown in Figure 2:
  

• (3) Then, to learn item latent factor $z_j$, we also propose to aggregate opinion-aware interaction representation of users in $B(j)$ for item $v_j$. The users aggregation function is denoted as $ASggr{e}_{u}sers$, which is to aggregate opinion-aware interaction representation of users in $\{f_{jt},\forall t\in B(j)\}$ as: (然后，学习项目潜在因素$z_j$ , 我们还建议在$B（j）$中为$v_j$项聚合用户的观点感知交互表示​ . 用户聚合函数表示为)
  

• (4) In addition, we introduce an attention mechanism to differentiate the importance weight ${\mu }_{jt}$ of users with a two-layer neural attention network, taking $f_{jt}$ and $q_j$ as the input,
  

  • This user attention ${\mu }_{jt}$ is to capture heterogeneous influence from user-item interactions on learning item latent factor. (这个用户关注${\mu }_{jt}$是为了捕捉用户项目交互对学习项目潜在因素的异质性影响。)

2.5 Rating Prediction

• In this subsection, we will design recommendation tasks to learn model parameters. There are various recommendation tasks such as item ranking and rating prediction. In this work, we apply the proposed GraphRec model for the recommendation task of rating prediction. With the latent factors of users and items (i.e., $h_i$ and $z_j$), we can first concatenate them $[h_i\oplus z_j]$ and then feed it into MLP for rating prediction as: (在本小节中，我们将设计推荐任务来学习模型参数。有各种各样的推荐任务，比如项目排名和评分预测。在这项工作中，我们将提出的GraphRec模型应用于评级预测的推荐任务。用户和项目的潜在因素（即$h_i$ 和 $z_j$ ), 我们可以先将它们连接起来$[h_i\oplus z_j]$然后将其输入MLP进行评分预测，如下所示：)
  
  • where $l$ is the index of a hidden layer, and $r{\prime }_{ij}$ is the predicted rating from $u_i$ to $v_j$. (其中$l$是隐藏层的索引，$r{\prime }_{ij}$​ 是$u_i$对$v_j$的预测评级​.)

2.6 Model Training

• (1) To estimate model parameters of GraphRec, we need to specify an objective function to optimize. Since the task we focus on in this work is rating prediction, a commonly used objective function is formulated as, (为了估计GraphRec的模型参数，我们需要指定一个目标函数进行优化。由于我们在这项工作中关注的任务是评级预测，一个常用的目标函数公式如下：，)
  

  • where $|O|$ is the number of observed ratings , and $r_{ij}$is the ground truth rating assigned by the user $i$ on the item $j$. ($|O|$是观察到的评分数，$r_{ij}$是用户$i$在$j$项上分配的真值。)

• (2) To optimize the objective function, we adopt the RMSprop [31] as the optimizer in our implementation, rather than the vanilla SGD. (为了优化目标函数，我们在实现中采用RMSprop[31]作为优化器，而不是普通的SGD。)

  • At each time, it randomly selects a training instance and updates each model parameter towards the direction of its negative gradient. (每次，它随机选择一个训练实例，并朝负梯度方向更新每个模型参数。)
  • There are three embedding in our model, including (在我们的模型中有三种嵌入，包括)
    • item embedding $q_j$,
    • user embedding $p_i$,
    • and opinion embedding $e_r$.
  • They are randomly initialized and jointly learned during the training stage. (它们是随机初始化的，并在培训阶段共同学习。)
  • We do not use one-hot vectors to represent each user and item, since the raw features are very large and highly sparse. (我们不使用一个热向量来表示每个用户和项目，因为原始特征非常大且非常稀疏。)
  • By embedding high-dimensional sparse features into a low-dimensional latent space, the model can be easy to train [11] (通过将高维稀疏特征嵌入低维潜在空间，模型可以很容易训练[11]。) .
  • Opinion embedding matrix $e$ depends on the rating scale of the system. (意见嵌入矩阵$e$取决于系统的评分量表)
    • For example, for a 5-star rating system, opinion embedding matrix e contains 5 different embedding vectors to denote scores in {1,2,3,4,5}. (例如，对于五星评级系统，意见嵌入矩阵$e$包含5个不同的嵌入向量来表示{1,2,3,4,5}中的分数。)
  • Overfitting is a perpetual problem in optimizing deep neural network models. To alleviate this issue, the dropout strategy [26] has been applied to our model. The idea of dropout is to randomly drop some neurons during the training process. When updating parameters, only part of them will be updated. Moreover, as dropout is disabled during testing, the whole network is used for prediction. (过度拟合是深度神经网络模型优化中的一个永恒问题。为了缓解这个问题，丢弃策略[26]已经应用到我们的模型中。丢弃的概念是在训练过程中随机丢弃一些神经元。更新参数时，只会更新部分参数。此外，由于测试期间禁用了丢弃功能，因此整个网络用于预测。)

3 EXPERIMENT

3.1 Experimental Settings

3.1.1 Datasets.

• (1) In our experiments, we choose two representative datasets Ciao and Epinions1, which are taken from popular social networking websites Ciao (http://www.ciao.co.uk) and Epinions (www.epinions.com).
• Each social networking service allows users to rate items, browse/write reviews, and add friends to their ‘Circle of Trust’. Hence, they provide a large amount of rating information and social information. The ratings scale is from 1 to 5. We randomly initialize opinion embedding with 5 different embedding vectors based on 5 scores in {1,2,3,4,5}. The statistics of these two datasets are presented in Table 2.
  

3.1.2 Evaluation Metrics.

• (1) In order to evaluate the quality of the recommendation algorithms, two popular metrics are adopted to evaluate the predictive accuracy, namely (为了评估推荐算法的质量，采用了两种流行的度量来评估预测精度，即)
  • Mean Absolute Error (MAE) and (平均绝对误差（MAE）)
  • Root Mean Square Error (RMSE) [34]. (均方根误差（RMSE）)
• Smaller values of MAE and RMSE indicate better predictive accuracy. Note that small improvement in RMSE or MAE terms can have a significant impact on the quality of the top-few recommendations [16]. (MAE和RMSE值越小，预测准确率越高。请注意，RMSE或MAE项的微小改进可能会对前几条建议的质量产生重大影响[16]。)

3.1.3 Baselines.

• (1) To evaluate the performance, we compared our GraphRec with three groups of methods including traditional recommender systems, traditional social recommender systems, and deep neural network based recommender systems. For each group, we select representative baselines and below we will detail them. (为了评估性能，我们将GraphRec与三组方法进行了比较，包括传统推荐系统、传统社会推荐系统和基于深度神经网络的推荐系统。对于每组，我们选择有代表性的基线，下面我们将详细介绍它们。)

• PMF [24]: Probabilistic Matrix Factorization utilizes user-item rating matrix only and models latent factors of users and items by Gaussian distributions. (概率矩阵分解仅利用用户项目评分矩阵，并通过高斯分布对用户和项目的潜在因素进行建模。)

• SoRec[17]:SocialRecommendation performs co-factorization on the user-item rating matrix and user-user social relations matrix. (SocialRecommension对用户项目评分矩阵和用户社会关系矩阵执行协因子分解。)

• SoReg [18]: Social Regularization models social network information as regularization terms to constrain the matrix factorization framework. (社会正则化将社会网络信息建模为正则化项，以约束矩阵分解框架。)

• SocialMF [13]: It considers the trust information and propagation of trust information into the matrix factorization model for recommender systems. (它考虑了信任信息和信任信息在推荐系统矩阵分解模型中的传播。)

• TrustMF [37]: This method adopts matrix factorization technique that maps users into two low-dimensional spaces: truster space and trustee space, by factorizing trust networks according to the directional property of trust. (该方法采用矩阵分解技术，根据信任的方向性对信任网络进行分解，将用户映射到两个低维空间：信任者空间和信任者空间。)

• NeuMF [11]: This method is a state-of-the-art matrix factorization model with neural network architecture. The original implementation is for recommendation ranking task and we adjust its loss to the squared loss for rating prediction. (该方法是一种具有神经网络结构的先进矩阵分解模型。最初的实现是用于推荐排名任务，我们将其损失调整为用于评级预测的平方损失。)

• DeepSoR [8]: This model employs a deep neural network to learn representations of each user from social relations, and to integrate into probabilistic matrix factorization for rating prediction. (该模型采用深度神经网络从社会关系中学习每个用户的表示，并集成到概率矩阵分解中进行评级预测。)

• GCMC+SN [1]: This model is a state-of-the-art recommender system with graph neural network architecture. In order to incorporate social network information into GCMC, we utilize the node2vec [9] to generate user embedding as user side information, instead of using the raw feature social connections ($T\in R^{n\times n}$) directly. The reason is that the raw feature input vectors is highly sparse and highdimensional. Using the network embedding techniques can help compress the raw input feature vector to a low-dimensional and dense vector, then the model can be easy to train. (GCMC+SN[1]：该模型是一个具有图形神经网络结构的最先进的推荐系统。为了将社交网络信息整合到GCMC中，我们利用node2vec[9]生成用户嵌入作为用户侧信息，而不是使用原始特征社交连接（$T\in R^{n\times n}$）直接。原因是原始特征输入向量是高度稀疏和高维的。利用网络嵌入技术可以将原始输入特征向量压缩为低维密集向量，从而使模型易于训练。)

• PMF and NeuMF are pure collaborative filtering model without social network information for rating prediction, while the others are social recommendation. Besides, we compared GraphRec with two state-of-the-art neural network based social recommender systems, i.e., DeepSoR and GCMC+SN. (PMF和NeuMF是纯粹的协同过滤模型，没有用于评级预测的社交网络信息，而其他模型是社交推荐。此外，我们还将GraphRec与两个最先进的基于神经网络的社会推荐系统，即DeepSoR和GCMC+SN进行了比较。)

3.1.4 Parameter Settings.

• (1) We implemented our proposed method on the basis of Pytorch2, a well-known Python library for neural networks. (我们在Pytorch2的基础上实现了我们提出的方法，Pytorch2是一个著名的Python神经网络库)
  • For each dataset, we used $x\%$ as a training set to learning parameters, (对于每个数据集，我们使用$x\%$作为学习参数的训练集，)
  • $(1-x\%)/2$ as a validation set to tune hyper-parameters, ($(1-x\%)/2$作为调整超参数的验证集，)
  • and $(1-x\%)/2$ as a testing set for the final performance comparison,
  • where $x$ was varied as {80%,60%}.
• For the embedding size $d$, we tested the value of [ 8, 16, 32, 64, 128, 256 ]. (对于嵌入大小$d$)
• The batch size and learning rate was searched in [ 32, 64, 128, 512 ] and [ 0.0005, 0.001, 0.005, 0.01, 0.05, 0.1 ], respectively.
• Moreover, we empirically set the size of the hidden layer the same as the embedding size (此外，我们根据经验将隐藏层的大小设置为与嵌入大小相同的大小)
• and the activation function as ReLU.
• Without special mention, we employed three hidden layers for all the neural components. (在没有特别提及的情况下，我们为所有神经组件使用了三个隐藏层。)
• The early stopping strategy was performed, where we stopped training if the RMSE on validation set increased for 5 successive epochs. (执行早期停止策略，如果验证集上的RMSE连续5个时期增加，我们停止训练。)
• For all neural network methods, we randomly initialized model parameters with a Gaussian distribution, where the mean and standard deviation is 0 and 0.1, respectively. (对于所有神经网络方法，我们使用高斯分布随机初始化模型参数，其中平均值和标准偏差分别为0和0.1。)
• The parameters for the baseline algorithms were initialized as in the corresponding papers and were then carefully tuned to achieve optimal performance. (基线算法的参数在相应的论文中进行了初始化，然后仔细调整以实现最佳性能。)
  

3.2 Performance Comparison of Recommender

• (1) Systems We first compare the recommendation performance of all methods. Table 3 shows the overall rating prediction error w.r.t. RMSE and MAE among the recommendation methods on Ciao and Epinions datasets. We have the following main findings: (我们首先比较所有方法的推荐性能。表3显示了Ciao和EPIONS数据集推荐方法中的整体评级预测误差w.r.t.RMSE和MAE。我们有以下主要发现：)

  • SoRec, SoReg, SocialMF, and TrustMF always outperform PMF. All of these methods are based on matrix factorization. SoRec, SoReg, SocialMF, and TrustMF leverage both the rating and social network information; while PMF only uses the rating information. These results support that social network information is complementary to rating information for recommendations. (SoRec、SoReg、SocialMF和TrustMF的表现总是优于PMF。所有这些方法都是基于矩阵分解的。SoRec、SoReg、SocialMF和TrustMF利用评级和社交网络信息；而PMF只使用评级信息。这些结果支持社交网络信息是对推荐评级信息的补充。)
  • NeuMF obtains much better performance than PMF. Both methods only utilize the rating information. However, NeuMF is based on neural network architecture, which suggests the power of neural network models in recommender systems. (NeuMF的性能比PMF好得多。这两种方法都只利用评级信息。然而，NeuMF基于神经网络架构，这表明了神经网络模型在推荐系统中的威力。)
  • DeepSoR and GCMC+SN perform better than SoRec, SoReg, SocialMF, and TrustMF. All of them take advantage of both rating and social network information. However, DeepSoR and GCMC+SN are based on neural network architectures, which further indicate the power of neural network models in recommendations. (DeepSoR和GCMC+SN的表现优于SoRec、SoReg、SocialMF和TrustMF。它们都利用了评级和社交网络信息。然而，DeepSoR和GCMC+SN基于神经网络架构，这进一步表明了神经网络模型在推荐中的威力。)
  • Among baselines, GCMC+SN shows quite strong performance. It implies that the GNNs are powerful in representation learning for graph data, since it naturally integrates the node information as well as topological structure. (在基线中，GCMC+SN表现出相当强的性能。这意味着GNN在图形数据的表示学习方面非常强大，因为它自然地集成了节点信息和拓扑结构。)
  • Our method GraphRec consistently outperforms all the baseline methods. Compared to DeepSoR and GCMC+SN, our model provides advanced model components to integrate rating and social network information. In addition, our model provides a way to consider both interactions and opinions in the user-item graph. We will provide further investigations to better understand the contributions of model components to the proposed framework in the following subsection. (我们的GraphRec方法始终优于所有基线方法。与DeepSoR和GCMC+SN相比，我们的模型提供了集成评级和社交网络信息的高级模型组件。此外，我们的模型提供了一种考虑用户项图中的交互和意见的方法。我们将在下面的小节中提供进一步的调查，以更好地了解模型组件对拟议框架的贡献。)

• (2) To sum up, the comparison results suggest

  • (1) social network information is helpful for recommendations; (社交网络信息有助于推荐；)
  • (2) neural network models can boost recommendation performance (神经网络模型可以提高推荐性能)
  • and (3) the proposed framework outperforms representative baselines. (提议的框架优于有代表性的基线。)

3.3 Model Analysis

In this subsection, we study the impact of model components and model hyper-parameters. (在本小节中，我们将研究模型组件和模型超参数的影响。)

3.3.1 Effect of Social Network and User Opinions.

• (1) In the last subsection, we have demonstrated the effectiveness of the proposed framework. The proposed framework provides model components to (1) integrate social network information and (2) incorporate users’ opinions about the interactions with items. (在最后一小节中，我们展示了拟议框架的有效性。提出的框架提供了模型组件，用于（1）整合社交网络信息，以及（2）整合用户对项目交互的意见。)
• To understand the working of GraphRec, we compare GraphRec with its two variants: GraphRec-SN, and GraphRec-Opinion. These two variants are defined in the following: （为了理解GraphRec的工作原理，我们将GraphRec与其两个变体进行比较：GraphRec SN和GraphRec Opinion。这两种变体的定义如下：）
  • GraphRec-SN: The social network information of GraphRec is removed . This variant only uses the item-space user latent factor $h_i^I$ to represent user latent factors $h_i$; while ignoring the social-space user latent factors $h_i^S$. (GraphRec SN：删除GraphRec的社交网络信息。此变体仅使用项目空间用户潜在因子$h_i^I$代表用户潜在因素$h_i$; 而忽略了社交空间用户的潜在因素​$h_i^S$.)
  • GraphRec-Opinion: For learning item-space user latent factor and item latent factor, the opinion embedding is removed during learning $x_{ia}$ and $f_{jt}$. This variant gnores the users’ opinion on the user-item interactions. (GraphRec Opinion：对于学习项目空间的用户潜在因素和项目潜在因素，在学习$x_{ia}$和$f_{jt}$时删除意见嵌入。此变体忽略用户对用户项交互的意见。)
    
• (2) The performance of GraphRec and its variants on Ciao and Epinions are given in Figure 3. From the results, we have the following findings: (GraphRec及其变体在Ciao和ePionions上的性能如图3所示。从结果来看，我们有以下发现：)
  • Social Network Information. We now focus on analyzing the effectiveness of social network information. GraphRec-SN performs worse than GraphRec. It verifies that social network information is important to learn user latent factors and boost the recommendation performance. (社交网络信息。我们现在重点分析社交网络信息的有效性。GraphRec SN的性能比GraphRec差。验证了社交网络信息对了解用户潜在因素和提高推荐性能的重要性。)
  • Opinions in Interaction. We can see that without opinion information, the performance of rating prediction is deteriorated significantly. For example, on average, the relative reduction on Ciao and Epinions is 3.50% and 2.64% on RMSE metric, and 5.84% and 5.02% on MAE metric, respectively. It justifies our assumption that opinions on user-item interactions have informative information that can help to learn user or item latent factors and improve the performance of recommendation. (互动中的观点。我们可以看到，如果没有意见信息，评级预测的性能会显著恶化。例如，平均而言，Ciao和ePionions的相对减少在RMSE指标上分别为3.50%和2.64%，在MAE指标上分别为5.84%和5.02%。这证明了我们的假设，即关于用户-项目交互的意见具有信息性信息，有助于了解用户或项目的潜在因素，并提高推荐的性能。)

3.3.2 Effect of Attention Mechanisms.

• (1) To get a better understanding of the proposed GraphRec model, we further evaluate the key components of GraphRec - Attention mechanisms. There are three different attention mechanisms during aggregation, including
  • item attention $\alpha$,
  • social attention $\beta$,
  • and user attention $\mu$.
• We compare GraphRec with its four variants: -GraphRec-α, GraphRec-β, GraphRec-α&β, and GraphRec-µ. These four variants are defined in the following:
  • GraphRec-α: The item attentionα of GraphRec is eliminated during aggregating the opinion-aware interaction representation of items. This variant employs the mean-based aggregation function on item aggregation for modeling itemspace user latent factors. (GraphRec-α：GraphRec的项目注意α在聚合项目的观点感知交互表示时被消除。该变体采用基于平均数的聚合函数对item aggregation进行建模，以模拟itemspace用户的潜在因素。)
  • GraphRec-β: The social attention α is to model users’ tie strengths. The social attention α of GraphRec in this variant is eliminated during aggregating user’s neighbors. This variant employs the mean-based aggregation function on social aggregation for modeling social-space user latent factors. (GraphReC-β：社交关注度α是用来模拟用户的关系强度。这种变体中GraphRec的社交注意α在聚合用户的邻居时被消除。该变体采用基于平均数的社会聚集函数来建模社会空间用户潜在因素。)
  • GraphRec-α&β: This variant eliminates two attention mechanisms (item attention α and social attention β) on item aggregation and social aggregation for modeling user latent factors. (该变体消除了项目聚合和社会聚合上的两种注意机制（项目注意α和社会注意β），用于建模用户潜在因素。)
  • GraphRec-µ: The user attention µ of GraphRec is eliminated during aggregating opinion-aware interaction user representation. This variant employs the mean-based aggregation function on user aggregation for modeling item latent factors. (在聚合观点感知交互用户表示的过程中，GraphRec的用户注意力被消除。该变量使用基于用户聚合的平均值聚合函数来建模项目潜在因素。)

• (2)The results of different attention mechanisms on GraphRec are shown in Figure 4. From the results, we have the following findings, (GraphRec上不同注意机制的结果如图4所示。从结果来看，我们有以下发现：，)

  • Not all interacted items (purchased history) of one user contribute equally to the item-space user latent factor, and not all interacted users (buyers) have the same importance to learning item latent factor. Based on these assumptions our model considers these difference among users and items by using two different attention mechanisms (α and µ). From the results, we can observe that GraphRec-α and GraphRec- µ obtain worse performance than GraphRec. These results demonstrate the benefits of the attention mechanisms on item aggregation and user aggregation. (并非一个用户的所有交互项目（购买历史）对项目空间用户潜在因素的贡献相同，也并非所有交互用户（买家）对学习项目潜在因素的重要性相同。基于这些假设，我们的模型通过使用两种不同的注意机制（α和µ）来考虑用户和项目之间的差异。从结果中，我们可以观察到GraphRec-α和GraphRec-µ的性能比GraphRec差。这些结果证明了注意机制对项目聚合和用户聚合的好处。)
  • As mentioned before, users are likely to share more similar tastes with strong ties than weak ties. The attention mechanism β at social aggregation considers heterogeneous strengths of social relations. When the attention mechanism β is removed, the performance of GraphRec-β is dropped significantly. It justifies our assumption that during social aggregation, different social friends should have different influence for learning social-space user latent factor. It’s important to distinguish social relations with heterogeneous strengths. (如前所述，与弱关系相比，强关系的用户可能更喜欢相似的口味。社会聚集的注意机制β考虑了社会关系的异质性。当注意机制β被移除时，GraphRec-β的表现会显著下降。这证明了我们的假设，即在社会聚集过程中，不同的社会朋友应该对学习社会空间的用户潜在因素有不同的影响。区分具有异质力量的社会关系很重要。)

• (3) To sum up, GraphRec can capture the heterogeneity in aggregation operations of the proposed framework via attention mechanisms, which can boost the recommendation performance. (GraphRec可以通过注意机制捕获所提出框架聚合操作中的异构性，从而提高推荐性能。)

3.3.3 Effect of Embedding Size.

• (1) In this subsection, to analyze the effect of embedding size of user embedding $p$ , item embedding $q$, and opinion embedding $e$, on the performance of our model. (在本小节中，分析用户嵌入$p$、项目嵌入$q$和意见嵌入$e$的嵌入大小对我们模型性能的影响。)
  
• (2) Figure 5 presents the performance comparison w.r.t. the length of embedding of our proposed model on Ciao and Epinions datasets. In general, with the increase of the embedding size, the performance first increases and then decreases. When increasing the embedding size from 8 to 64 can improve the performance significantly. However, with the embedding size of 256, GraphRec degrades the performance. It demonstrates that using a large number of the embedding size has powerful representation. Nevertheless, if the length of embedding is too large, the complexity of our model will significantly increase. Therefore, we need to find a proper length of embedding in order to balance the trade-off between the performance and the complexity. (图5显示了与Ciao和Epinions数据集上我们提出的模型嵌入长度的性能比较。一般来说，随着嵌入大小的增加，性能先增加后降低。将嵌入大小从8增加到64可以显著提高性能。然而，当嵌入大小为256时，GraphRec会降低性能。它表明，使用一个更大的嵌入大小具有强大的代表性。然而，如果嵌入的长度太长，我们模型的复杂性将显著增加。因此，我们需要找到一个合适的嵌入长度，以平衡性能和复杂性之间的平衡。)

4 RELATED WORK

• (1) In this section, we briefly review some related work about social recommendation, deep neural network techniques employed for recommendation, and the advanced graph neural networks. (在这一部分中，我们简要回顾了有关社会推荐的一些相关工作，推荐中使用的深层神经网络技术，以及高级图神经网络。)

• (2) Exploiting social relations for recommendations has attracted significant attention in recent years [27, 28, 37]. One common assumption about these models is that a user’s preference is similar to or influenced by the people around him/her (nearest neighbours), which can be proven by social correlation theories [20, 21]. Along with this line, (近年来，利用社会关系提出建议引起了广泛关注[27,28,37]。关于这些模型的一个常见假设是，用户的偏好与他/她周围的人（最近的邻居）相似或受其影响，这可以通过社会关联理论得到证明[20,21]。沿着这条线，)

  • SoRec [17] proposed a co-factorization method, which shares a common latent user-feature matrix factorized by ratings and by social relations. (SoRec[17]提出了一种共因式分解方法，该方法共享一个由评级和社会关系分解的公共潜在用户特征矩阵。)
  • TrustMF [37] modeled mutual influence between users, and mapped users into two low-dimensional spaces: truster space and trustee space, by factorizing social trust networks. (TrustMF[37]通过分解社会信任网络，对用户之间的相互影响进行建模，并将用户映射到两个低维空间：信任者空间和受托者空间。)
  • SoDimRec [30] first adopted a community detection algorithm to partition users into several clusters, and then exploited the heterogeneity of social relations and weak dependency connections for recommendation. Comprehensive overviews on social recommender systems can be found in surveys [29]. (SoDimRec[30]首先采用 社区检测算法 将用户划分为多个集群，然后利用社会关系的异质性和弱依赖关系进行推荐。关于社会推荐系统的全面概述可以在调查[29]中找到。)

• (2) In recent years, deep neural network models had a great impact on learning effective feature representations in various fields, such as speech recognition [12], Computer Vision (CV) [14] and Natural Language Processing (NLP) [4]. Some recent efforts have applied deep neural networks to recommendation tasks and shown promising results [41], but most of them used deep neural networks to model audio features of music [32], textual description of items [3,33], and visual content of images [40]. Besides, NeuMF [11] presented a Neural Collaborative Filtering framework to learn the non-linear interactions between users and items. (近年来，深度神经网络模型在语音识别[12]、计算机视觉（CV）[14]和自然语言处理（NLP）[4]等领域对学习有效的特征表示产生了重大影响。最近的一些研究已经将深度神经网络应用于推荐任务，并显示了有希望的结果[41]，但大多数研究都使用深度神经网络对音乐的音频特征[32]、项目的文本描述[3,33]和图像的视觉内容[40]进行建模。此外，NeuMF[11]提出了一个神经协同过滤框架来学习用户和项目之间的非线性交互。)

• (3) However, the application of deep neural network in social recommender systems is rare until very recently. (然而，直到最近，深层神经网络在社会推荐系统中的应用还很少见。)

  • In particular, NSCR [35] extended the NeuMF [11] model to cross-domain social recommendations, i.e., recommending items of information domains to potential users of social networks, and presented a neural social collaborative ranking recommender system. However, the limitation is NSCR requires users with one or more social networks accounts (e.g., Facebook, Twitter, Instagram), which limits the data collections and its applications in practice. (特别是，NSCR[35]将NeuMF[11]模型扩展到跨领域的社会推荐，即向社交网络的潜在用户推荐信息领域的项目，并提出了一个神经社会协作排名推荐系统。然而，NSCR的限制是要求用户拥有一个或多个社交网络账户（如Facebook、Twitter、Instagram），这限制了数据收集及其实际应用。)
  • SMR- MNRL [42] developed social-aware movie recommendation in social media from the viewpoint of learning a multimodal heterogeneous network representation for ranking. They exploited the recurrent neural network and convolutional neural network to learn the representation of movies’ textual description and poster image, and adopted a random-walk based learning method into multimodal neural networks. In all these works [35] [42], they addressed the task of cross-domain social recommendations for ranking metric, which is different from traditional social recommender systems. (SMR-MNRL[42]从学习多模态异构网络表示的角度，开发了社交媒体中的社交感知电影推荐。他们利用递归神经网络和卷积神经网络学习电影文本描述和海报图像的表示，并将基于随机行走的学习方法引入多模态神经网络。在所有这些工作[35][42]中，他们解决了跨领域社会推荐的任务，以获得不同于传统社会推荐系统的排名指标。)

• (4) Most related to our task with neural networks includes DLMF [6] and DeepSoR [8]. (与我们的神经网络任务最相关的包括DLMF[6]和DeepSoR[8]。)

  • DLMF [6] used auto-encoder on ratings to learn representation for initializing an existing matrix factorization. A two-phase trust-aware recommendation process is proposed to utilize deep neural networks in matrix factorization’s initialization and to synthesize the user’s interests and their trust friends’ interests together with the impact of community effect based on matrix factorization for recommendations. (DLMF[6]使用评级上的 自动编码器 来学习初始化现有矩阵分解的表示法。提出了一种两阶段信任感知推荐过程，利用深度神经网络进行矩阵分解初始化，并基于矩阵分解综合用户兴趣和信任朋友的兴趣以及社区效应对推荐的影响。)
  • DeepSoR [8] integrated neural networks for user’s social relations into probabilistic matrix factorization. They first represented users using pre-trained node embedding technique, and further exploited k-nearest neighbors to bridge user embedding features and neural network. （DeepSoR[8]将用户社会关系的神经网络集成到 概率矩阵分解中 。他们首先使用预先训练好的节点嵌入技术来表示用户，然后进一步利用k-最近邻来连接用户嵌入特征和神经网络。）

• (5) More recently, Graph Neural Networks (GNNs) have been proven to be capable of learning on graph structure data [2, 5, 7, 15, 25]. In the task of recommender systems, the user-item interaction contains the ratings on items by users, which is a typical graph data. Therefore, GNNs have been proposed to solve the recommendation problem [1, 22, 39]. (最近，图形神经网络（GNN）已被证明能够对图形结构数据进行学习[2,5,7,15,25]。在推荐系统的任务中，用户项目交互包含用户对项目的评分，这是一个典型的图形数据。因此，有人提出GNN来解决推荐问题[1,22,39]。)

  • sRMGCNN [22] adopted GNNs to extract graph embeddings for users and items, and then combined with recurrent neural network to perform a diffusion process. (sRMGCNN[22]采用GNNs为用户和项目提取图形嵌入，然后与递归神经网络结合执行扩散过程。)
  • GCMC [1] proposed a graph auto-encoder framework, which produced latent features of users and items through a form of differentiable message passing on the user-item graph. (GCMC[1]提出了一种图形自动编码框架，该框架通过在用户项目图上 传递可微消息 的形式来产生用户和项目的潜在特征。PinSage[39]提出了一种随机游走图神经网络来学习网络规模图中节点的嵌入。尽管之前的工作取得了令人信服的成功，但人们很少关注GNNs的社会推荐。在本文中，我们提出了一种用于社会推荐的图神经网络来填补这一空白。)
  • PinSage [39] proposed a random-walk graph neural network to learn embedding for nodes in web-scale graphs. (PinSage[39]提出了一种随机游走图神经网络来学习网络规模图中节点的嵌入。)

• (6) Despite the compelling success achieved by previous work, little attention has been paid to social recommendation with GNNs. In this paper, we propose a graph neural network for social recommendation to fill this gap. (尽管之前的工作取得了令人信服的成功，但人们很少关注GNNs的社会推荐。在本文中，我们提出了一种用于社会推荐的图神经网络来填补这一空白。)

5 CONCLUSION AND FUTURE WORK

• (1) We have presented a Graph Network model (GraphRec) to model social recommendation for rating prediction (我们提出了一个图网络模型（GraphRec）来为评级预测的社会推荐建模。) .

• (2) Particularly, we provide a principled approach to jointly capture interactions and opinions in the user-item graph.(特别是，我们提供了一种原则性的方法来共同捕获用户项目图中的交互和观点。)

• (3) Our experiments reveal that the opinion information plays a crucial role in the improvement of our model performance.

• (4) In addition, our GraphRec can differentiate the ties strengths by considering heterogeneous strengths of social relations. (此外，我们的GraphRec可以通过考虑社会关系的异质性强度来区分关系强度。)

• Experimental results on two real-world datasets show that GraphRec can outperform state-of-the-art baselines. (在两个真实数据集上的实验结果表明，GraphRec的性能优于最先进的基线)

• Currently we only incorporate the social graph into recommendation, while many real-world industries are associated rich other side information on users as well as items. For example, users and items are associated with rich attributes. Therefore, exploring graph neural networks for recommendation with attributes would be an interesting future direction. Beyond that, now we consider both rating and social information static. However, rating and social information are naturally dynamic. Hence, we will consider building dynamic graph neural networks for social recommendations with dynamic. (目前，我们只将社交图纳入推荐中，而现实世界中的许多行业都与用户和项目的丰富其他方面信息相关联。例如，用户和项目与丰富的属性相关联。因此，探索利用属性推荐的图神经网络将是一个有趣的未来方向。除此之外，现在我们认为评级和社会信息都是静态的。然而，评级和社会信息自然是动态的。因此，我们将考虑建立动态图形神经网络的动态社会推荐。)

ACKNOWLEDGMENTS

REFERENCES