Disentangled Graph Social Recommendation ^†^†thanks: †Equal contribution. Corresponding author: Chao Huang.
解耦图社交推荐 ^†^†thanks: †Equal contribution. Corresponding author: Chao Huang.

Lianghao Xia^1,†, Yizhen Shao^2,†, Chao Huang^1,∗, Yong Xu², Huance Xu², Jian Pei³ yxu@scut.edu.cn, j.pei@duke.edu
夏亮浩 ^1,† , 邵一珍 ^2,† , 黄超 ^1,∗ , 许勇 ² , 许汉川 ² , 裴健 ³ yxu@scut.edu.cn, j.pei@duke.edu University of Hong Kong¹, South China University of Technology², Duke University³
香港大学 ¹ , 华南理工大学 ² , 杜克大学 ³
aka_xia@foxmail.com, chaohuang75@gmail.com, {csyzshao, cshuance.xu}@mail.scut.edu.cn

Abstract 摘要

Social recommender systems have drawn a lot of attention in many online web services, because of the incorporation of social information between users in improving recommendation results. Despite the significant progress made by existing solutions, we argue that current methods fall short in two limitations: (1) Existing social-aware recommendation models only consider collaborative similarity between items, how to incorporate item-wise semantic relatedness is less explored in current recommendation paradigms. (2) Current social recommender systems neglect the entanglement of the latent factors over heterogeneous relations (e.g., social connections, user-item interactions). Learning the disentangled representations with relation heterogeneity poses great challenge for social recommendation. In this work, we design a Disentangled Graph Neural Network (DGNN) with the integration of latent memory units, which empowers DGNN to maintain factorized representations for heterogeneous types of user and item connections. Additionally, we devise new memory-augmented message propagation and aggregation schemes under the graph neural architecture, allowing us to recursively distill semantic relatedness into the representations of users and items in a fully automatic manner. Extensive experiments on three benchmark datasets verify the effectiveness of our model by achieving great improvement over state-of-the-art recommendation techniques. The source code is publicly available at: https://github.com/HKUDS/DGNN.
社交推荐系统在许多在线网络服务中备受关注，因为用户之间的社交信息被整合进来以改善推荐结果。尽管现有解决方案取得了显著进展，但我们认为当前方法存在两个局限性：(1) 现有的社交感知推荐模型仅考虑项目间的协同相似性，如何在推荐范式中将项目级的语义相关性整合进来尚未得到充分探索。(2) 当前的社交推荐系统忽视了异构关系（例如社交连接、用户-项目交互）中潜在因素的纠缠。学习具有关系异构性的解纠缠表示对社会推荐提出了巨大挑战。在这项工作中，我们设计了一个整合潜在记忆单元的解纠缠图神经网络（DGNN），该设计使 DGNN 能够为异构类型的用户和项目连接维持分解表示。此外，我们在图神经网络架构下设计了新的记忆增强消息传播和聚合方案，使我们能够以全自动的方式递归地将语义相关性提炼到用户和物品的表示中。在三个基准数据集上的大量实验验证了我们的模型的有效性，其相较于最先进的推荐技术取得了显著的改进。源代码公开可在：https://github.com/HKUDS/DGNN。

I Introduction I 引言

Recommender systems which aim to suggest items with the learning of user’s personalized interests, have provided essential web services (e.g., E-commerce sites [23], online review systems [29] and advertising platforms [27]) to alleviate the information overload problem [55]. To address the sparse data limitation of conventional collaborative filtering models, there exist many recommendation paradigms leveraging social relationships between users, to enhance the user-item interaction modeling with external information source. These approaches explicitly characterize the cross-user influence with respect to their interaction preference in recommendation [20].
旨在通过学习用户的个性化兴趣来推荐物品的推荐系统，已经为缓解信息过载问题提供了重要的网络服务（例如，电子商务网站[23]、在线评论系统[29]和广告平台[27]）。为了解决传统协同过滤模型的稀疏数据限制，存在许多利用用户之间的社交关系来增强用户-物品交互建模的推荐范式，通过外部信息源来增强交互。这些方法明确地以推荐中的交互偏好为基准，刻画了跨用户的影响力[20]。

Motivated by the prevalence of graph neural networks (GNNs), recently emerged social recommendation methods utilize graph neural encoders to shine a light on modeling graph structure of social connections, and iteratively aggregate feature information from local neighborhoods. For example, recent efforts (e.g., DiffNet [50], MHCN [61] and KCGN [19]) employ graph convolution to capture the social-aware collaborative filtering signals and guide the user representation learning. GraphRec [12] and DANSER [51] are developed based on graph attention mechanism to discriminate relations that connect interacted users. Such GNN-based social-aware recommender systems have generated state-of-the-art performance by modeling the high-order connectivity among users and items. Additionally, another relevant attempts for jointly exploiting user-user and user-item relational structure lie in the feature transfer learning from social domain to user-item interaction encoding process [5, 53].
受图神经网络（GNNs）的普及启发，最近涌现的社会推荐方法利用图神经网络编码器来揭示社会连接的图结构建模，并迭代地聚合局部邻域的特征信息。例如，最近的努力（如 DiffNet [ 50]、MHCN [ 61] 和 KCGN [ 19]）采用图卷积来捕获社会感知的协同过滤信号，并指导用户表示学习。GraphRec [ 12] 和 DANSER [ 51] 基于图注意力机制开发，用于区分连接交互用户的关联关系。这类基于 GNN 的社会感知推荐系统通过建模用户和物品之间的高阶连接性，产生了最先进的性能。此外，另一项联合利用用户-用户和用户-物品关系结构的尝试在于从社交领域到用户-物品交互编码过程的特征迁移学习 [ 5, 53]。

Despite their effectiveness, we argue that existing social recommender systems fall short in two limitations:
尽管有效，我们认为现有的社会推荐系统存在两个局限性：

(1) The rich semantic relatedness among items remains unexplored by most existing learning solutions. In real-world recommendation scenarios, there typically exist dependencies across items, e.g., product categories/functionality, spatial similarities of venues [37, 17]. Such rich semantic relatedness among items can help explore their latent dependencies, which is helpful to understand complex interests of users [42, 56]. As a result, user’s preference over different items may not only be affected by his/her social connections, but also be inferred from the fine-grained relational knowledge on items. Despite the above benefits, incorporating the cross-item dependencies in social recommendation is challenging due to the heterogeneity nature of various relations.
(1) 现有大多数学习方案尚未探索物品间丰富的语义相关性。在现实世界的推荐场景中，物品之间通常存在依赖关系，例如产品类别/功能、场所的空间相似性[37, 17]。物品间丰富的语义相关性有助于探索其潜在依赖关系，这对于理解用户的复杂兴趣[42, 56]是有帮助的。因此，用户对不同物品的偏好不仅可能受其社交连接的影响，还可以从物品的细粒度关系知识中推断出来。尽管有上述优势，但由于各种关系的异构性，将跨物品依赖纳入社交推荐仍然具有挑战性。

(2) Most of current social recommender systems ignore the fact that connections are driven by complex factors. For instance, user’s intent on interacting (e.g., click, or purchase) an item may be influenced by diverse factors due to different item characteristics, such as the brand and color of products, director of a movie [46, 40]. The overlook of finer-grained user interest with the factor-level representation learning, may produce suboptimal recommendation results. Moreover, in real-life social recommendation scenario, users are socially connected due to multifaceted motives [26, 10], e.g., communities with disparate interests, colleagues, or family members. If we represent user-wise influence without the disentanglement of such social polysemy, the learned user preference is hard to be reflective of multiple social contexts. Therefore, the heterogeneous relations driven by complex latent factors, brings an urge for the model to encode factorized embeddings pertinent to type-specific relation semantics.
(2) 目前大多数社交推荐系统忽略了连接是由复杂因素驱动的这一事实。例如，用户与某个物品互动的意图（如点击或购买）可能受到多种因素的影响，这些因素包括物品的不同特性，如产品的品牌和颜色、电影导演[46,40]。在用因素级别的表示学习方法忽略更细粒度的用户兴趣时，可能会产生次优的推荐结果。此外，在现实生活中的社交推荐场景中，用户由于多方面的动机而相互连接[26,10]，例如具有不同兴趣的社区、同事或家庭成员。如果我们不通过解耦这种社交多义性来表示用户层面的影响，那么学习到的用户偏好很难反映多个社交环境。因此，由复杂潜在因素驱动的异构关系，使得模型需要编码与特定关系语义相关的分解嵌入。

State-of-the-art recommender systems are proposed to add disentangled representation learning into the user-item interaction modeling. However, they merely focus on single type of relation disentanglement, which are limited to incorporate heterogeneous relational semantics into recommender systems. In other words, an important fact in recommendation has been ignored: diverse semantics with relation heterogeneity can be utilized to enhance the user preference learning in recommender system. Hence, we need to learn disentangled user/item factorized embeddings with the awareness of heterogeneous side context for enhancing the representation power of neural recommendation models in real-life applications.
当前最先进的推荐系统被提出将解耦表示学习融入用户-物品交互建模中。然而，它们仅关注单一类型的关联解耦，这限制了将异构关系语义整合到推荐系统中的能力。换句话说，推荐中的一个重要事实被忽视了：具有关系异构性的多样化语义可以被用来增强推荐系统中的用户偏好学习。因此，我们需要学习具有异构侧上下文感知的解耦用户/物品分解嵌入，以增强神经推荐模型在实际应用中的表示能力。

One feasible way of modeling heterogeneous relations in social recommendation is to rely on the heterogeneous graph learning approaches [34, 11, 45]. Specifically, those methods exploit the connection structures of user-user and item-item relations into the graph learning model. However, these methods heavily rely on manually designed meta-paths between users/items with the requirement of specific domain knowledge, which can hardly be adaptive in diverse recommendation scenarios. They either simply keep distinct transformation weights during the feature representation for either node type or edge type alone. It makes them insufficient to comprehensively capture heterogeneous relational context from both user and item side, as well as the underlying interaction context between user- and item-wise relations.
在社会推荐中建模异构关系的一种可行方法是依赖异构图学习方法[34, 11, 45]。具体来说，这些方法将用户-用户和物品-物品关系的连接结构利用到图学习模型中。然而，这些方法严重依赖于手动设计的用户/物品之间的元路径，需要特定的领域知识，难以适应多样的推荐场景。它们要么仅对节点类型或边类型保持不同的转换权重，要么在特征表示过程中单独处理。这使得它们无法全面捕捉来自用户和物品两边的异构关系上下文，以及用户-物品关系之间的潜在交互上下文。

While having realized the vital role of encoding disentangled relation heterogeneity in recommendation, it is a non-trivial task due to the following key challenges: i) Learning the disentangled factors with relation heterogeneity brings the challenge of graph neural networks. In our method, we develop a node- and edge-type dependent memory-augmented network to preserve dedicated semantic representations for different types of interactions, i.e., user-user, item-item and user-item relationships. ii) Capturing the implicit inter-dependencies among different encoded disentangled relation factors. The new designed graph neural network should enable the recommender system to learn the cross-factor inter-dependencies for expressive disentangled representation learning.
在认识到编码解耦关系异质性的重要性的同时，由于以下关键挑战，这并非一项简单的任务：i) 学习具有关系异质性的解耦因素给图神经网络带来了挑战。在我们的方法中，我们开发了一个节点和边类型相关的记忆增强网络，以保留不同类型交互的专用语义表示，即用户-用户、物品-物品和用户-物品关系。ii) 捕获不同编码解耦关系因素之间的隐式相互依赖性。新设计的图神经网络应使推荐系统能够学习跨因素的相互依赖性，以实现表达性解耦表示学习。

In light of these limitations and challenges, we propose a Disentangled Graph Neural Network (DGNN), to study the social recommendation with the learning of disentangled heterogeneous factors. To handle relation heterogeneity with disentangled relation modeling, we develop a node- and edge-type dependent memory-augmented network to preserve dedicated feature representations for different types of interactions, i.e., user-user, item-item and user-item relationships. Particularly, DGNN utilizes external memory units with differentiable embedding propagation operators, allowing graph neural architecture to explicitly capture the heterogeneous graph relations for social recommendation. Additionally, instead of parameterizing each type of relations, the introduced memory neural layers endow the relation heterogeneity encoding under disentangled latent representation spaces in a fully automatic and interact manner, without customized meta paths.
鉴于这些局限性和挑战，我们提出了一种解耦图神经网络（DGNN），用于研究具有解耦异构因素学习的社交推荐。为了通过解耦关系建模处理关系异构性，我们开发了一个节点和边类型相关的记忆增强网络，以保留不同类型交互的专用特征表示，即用户-用户、物品-物品和用户-物品关系。特别地，DGNN 利用具有可微嵌入传播算子的外部记忆单元，使图神经网络能够明确捕获社交推荐中的异构图关系。此外，而不是参数化每种关系类型，引入的记忆神经网络层以完全自动和交互的方式，在解耦潜在表示空间中编码关系异构性，而无需自定义元路径。

To summarize, we make the following contributions:
总之，我们做出了以下贡献：

•

We emphasize the importance of integrating the heterogeneous relationships with latent factor disentanglement in social recommender systems. It empowers the user preference representation paradigm with the exploration of attractive source of information from both user and item domains.
我们强调了在社会推荐系统中整合异构关系与潜在因子解耦的重要性。这赋予了用户偏好表示范式以探索来自用户和物品域的吸引信息源的能力。
•

We propose a disentangled graph neural networks DGNN which generalizes the relation heterogeneity encoding by maintaining the relation-aware disentangled representations. Our proposed DGNN is built upon the heterogeneous graph memory-augmented message passing.
我们提出了一种解耦图神经网络 DGNN，它通过保持关系感知的解耦表示来泛化关系异构性编码。我们提出的 DGNN 基于异构图记忆增强的消息传递构建。
•

Extensive experiments on three real-world datasets demonstrate that DGNN significantly beats various state-of-the-art recommendation methods. In addition, the elaborated model ablation study helps justify the model effectiveness and component-wise impact in performance improvement.
在三个真实世界数据集上的大量实验表明，DGNN 显著优于各种最先进的推荐方法。此外，详细的模型消融研究有助于证明模型的有效性和性能提升的组件级影响。

II Related Work II 相关工作

II-A Social-aware Recommendation Methods
II-A 社会感知推荐方法

To improve the recommendation results, many social recommendation methods have been proposed to incorporate the online social relationships between users into the recommendation framework as side information [25, 21, 24]. Most traditional methods (e.g., Sorec [30], TrustMF [58]) are built based on the matrix factorization architecture to project users into latent factors. The common rationale behind those approaches is that users are more likely to share similar interests over items with their socially connected friends [36].
为了提高推荐结果，许多社会推荐方法已被提出，将用户之间的在线社交关系作为辅助信息融入推荐框架中[25, 21, 24]。大多数传统方法（例如 Sorec[30]、TrustMF[58]）基于矩阵分解架构，将用户映射到潜在因子。这些方法背后的共同原理是，用户更有可能与社交关系密切的朋友在物品上分享相似的兴趣[36]。

Deep learning-based social recommendation models have received increasing attention, due to the ability of neural networks for knowledge representation [60, 13]. Specifically, some studies focus on applying graph convolutional network to simultaneously model the user-user and user-item relationships, like DiffNet [50], RecoGCN [57] and KCGN [19]. Additionally, attention mechanisms have been introduced to differentiate influence among users for characterizing their preference, such as SAMN [4] and GraphRec [12]. For example, GraphRec distinguishes the strength of social ties when aggregating information from both social and user-item interaction graph. Motivated by self-supervised learning, data augmentation is applied in recent social recommender systems MHCN [61] and SMIN [28]. However, most of those recommendation methods disregard the latent factors underlying heterogeneous relationships. To fill this gap, this work therefore seeks for a new social recommender system that integrates the disentangled representation learning with heterogeneous semantics under a graph neural architecture.
基于深度学习的社交推荐模型因其神经网络在知识表示方面的能力而受到越来越多的关注[60,13]。具体来说，一些研究专注于将图卷积网络应用于同时建模用户-用户和用户-物品关系，例如 DiffNet[50]、RecoGCN[57]和 KCGN[19]。此外，注意力机制已被引入以区分用户间的影响力，从而表征他们的偏好，例如 SAMN[4]和 GraphRec[12]。例如，GraphRec 在聚合来自社交网络和用户-物品交互图的信息时，区分了社交关系的强度。受自监督学习的启发，数据增强技术被应用于最近的社会推荐系统 MHCN[61]和 SMIN[28]。然而，大多数推荐方法忽略了异构关系背后的潜在因素。为了填补这一空白，本研究因此寻求在图神经网络架构下，将解耦表示学习与异构语义相结合的新型社交推荐系统。

II-B Graph Neural Network for Recommendation
II-B 用于推荐的图神经网络

Due to the strength in representation learning over graph-structured data, a line of research for recommendation focuses on enhancing the user-item interaction modeling with graph neural architectures [16, 7, 52]. Inspired by the effectiveness of spectral graph convolutional network, NGCF [43] proposes to capture high-order relationship between user and item by performing the convolutional operations. Furthermore, another line of GNN-based recommender systems explores the spatial GNNs through attentively aggregating information from neighboring nodes, such as KGAT [42] and DGRec [35].
由于在图结构数据表示学习方面的优势，推荐领域的研究一直聚焦于通过图神经网络架构增强用户-物品交互建模[16, 7, 52]。受谱图卷积网络有效性的启发，NGCF[43]提出通过执行卷积操作来捕获用户和物品之间的高阶关系。此外，另一类基于 GNN 的推荐系统通过关注地聚合来自邻近节点的信息来探索空间 GNN，例如 KGAT[42]和 DGRec[35]。

In addition, amongst the GNN research, heterogeneous graph representation has become the promising solution to integrate the diverse relational context into the node representation [45, 14, 8, 18, 48]. For example, HERec [34] attempts to incorporate various side information to enhance the user preference learning based on the generated meta-path connections. Multi-typed user-item interactions (e.g., click, purchase) are considered to encode relation heterogeneity [15, 54]. However, the accurate prediction results from most of them largely rely on the effectiveness of the constructed meta-path-based connections, which requires domain-specific knowledge. Different from them, our DGNN model automatically capture heterogeneous relationships across users and items, by designing the memory-augmented message passing scheme. Additionally, the latent factor encoding with disentangled representations has largely been unexplored in existing recommenders which consider heterogeneous context.
此外，在 GNN 研究中，异构图表示已成为将多样化的关系上下文整合到节点表示中的有前景的解决方案[45,14,8,18,48]。例如，HERec[34]试图通过生成的元路径连接来整合各种辅助信息，以增强基于元路径连接的用户偏好学习。多类型用户-物品交互（例如，点击、购买）被考虑用于编码关系异质性[15,54]。然而，它们中的大多数准确预测结果在很大程度上依赖于所构建的基于元路径连接的有效性，这需要特定领域的知识。与它们不同，我们的 DGNN 模型通过设计记忆增强的消息传递方案，自动捕获用户和物品之间的异构关系。此外，具有解耦表示的潜在因子编码在考虑异构上下文的现有推荐系统中尚未得到充分探索。

II-C Disentangled Learning for Recommendation
II-C 推荐的解耦学习

There exist some recent studies focusing on learning disentangled representations from user-item interactions to distill the latent factors driving the observed connections [32]. For example, DGCF [46] designs routing mechanism with capsule network to model the disentangled relationships between users and items. Chen et al. [6] propose a curriculum learning-based method to disentangle multi-typed feedback of users. In multimedia recommendation domain, the multi-modal features are incorporated into the disentangled representation learning in a weakly supervised way [41].
近期存在一些研究专注于从用户-物品交互中学习解耦表示，以提炼驱动观察到的连接的潜在因素[32]。例如，DGCF[46]设计了使用胶囊网络的路由机制来建模用户和物品之间的解耦关系。Chen 等人[6]提出了一种基于课程学习的解耦用户多类型反馈的方法。在多媒体推荐领域，多模态特征以弱监督的方式被结合到解耦表示学习中[41]。

While there exist some works on disentangled learning for recommendation, our new recommender system differs from those studies from the following two aspects: i) most of those models are designed to model the homogeneous relations in recommender system, which cannot be easily adaptive to disentangle the diverse factors behind the heterogeneous relationships due to their various semantics. To fill this gap, our disentangled graph neural network is designed to maintain customized factorized representations for relation heterogeneity and distill the relational knowledge in a fully automatic manner. ii) The complex dependencies among the encoded latent factors are ignored in most current studies. In contrast, our DGNN method captures the latent factor-wise inter-dependencies with our designed differentiable memory networks under multiple latent representation spaces. By doing so, the relation-aware latent factors can effectively preserve the disentangled heterogeneous semantics.
虽然已有一些关于推荐系统解耦学习的研究，但我们的新推荐系统与这些研究存在以下两点差异：i) 大多数模型设计用于建模推荐系统中的同质关系，由于这些关系的语义各不相同，它们无法轻易适应解耦异质关系背后的多样化因素。为了填补这一空白，我们设计的解耦图神经网络旨在维护针对关系异质性的定制分解表示，并以全自动的方式提炼关系知识。ii) 大多数当前研究忽略了编码潜在因素之间的复杂依赖关系。相比之下，我们的 DGNN 方法在多个潜在表示空间下，通过我们设计的可微分记忆网络捕获潜在因素之间的相互依赖关系。通过这种方式，关系感知的潜在因素可以有效地保留解耦的异质语义。

II-D Context-aware Recommender Systems
II-D 基于上下文的推荐系统

There exist some relevant research works focusing in developing context-aware recommender systems with the consideration of various context in different recommendation scenarios [1, 22]. From the user dimension, STARS [22] combines the user-wise relations from online social network and user-specific contextual features to enhance collaborative filtering. From the item content dimension, LBSNs [2] learns the mapping from items’ contextual features to users’ preference tags in Point-of-Interest recommendation. CARL [49] proposes to fuse the textual context information of items and the interaction-based embeddings for better representation learning. Additionally, knowledge graphs have also been considered as useful contextual signals to be incorporated into recommender system to improve performance in knowledge-aware recommenders KGIN [44], CASR [31] and KGCL [59].
目前存在一些相关研究工作，专注于开发考虑不同推荐场景中各种上下文的推荐系统[1, 22]。从用户维度来看，STARS[22]结合了在线社交网络中的用户间关系和用户特定的上下文特征，以增强协同过滤。从物品内容维度来看，LBSNs[2]学习将物品的上下文特征映射到用户偏好标签，用于兴趣点推荐。CARL[49]提出融合物品的文本上下文信息和基于交互的嵌入，以实现更好的表示学习。此外，知识图谱也被视为有用的上下文信号，可以将其整合到推荐系统中，以提高知识感知推荐器 KGIN[44]、CASR[31]和 KGCL[59]的性能。

III Preliminaries III 预备知识

Refer to caption — Figure 1: The model flow of the proposed DGNN architecture. The collaborative heterogeneous graph together with the initial user/item/relation-node embeddings are fed into our DGNN composed of the disentangled heterogeneity encoder and the heterogeneous graph message aggregator. $\eta(m)$ represents the learned importance weight of the $m$ -th memory unit corresponding to the encoded factorized embeddings.
图 1：所提出的 DGNN 架构的模型流程。协同异构图与初始的用户/物品/关系节点嵌入被输入到由解耦异构编码器和异构图消息聚合器组成的我们的 DGNN 中。 $\eta(m)$ 代表与编码的分解嵌入对应的第 $m$ 个记忆单元的学习重要性权重。

We consider a scenario with the sets of users $\mathcal{U}=\{u_{1},...,u_{i},...,u_{I}\}$ and items $\mathcal{V}=\{v_{1},...,v_{j},...,v_{J}\}$ . The user-item interactions are denoted by matrix $\textbf{Y}\in\mathbb{R}^{I\times J}=\{y_{i,j}|u\in\mathcal{U},v\in\mathcal{V}\}$ , where $y_{i,j}=1$ if the interaction (e.g., browse, or purchase) between user $u_{i}$ and item $v_{j}$ is observed and $y_{i,j}=0$ otherwise. In addition to the interaction matrix Y, we also have the social connections between users which are represented by the defined user social matrix $\textbf{S}\in\mathbb{R}^{I\times I}$ , where each entry $s_{i,i^{\prime}}=1$ if there exists a social tie between user $u_{i}$ and $u_{i^{\prime}}$ and zero otherwise. In this work, we propose to enhance the social recommendation with the incorporation of item relations. Hence, given an item pair ( $v_{j}$ , $v_{j^{\prime}}$ ), their relationships are defined as an entity-relation-entity triple $(v_{j},r,v_{j^{\prime}})$ , where $r\in\mathcal{R}$ is the intermediate relation node for cross-item meta relation (e.g., categorical relations between items), where $v_{j}$ , $v_{j^{\prime}}\in\mathcal{V}$ . We use the item-relation connections $(v_{j},r)$ to construct the item relation matrix $\textbf{T}\in\mathbb{R}^{J\times R}$ , where $R$ denotes the number of relations.
我们考虑一个包含用户集 $\mathcal{U}=\{u_{1},...,u_{i},...,u_{I}\}$ 和物品集 $\mathcal{V}=\{v_{1},...,v_{j},...,v_{J}\}$ 的场景。用户-物品交互用矩阵 $\textbf{Y}\in\mathbb{R}^{I\times J}=\{y_{i,j}|u\in\mathcal{U},v\in\mathcal{V}\}$ 表示，其中如果用户 $u_{i}$ 和物品 $v_{j}$ 之间观察到交互（例如浏览或购买），则 $y_{i,j}=1$ ，否则为 $y_{i,j}=0$ 。除了交互矩阵 Y，我们还拥有用户之间的社交连接，这些连接由定义的用户社交矩阵 $\textbf{S}\in\mathbb{R}^{I\times I}$ 表示，其中如果用户 $u_{i}$ 和 $u_{i^{\prime}}$ 之间存在社交关系，则 $s_{i,i^{\prime}}=1$ 为 1，否则为 0。在这项工作中，我们提出通过结合物品关系来增强社交推荐。因此，对于物品对 ( $v_{j}$ , $v_{j^{\prime}}$ )，它们的关系被定义为实体-关系-实体三元组 $(v_{j},r,v_{j^{\prime}})$ ，其中 $r\in\mathcal{R}$ 是跨物品元关系的中间关系节点（例如物品之间的分类关系）， $v_{j}$ ， $v_{j^{\prime}}\in\mathcal{V}$ 。我们使用物品-关系连接 $(v_{j},r)$ 来构建物品关系矩阵 $\textbf{T}\in\mathbb{R}^{J\times R}$ ，其中 $R$ 表示关系的数量。

Task Description. With the above definitions, we define the task of social recommendation with item relations as: Input the user-item interaction history records Y, the user social relation matrix S, and the item-relation matrix T. Output a trained model $\xi(\cdot)$ that forecasts the preference of each user $u_{i}$ over unobserved items $v_{j}$ by $\hat{y}_{i,j}=\xi(u_{i},v_{j};\textbf{Y},\textbf{S},\textbf{T})$
任务描述。根据上述定义，我们定义具有物品关系的社会推荐任务为：输入用户-物品交互历史记录 Y、用户社交关系矩阵 S 和物品关系矩阵 T，输出一个训练好的模型 $\xi(\cdot)$ ，该模型通过 $\hat{y}_{i,j}=\xi(u_{i},v_{j};\textbf{Y},\textbf{S},\textbf{T})$ 预测每个用户 $u_{i}$ 对未观察物品 $v_{j}$ 的偏好。

IV Methodology IV 方法论

In this section, we present the details of our DGNN framework. Our new method consists of three key components: i) Memory-augmented relation heterogeneity encoder which parameterizes the relation heterogeneity into vertex- and edge-type dependent embeddings. ii) Disentangled message aggregation with relation heterogeneity that fuses the disentangled relational context from both interactive patterns and side information. iii) Model forecasting stage which incorporates the heterogeneous factorized embeddings into the model optimized objective for recommendation. The overall architecture of our proposed DGNN is shown in Figure 1.
在本节中，我们介绍了我们的 DGNN 框架的详细信息。我们的新方法由三个关键组件组成：i) 增强记忆的关系异构编码器，将关系异构参数化为与顶点和边类型相关的嵌入。ii) 带关系异构的解耦消息聚合，融合来自交互模式和侧信息的解耦关系上下文。iii) 模型预测阶段，将异构因子化嵌入结合到用于推荐的模型优化目标中。我们提出的 DGNN 的整体架构如图 1 所示。

IV-A Collaborative Heterogeneous Graph
IV-A 协同异构图

To jointly preserve the user-item interactions Y, the user-user social connections S, and the item-wise relations T, we define a unified graph structure $\mathcal{G}=(\mathcal{D},\mathcal{E},\mathcal{A},\mathcal{B})$ where each vertex $d\in\mathcal{D}$ and each edge $e\in\mathcal{E}$ are associated with their mapping functions: $\mathcal{D}\rightarrow\mathcal{A}$ and edges $\mathcal{E}\rightarrow\mathcal{B}$ . Here, $\mathcal{A}$ and $\mathcal{B}$ denotes the sets of vertices and relation edge types, respectively. In graph $\mathcal{G}$ , we characterize the relation heterogeneity with various connections across users and items by performing the integration as follows:
为了共同保留用户-物品交互 Y、用户-用户社交连接 S 以及物品间关系 T，我们定义了一个统一图结构 $\mathcal{G}=(\mathcal{D},\mathcal{E},\mathcal{A},\mathcal{B})$ ，其中每个顶点 $d\in\mathcal{D}$ 和每条边 $e\in\mathcal{E}$ 都与它们的映射函数相关联： $\mathcal{D}\rightarrow\mathcal{A}$ 和边 $\mathcal{E}\rightarrow\mathcal{B}$ 。这里， $\mathcal{A}$ 和 $\mathcal{B}$ 分别表示顶点集和关系边类型。在图 $\mathcal{G}$ 中，我们通过以下方式对关系异构性进行表征，通过跨用户和物品的各种连接进行整合：

\displaystyle\mathcal{D}=\mathcal{U}\cup\mathcal{V}\cup\mathcal{R};\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \mathcal{E}=\mathcal{S}\cup\mathcal{T}\cup\mathcal{Y}

(1)

where $\mathcal{S},\mathcal{T},\mathcal{Y}$ denote the sets of observed edges in the adjacent matrices $\textbf{S},\textbf{T},\textbf{Y}$ , respectively (e.g. $\mathcal{Y}=\{(u_{i},v_{j}):y_{i,j}=1\}$ ). With the unified heterogeneous graph integrating three types of relations, we then design our heterogeneous GNN architecture with disentangled factor representations.
其中 $\mathcal{S},\mathcal{T},\mathcal{Y}$ 分别表示在邻接矩阵 $\textbf{S},\textbf{T},\textbf{Y}$ 中观察到的边集（例如 $\mathcal{Y}=\{(u_{i},v_{j}):y_{i,j}=1\}$ ）。通过整合三种类型关系的统一异构图，我们设计了具有解耦因子表示的异构 GNN 架构。

IV-B Disentangled Heterogeneous Graph Memory Network
IV-B 解耦异构图记忆网络

Despite the progress, most existing methods for heterogeneous graph data barely pay attention to the latent factors that generate the complex semantics of the heterogeneous data. For example, HGT [45] assigns each node/edge type with an individual parameter set directly. This hinders the deep understanding of heterogeneous data such as latent type-wise dependencies. Inspired by the strength of memory neural networks in disentangled representation learning [33, 4], our DGNN proposes to augment the graph neural network with differentiable memory components under multiple latent representation space. DGNN adaptively learns the connections between node/edge types and latent factors, so as to better preserve the disentangled heterogeneous semantics.
尽管取得了进展，大多数现有的异构图数据方法几乎未关注生成异构图复杂语义的潜在因素。例如，HGT [ 45] 直接为每个节点/边类型分配独立的参数集。这阻碍了对异构图数据的深入理解，如类型依赖的潜在关系。受记忆神经网络在解耦表示学习中的优势 [ 33, 4] 的启发，我们的 DGNN 提出在多个潜在表示空间下为图神经网络增加可微分的记忆组件。DGNN 自适应地学习节点/边类型与潜在因素之间的连接，以便更好地保留解耦的异构语义。

Our DGNN takes $\mathcal{G}$ as the input computation graph for information propagation. During the message passing, we first perform the local feature transformation and nonlinear activation, and then aggregate relation-aware contextual representations. Formally, it can be represented with the following form (from the $(l)$ -th layer to $(l+1)$ -th layer):
我们的 DGNN 将 $\mathcal{G}$ 作为信息传播的输入计算图。在消息传递过程中，我们首先进行局部特征转换和非线性激活，然后聚合关系感知的上下文表示。形式上，它可以表示为以下形式（从第 $(l)$ 层到第 $(l+1)$ 层）：

\displaystyle\textbf{H}^{(l+1)}[t]\leftarrow\mathop{\text{Aggre}}\limits_{\forall s\in\mathcal{N}(t)}\Big{(}\varphi(\textbf{H}^{(l)}[t],\textbf{H}^{(l)}[s],e_{s,t})\Big{)}

(2)

where we define $\textbf{H}^{l}[t]$ as the latent representation of target node $t$ for the $l$ -th graph layer. $\mathcal{N}(t)$ denotes the set of neighboring nodes (i.e., source node $s$ ) of node $t$ . Edge $e_{s,t}$ connects node $s$ and $t$ . In the message passing paradigm, DGNN consists of two key operators: relation heterogeneity encoder $\varphi(\cdot)$ and embedding aggregation function Aggre $(\cdot)$ .
我们在其中将 $\textbf{H}^{l}[t]$ 定义为第 $l$ 层目标节点 $t$ 的潜在表示。 $\mathcal{N}(t)$ 表示节点 $t$ 的邻近节点集（即源节点 $s$ ）。边 $e_{s,t}$ 连接节点 $s$ 和 $t$ 。在消息传递范式中，DGNN 由两个关键算子组成：关系异构编码器 $\varphi(\cdot)$ 和嵌入聚合函数 Aggre $(\cdot)$ 。

IV-B1 Memory-Augmented Relation Heterogeneity Encoder
IV-B1 增强记忆关系异构编码器

To capture the heterogeneous characteristic in the knowledge-enhanced social recommendation, we propose to parameterize the relation heterogeneity into vertex- and edge-type dependent embedding projection through external memory units (as shown in Figure 2. Specifically, we first define $\mathcal{M}$ be the set of memory units corresponding to factor prototype learning $\varphi(\cdot)$ for type-specific relation semantics as below:
为了捕捉知识增强社交推荐中的异构特性，我们提出通过外部记忆单元（如图 2 所示）将关系异构参数化为与顶点和边类型相关的嵌入投影。具体来说，我们首先定义 $\mathcal{M}$ 为对应于特定关系语义因子原型学习的记忆单元集合 $\varphi(\cdot)$ ，如下所示：

	$\displaystyle\varphi(\textbf{H}^{(l)}[t],\textbf{H}^{(l)}[s])$	$\displaystyle=\Big{(}\sum_{m=1}^{\|\mathcal{M}\|}\eta(\textbf{H}^{(l)}[t],m)\textbf{W}_{m}^{1}\Big{)}\textbf{H}^{(l)}[s]$
	$\displaystyle\eta(\textbf{H}^{(l)}[t],m)$	$\displaystyle=\sigma(\textbf{H}^{(l)}[t]\cdot\textbf{W}_{m}^{2}+\textbf{b}_{m})$		(3)

where $\eta(\cdot)$ represents the target node-specific embedding function. The trainable transformation matrices and bias terms are denoted as: $\textbf{W}_{m}^{1}\in\mathbb{R}^{d\times d}$ , $\textbf{W}_{m}^{2}\in\mathbb{R}^{d}$ and $\textbf{b}_{m}\in\mathbb{R}$ . The encoded feature embeddings of source and target nodes are represented as $\textbf{H}^{(l)}[s]\in\mathbb{R}^{d}$ and $\textbf{H}^{(l)}[t]\in\mathbb{R}^{d}$ , respectively. We apply the LeakyReLU as the activation function $\sigma(\cdot)$ , i.e., $\sigma(x)=\text{max}(x,\alpha x)$ . The negative slope $\alpha$ is set as 0.2 for better gradient back-propagation. Our memory-augmented network allows the graph encoder to learn relation representation with hierarchical non-linear property. To maintain dedicated representations for different types of nodes (e.g., users, item) and edges (i.e., interactions, social connections, inter-item relationships), we also perform the encoding for edge type-specific relation with non-sharing hyperparameter space. By doing so, the learned disentangled representations are able to preserve diverse latent factors pertinent to different relations in the collaborative heterogeneous graph $\mathcal{G}$ .
其中 $\eta(\cdot)$ 表示目标节点特定的嵌入函数。可训练的变换矩阵和偏置项表示为： $\textbf{W}_{m}^{1}\in\mathbb{R}^{d\times d}$ 、 $\textbf{W}_{m}^{2}\in\mathbb{R}^{d}$ 和 $\textbf{b}_{m}\in\mathbb{R}$ 。源节点和目标节点的编码特征嵌入分别表示为 $\textbf{H}^{(l)}[s]\in\mathbb{R}^{d}$ 和 $\textbf{H}^{(l)}[t]\in\mathbb{R}^{d}$ 。我们采用 LeakyReLU 作为激活函数 $\sigma(\cdot)$ ，即 $\sigma(x)=\text{max}(x,\alpha x)$ 。负斜率 $\alpha$ 设置为 0.2 以实现更好的梯度反向传播。我们的记忆增强网络允许图编码器学习具有分层非线性特性的关系表示。为了对不同类型的节点（例如，用户、物品）和边（即，交互、社交连接、物品间关系）保持专门的表示，我们还对边类型特定的关系进行编码，并使用不共享的超参数空间。通过这种方式，学习到的解耦表示能够保留协作异构图 $\mathcal{G}$ 中与不同关系相关的多种潜在因素。

IV-B2 Message Aggregation with Relation Heterogeneity
IV-B2 基于关系异构的消息聚合

After encoding the heterogeneous relation properties from local neighbor interactions with $\textbf{H}^{(l)}[v]$ , we next aggregate message from different information sources from both user and item domains (illustrated in Figure 3). For example, we fuse the relational context from both interactive patterns and social influence in the message aggregator for users ( $u_{i}$ ) as:
在通过 $\textbf{H}^{(l)}[v]$ 对本地邻居交互中的异构关系属性进行编码后，我们接下来从用户域和物品域的不同信息源聚合消息（如图 3 所示）。例如，我们在用户的消息聚合器（ $u_{i}$ ）中融合了交互模式和社交影响的关系上下文，表示为：

	$\displaystyle\textbf{H}^{(l+1)}[u_{i}]$	$\displaystyle=\frac{1}{\|\mathcal{N}_{u_{i}}^{S}\|+\|\mathcal{N}_{u_{i}}^{Y}\|}\Big{(}\sum_{u_{i}^{\prime}\in\mathcal{N}_{u_{i}}^{S}}\varphi(\textbf{H}^{(l)}[u_{i}^{\prime}],\textbf{H}^{(l)}[u_{i}])$
	$\displaystyle+$	$\displaystyle\sum_{v_{j}\in\mathcal{N}_{u_{i}}^{Y}}(\sum_{m=1}^{\|\mathcal{M}\|}\eta(\textbf{H}^{(l)}[v_{j}],m)\textbf{W}^{m,1}_{i\leftarrow j}\Big{)}\textbf{H}^{(l)}[u_{i}]\Big{)}$		(4)

where $|\mathcal{N}_{u_{i}}^{S}|$ and $|\mathcal{N}_{u_{i}}^{Y}|$ denote the number of neighboring nodes of $u_{i}$ , in the user-user social graph and in the user-item interaction graph, respectively. $\textbf{W}_{i\leftarrow j}^{m,1}\in\mathbb{R}^{d\times d}$ denotes the transformation matrix for mapping from the item representation space to the user representation space, with respect to the $m$ -th memory unit of disentangled factor.
其中 $|\mathcal{N}_{u_{i}}^{S}|$ 和 $|\mathcal{N}_{u_{i}}^{Y}|$ 分别表示 $u_{i}$ 在用户-用户社交图和用户-物品交互图中的邻居节点数量。 $\textbf{W}_{i\leftarrow j}^{m,1}\in\mathbb{R}^{d\times d}$ 表示从物品表示空间映射到用户表示空间的转换矩阵，针对解耦因子的第 $m$ 个记忆单元。

With the incorporation of knowledge-aware item relations, the embedding propagation process for item side can be formally presented as follows:
通过结合知识感知的物品关系，物品侧的嵌入传播过程可以正式表示如下：

\displaystyle\textbf{H}^{(l+1)}[v_{j}]=\rho_{i,j}(\sum_{v_{j}\in\mathcal{N}_{v_{j}}^{Y}}\text{Meg}^{(l)}_{v_{j}\leftarrow u_{i}}+\sum_{r\in N_{v_{j}}^{T}}\text{Meg}^{(l)}_{v_{j}\leftarrow r})

(5)

where $\rho_{i,j}$ indicates the normalization term as $\rho_{i,j}=1/({|N_{v_{j}}^{Y}|+|N_{v_{j}}^{T}|})$ . The propagated message ( $\text{Meg}_{v_{j}\leftarrow u_{i}}$ and $\text{Meg}_{v_{j}\leftarrow r}$ ) is determined by the memory-based encoding function $\varphi(\cdot)$ . Furthermore, the embedding propagation between items (e.g., $v_{j}$ ) and meta relation node ( $r$ ) is shown below:
其中 $\rho_{i,j}$ 表示归一化项 $\rho_{i,j}=1/({|N_{v_{j}}^{Y}|+|N_{v_{j}}^{T}|})$ 。传播的消息（ $\text{Meg}_{v_{j}\leftarrow u_{i}}$ 和 $\text{Meg}_{v_{j}\leftarrow r}$ ）由基于记忆的编码函数 $\varphi(\cdot)$ 决定。此外，物品（例如 $v_{j}$ ）与元关系节点（ $r$ ）之间的嵌入传播如下所示：

\displaystyle\textbf{H}^{(l+1)}[r]=\frac{1}{|\mathcal{N}_{r}|}\sum_{v_{j}\in N_{r}}(\sum_{m=1}^{|\mathcal{M}|}\eta(\textbf{H}^{(l)}[v_{j}],m)\textbf{W}^{m,1}_{r\leftarrow j})\textbf{H}^{(l)}[r]

(6)

where $\mathcal{N}_{r}$ denotes the set of neighbors for the meta relation node $r$ in the graph structure. $\textbf{W}_{r\leftarrow j}^{m,1}\in\mathbb{R}^{d\times d}$ denotes the $m$ -th memory-unit-specific transformation for mapping from the item space to the meta relation node space.
$\mathcal{N}_{r}$ 表示图结构中元关系节点 $r$ 的邻居集合。 $\textbf{W}_{r\leftarrow j}^{m,1}\in\mathbb{R}^{d\times d}$ 表示从物品空间映射到元关系节点空间的第 $m$ 个特定于记忆单元的变换。

We further generalize the heterogeneous message aggregation with the incorporation of self-propagation and layer normalization [3] to stabilize the network training:
我们进一步通过结合自传播和层归一化 [ 3] 来泛化异构消息聚合，以稳定网络训练：

	$\displaystyle\widetilde{\textbf{H}}^{(l+1)}[v]=\sigma(\omega_{1}\odot\frac{\textbf{H}^{(l+1)}[v]-\mu}{\sqrt{\sigma^{2}+\epsilon}}+\omega_{2})$		(7)
	$\displaystyle+\varphi(\textbf{H}^{(l)}[v])$

where $\omega_{1}$ and $\omega_{2}$ are learned scaling factors and bias terms. $\mu$ and $\sigma$ respectively denote the mean and variance of input vector $\textbf{H}^{(l+1)}[v]$ . $\odot$ denotes the element-wise multiplication operator. For the self-loop, instead of directly adding the embeddings from the last GNN iteration, DGNN also applies the relation heterogeneity encoder $\phi(\cdot)$ . To make fully use of the multi-order node embeddings, we further perform the cross-layer ( $L$ ) high-order embedding aggregation as follows:
其中 $\omega_{1}$ 和 $\omega_{2}$ 是学习到的缩放因子和偏置项。 $\mu$ 和 $\sigma$ 分别表示输入向量 $\textbf{H}^{(l+1)}[v]$ 的均值和方差。 $\odot$ 表示逐元素乘法运算符。对于自循环，DGNN 不仅直接添加来自上一个 GNN 迭代的嵌入，还应用了关系异构编码器 $\phi(\cdot)$ 。为了充分利用多阶节点嵌入，我们进一步执行交叉层（ $L$ ）高阶嵌入聚合，如下所示：

\displaystyle{\textbf{H}}^{*}[v]=\text{LayerNorm}(\widetilde{\textbf{H}}^{(0)}[v]\mathbin{\|}\widetilde{\textbf{H}}^{(1)}[v]\mathbin{\|}...\mathbin{\|}\widetilde{\textbf{H}}^{(L)}[v])

(8)

where $\textbf{H}^{*}[v]\in\mathbb{R}^{d}$ denotes the final node embeddings for vertex $v$ . $\text{LayerNorm}(\cdot)$ denotes the layer normalization.
其中 $\textbf{H}^{*}[v]\in\mathbb{R}^{d}$ 表示顶点 $v$ 的最终节点嵌入。 $\text{LayerNorm}(\cdot)$ 表示层归一化。

IV-C Model Forecasting Phase
IV-C 模型预测阶段

To inject the social influence into our forecasting phase of DGNN, we refine the learned user embedding with the representation recalibration function $\tau(\cdot)$ shown as follows:
为了将社会影响注入我们的 DGNN 预测阶段，我们使用如下所示的第 0 个表示重新校准函数来细化学习到的用户嵌入：

\displaystyle\tau(\textbf{H}^{*}[u_{i}])=\frac{1}{|\mathcal{N}_{u_{i}}^{S}|+1}\Bigm{(}\sum\limits_{u_{i}^{\prime}\in\mathcal{N}_{u_{i}}^{S}}\textbf{H}^{*}[u_{i}^{\prime}]+\textbf{H}^{*}[u_{i}]\Bigm{)}

(9)

The function averages the socially-connected user embeddings to directly incorporate social information in the following prediction phase. We formally present it as follows:
该函数平均社交连接的用户嵌入，以直接在后续预测阶段中整合社会信息。我们正式地将其表示如下：

	$\displaystyle\xi(u_{i},v_{j})=(\textbf{H}^{}[u_{i}]+\tau(\textbf{H}^{}[u_{i}]))^{\top}\cdot\textbf{H}^{*}[v_{j}]$
	$\displaystyle=\textbf{H}^{\top}[u_{i}]\cdot\textbf{H}^{}[v_{j}]$		(10)
	$\displaystyle+\frac{\textbf{H}^{\top}[v_{j}]}{\|N_{u_{i}}^{S}\|+1}\Bigm{(}\sum_{u_{i}^{\prime}\in N_{u_{i}}^{S}}\textbf{H}^{}[u_{i}^{\prime}]+\textbf{H}^{*}[u_{i}]\Bigm{)}$

Optimization Objective: We define our optimization objective with the integrative loss of pairwise BPR loss and weight-decay regularization term in the following equation:
优化目标：我们通过以下公式定义我们的优化目标，该目标包含成对 BPR 损失和权重衰减正则化项的综合损失：

\displaystyle\mathcal{L}=\sum_{(i,j^{+},j^{-})\in O}-\log\leavevmode\nobreak\ \delta(\xi(i,j^{+})-\xi(i,j^{-}))+\lambda\mathbin{\|}\mathbf{\Theta}\mathbin{\|}^{2}

(11)

The training data is denoted as $O=\{(i,j^{+},j^{-})|(i,j^{+})\in\textbf{Y}^{+},(u,j^{-})\in\textbf{Y}^{-}\}$ ( $\textbf{Y}^{+}$ , $\textbf{Y}^{-}$ denotes the observed and unobserved interactions, respectively. Training parameters are denoted as $\mathbf{\Theta}$ and $\delta(\cdot)$ denotes the sigmoid activation function. The learning process of our DGNN is elaborated in Alg 1.
训练数据表示为 $O=\{(i,j^{+},j^{-})|(i,j^{+})\in\textbf{Y}^{+},(u,j^{-})\in\textbf{Y}^{-}\}$ （ $\textbf{Y}^{+}$ 表示观察到的交互， $\textbf{Y}^{-}$ 表示未观察到的交互。训练参数表示为 $\mathbf{\Theta}$ ， $\delta(\cdot)$ 表示 Sigmoid 激活函数。我们的 DGNN 的学习过程在算法 1 中详细说明。

IV-D Model Efficiency Analysis
IV-D 模型效率分析

IV-D1 Time Complexity Analysis
IV-D1 时间复杂度分析

To calculate the attention weights for each edges on the memory units, DGNN takes $O(|\mathcal{M}|\times|\mathcal{E}|\times d)$ complexity, where $|\mathcal{M}|$ denotes the number of memory units for each graph (i.e. the user-item collaborative graph, the user-user social graph, and the item-relation graph). With the attention scores, the time complexity to obtain the dedicated transformation for each edge (i.e. $\sum_{m=1}^{|\mathcal{M}|}\eta(\textbf{H}^{(l)}[t],m)\textbf{W}_{m}^{1}$ ) is $O(|\mathcal{M}|\times|\mathcal{E}|\times d^{2})$ . Then DGNN takes $O(|\mathcal{V}|\times d^{2})$ time complexity to conduct embedding transformation, and needs $O(|\mathcal{E}|\times d)$ complexity for information propagation along the heterogeneous edges. Generally, $|\mathcal{V}|\times d<|\mathcal{E}|$ due to the purpose of information compression, thus $O(|\mathcal{V}|\times d^{2})<O(|\mathcal{E}|\times d)$ empirically. In conclusion, the overall time complexity of DGNN is $O(|\mathcal{M}|\times|\mathcal{E}|\times d^{2})$ .
为了计算每个记忆单元上边的注意力权重，DGNN 需要 $O(|\mathcal{M}|\times|\mathcal{E}|\times d)$ 复杂度，其中 $|\mathcal{M}|$ 表示每个图的记忆单元数量（即用户-物品协同图、用户-用户社交图和物品-关系图）。通过注意力分数，获得每个边的专用转换（即 $\sum_{m=1}^{|\mathcal{M}|}\eta(\textbf{H}^{(l)}[t],m)\textbf{W}_{m}^{1}$ ）的时间复杂度为 $O(|\mathcal{M}|\times|\mathcal{E}|\times d^{2})$ 。然后 DGNN 需要 $O(|\mathcal{V}|\times d^{2})$ 时间复杂度进行嵌入转换，并需要 $O(|\mathcal{E}|\times d)$ 复杂度沿异构边进行信息传播。通常由于信息压缩的目的，因此 $|\mathcal{V}|\times d<|\mathcal{E}|$ ，所以 $O(|\mathcal{V}|\times d^{2})<O(|\mathcal{E}|\times d)$ 是经验值。总之，DGNN 的整体时间复杂度是 $O(|\mathcal{M}|\times|\mathcal{E}|\times d^{2})$ 。

IV-D2 Space Complexity Analysis
IV-D2 空间复杂度分析

Although our DGNN uses latent memory blocks to enhance heterogeneous relation modeling, the extra parameters only costs $O(|\mathcal{M}|\times d^{2})$ space for storing the learnable parameters. DGNN also requires additional $O(|\mathcal{E}|\times d^{2})$ memory space for the edge-specific transformation matrices (i.e. $\sum_{m=1}^{|\mathcal{M}|}\eta(\textbf{H}^{(l)}[t],m)\textbf{W}_{m}^{1}$ ). In comparison, a standard GNN model requires $O(|\mathcal{V}|\times d)$ space to store node features. Also, $O(|\mathcal{E}|\times d)$ or $O(|\mathcal{E}|\times d^{2})$ extra space is needed due to the edge-specific parameter customization (e.g. GAT [39], HGT [45]).
尽管我们的 DGNN 使用潜在记忆块来增强异构关系建模，但额外的参数仅需要 $O(|\mathcal{M}|\times d^{2})$ 空间来存储可学习参数。DGNN 还需要额外的 $O(|\mathcal{E}|\times d^{2})$ 内存空间来存储边特定的转换矩阵（即 $\sum_{m=1}^{|\mathcal{M}|}\eta(\textbf{H}^{(l)}[t],m)\textbf{W}_{m}^{1}$ ）。相比之下，标准 GNN 模型需要 $O(|\mathcal{V}|\times d)$ 空间来存储节点特征。此外，由于边特定的参数定制（例如 GAT [ 39]、HGT [ 45]），还需要 $O(|\mathcal{E}|\times d)$ 或 $O(|\mathcal{E}|\times d^{2})$ 额外的空间。

Input: user set

U=\{u_{i}\}

, item set

V=\{v_{j}\}

, relation set

R=\{r\}

, user-item interaction matrix

\textbf{Y}\in\mathbb{R}^{I\times J}

, user-user social matrix

\textbf{S}\in\mathbb{R}^{I\times I}

, item-item relational matrix

\textbf{T}\in\mathbb{R}^{J\times|R|}

, learning rate

\eta

, and number of epochs

E

输入：用户集

U=\{u_{i}\}

，物品集

V=\{v_{j}\}

，关系集

R=\{r\}

，用户-物品交互矩阵

\textbf{Y}\in\mathbb{R}^{I\times J}

，用户-用户社交矩阵

\textbf{S}\in\mathbb{R}^{I\times I}

，物品-物品关系矩阵

\textbf{T}\in\mathbb{R}^{J\times|R|}

，学习率

\eta

，以及训练轮数

E

Output: trained model parameters

\mathbf{\Theta}

输出：训练模型参数

\mathbf{\Theta}

1 Initialize all parameters in

\mathbf{\Theta}

;
1 初始化

\mathbf{\Theta}

中的所有参数；

2 Construct the collaborative heterogeneous graph

\mathcal{G}=\{\mathcal{V},\mathcal{E}\}

based on the relation matrices

\textbf{Y},\textbf{S},\textbf{T}

;
2 基于关系矩阵

\textbf{Y},\textbf{S},\textbf{T}

构建协同异构图

\mathcal{G}=\{\mathcal{V},\mathcal{E}\}

；

3 for $e=1$ to $E$ do

4 for $l=1$ to $L$ do

5 for $(s,t)\in\mathcal{E}$ do

6 Calculate the propagated information

\varphi(\textbf{H}^{(l)}[t],\textbf{H}^{(l)}[s])

based on the memory-augmented encoder (Eq IV-B1);
6 基于记忆增强编码器（公式 IV-B1）计算传播信息

\varphi(\textbf{H}^{(l)}[t],\textbf{H}^{(l)}[s])

；

7 end for

8 for $u_{i}\in U$ do

9 Acquire aggregated information

\textbf{H}^{(l+1)}[u_{i}]

from social and item relations (Eq IV-B2);
9 从社交和物品关系中获取聚合信息

\textbf{H}^{(l+1)}[u_{i}]

（公式 IV-B2）；

10 end for

11 for $v_{j}\in V$ do

12 Calculate item embedding

\textbf{H}^{(l+1)}[v_{j}]

based on user and item-relation edges (Eq 5);
12 根据用户和物品关系边计算物品嵌入

\textbf{H}^{(l+1)}[v_{j}]

(公式 5)；

13 end for

14 for $r\in R$ do

15 Update the relation embedding

\textbf{H}^{(l+1)}[r]

from the connected items (Eq 6);
15 更新关系嵌入

\textbf{H}^{(l+1)}[r]

，来自连接项（式 6）；

16 end for
16 结束 for 循环

17 Incorporate layer normalization and self-propagation to get

\widetilde{\textbf{H}}^{(l+1)}

(Eq 7);
17 结合层归一化和自传播得到

\widetilde{\textbf{H}}^{(l+1)}

（式 7）；

19 end for
19 结束 for 循环

20 Perform cross-layer embedding aggregation for

\textbf{H}^{*}

;
20 对

\textbf{H}^{*}

执行跨层嵌入聚合；

21 Calculate loss

\mathcal{L}

for a training batch (Eq 11);
21 计算训练批次（公式 11）的损失

\mathcal{L}

；

22 for $\theta\in\mathbf{\Theta}$ do
22 对于

\theta\in\mathbf{\Theta}

执行

\theta=\theta-\eta\cdot\partial\mathcal{L}/\partial\theta

;

24 end for
24 结束

26 end for

return traind model with parameters

\mathbf{\Theta}

.
返回带参数

\mathbf{\Theta}

的训练模型。

Algorithm 1 The Proposed DGNN Algorithm
算法 1 所提出的 DGNN 算法

V Evaluation V 评估

In this section, we perform extensive experiments on three public real-world datasets for model performance evaluation by answering the research questions presented below:
在本节中，我们通过回答以下研究问题，在三个公开的真实世界数据集上对模型性能进行评估：

•

RQ1: Compared with various state-of-the-art models, how does DGNN perform for making recommendations?
RQ1：与各种最先进模型相比，DGNN 在推荐方面的表现如何？
•

RQ2: What is the impact of major components in DGNN?
RQ2：DGNN 中主要组件的影响是什么？
•

RQ3: How does different relation types (collaborative relations, social ties, and item-wise relations) contribute to the model performance of DGNN?
RQ3：不同关系类型（协作关系、社交关系和物品间关系）如何对 DGNN 的模型性能做出贡献？
•

RQ4: How does DGNN perform compared with baselines for user preference learning under data scarcity?
RQ4: 在数据稀缺的情况下，DGNN 与基线方法在用户偏好学习方面的表现如何？
•

RQ5: How do the key hyperparameters of DGNN model impact its performance with different settings?
RQ5: DGNN 模型的关键超参数在不同设置下如何影响其性能？
•

RQ6: How is the efficiency of our DGNN in both optimization phase and forecasting phase?
RQ6: 我们的 DGNN 在优化阶段和预测阶段的效率如何？
•

RQ7: With the embedding visualization, how do the learned latent representations benefit from the collectively encoding of relation heterogeneity, from the social- and knowledge-enhanced user-item interactive patterns?
RQ7: 通过嵌入可视化，学习到的潜在表示如何从关系异质性的共同编码、社会和知识增强的用户-物品交互模式中受益？

Table I: Statistics of Experimented Datasets.
表 I：实验数据集统计。

Dataset 数据集	Ciao	Epinions	Yelp
# of Users 用户数量	1,925	18,081	99,262
# of Items 物品数量	15,053	251,722	10,5142
# of User-Item Interactions 用户-物品交互数量	30,370	715,821	769,929
Interaction Density Degree 交互密度度	0.1048%	0.0157%	0.0074%
# of Social Ties 社交关系数量	65,084	572,784	1,298,522
Social Tie Density Degree 社交关系密度度	1.7564%	0.1752%	0.0132%

V-A Experimental Settings
V-A 实验设置

V-A1 Datasets V-A1 数据集

Our experiments are conducted on three real-world benchmark datasets for social recommendation: Ciao, Epinions and Yelp. These datasets are collected from different online review systems in real-life applications, where users can write reviews on different products. Furthermore, users can establish their social relationships by adding others into their trust lists. When constructing user-user connection network, an edge $e_{i,j}$ is added when user $u_{i}$ trust $u_{j}$ and vice versa. We summarize the statistics of our evaluation datasets in Table I. Following the settings in [42, 56], we generate the item-wise relations with external knowledge (e.g., product categories, business genres) from the item side.
我们的实验在三个用于社交推荐的真实世界基准数据集上进行：Ciao、Epinions 和 Yelp。这些数据集是从现实生活中的不同在线评论系统中收集的，用户可以在不同的产品上撰写评论。此外，用户可以通过将其他人添加到他们的信任列表中来建立他们的社交关系。在构建用户-用户连接网络时，当用户 $u_{i}$ 信任用户 $u_{j}$ 或反之时，会添加一条边 $e_{i,j}$ 。我们在表 I 中总结了我们的评估数据集的统计数据。遵循 [42, 56] 中的设置，我们从物品侧生成具有外部知识（例如，产品类别、商业类型）的物品间关系。

Table II: Performance comparison of all methods in terms of HR@10 and NDCG@10. “Imp” represents the relatively performance improvement between our DHGM network and each compared baseline.
表 II：所有方法在 HR@10 和 NDCG@10 方面的性能比较。“Imp”表示我们的 DHGM 网络与每个比较基线之间的相对性能提升。

Dataset 数据集	Metrics 指标	SAMN	EATNN	DiffNet	GraphRec	NGCF	GCCF	DGRec	KGAT	DGCF	DisenHAN	HAN	HGT	HERec	MHCN	DGNN
Ciao	HR	0.4677	0.4130	0.5202	0.4594	0.4843	0.4926	0.5086	0.4907	0.5189	0.4856	0.4856	0.4933	0.5298	0.5080	0.5515
	Imp	17.92%	33.54%	6.02%	20.05%	13.88%	11.96%	8.43%	12.39%	6.28%	13.57%	13.57%	11.80%	4.10%	8.56%	–
	NDCG	0.2838	0.2520	0.3201	0.2670	0.3088	0.3070	0.3113	0.2977	0.3166	0.2894	0.2608	0.3062	0.3104	0.3118	0.3338
	Imp	17.62%	32.46%	4.28%	25.02%	8.10%	8.73%	7.23%	12.13%	5.43%	15.34%	27.99%	9.01%	7.54%	7.06%	–
Epinions	HR	0.6390	0.6422	0.6323	0.6865	0.6944	0.6779	0.6268	0.6756	0.6635	0.6825	0.6673	0.7001	0.6767	0.6411	0.7335
	Imp	14.79%	14.22%	16.01%	6.85%	5.63%	8.20%	17.02%	8.57%	10.55%	7.47%	9.92%	4.77%	8.39%	14.41%	–
	NDCG	0.4259	0.4483	0.4160	0.4786	0.4763	0.4783	0.4127	0.4708	0.4594	0.4627	0.4371	0.4812	0.4572	0.4261	0.5215
	Imp	22.45%	16.33%	25.36%	8.96%	9.49%	9.03%	26.36%	10.77%	13.52%	12.71%	19.31%	8.37%	14.06%	22.39%	–
Yelp	HR	0.7971	0.7273	0.8222	0.8019	0.8204	0.8130	0.7830	0.7737	0.7956	0.8159	0.8169	0.8185	0.7047	0.8019	0.8373
	Imp	5.04%	15.12%	1.84%	4.41%	2.06%	2.99%	6.93%	8.22%	5.24%	2.62%	2.50%	2.30%	18.82%	4.41%	–
	NDCG	0.5293	0.5289	0.5524	0.5372	0.5651	0.5585	0.5386	0.5386	0.5410	0.5403	0.5511	0.5547	0.4990	0.5348	0.5873
	Imp	10.96%	11.04%	6.32%	9.33%	3.93%	5.16%	9.04%	9.04%	8.56%	8.70%	6.57%	5.88%	17.70%	9.82%	–

V-A2 Compared Baselines V-A2 与基线比较

For comprehensive evaluation of model effectiveness, we compare DGNN with state-of-the-art methods from various research lines, covering i) attentive social recommendation models (SAMN, EATNN), ii) GNN-based social recommender systems (GraphRec, DiffNet, MHCN), iii) social recommendation with temporal context (DGRec), iv) neural graph collaborative filtering (NGCF, GCCF), v) disentangled graph recommender systems (DGCF, DisenHAN), vi) knowledge-aware recommendation model (KGAT), vii) heterogeneous graph representation learning for recommendation (HAN, HERec, HGT).
为了全面评估模型的有效性，我们将 DGNN 与来自不同研究方向的当前最佳方法进行比较，包括 i) 注意力社交推荐模型（SAMN、EATNN）、ii) 基于 GNN 的社交推荐系统（GraphRec、DiffNet、MHCN）、iii) 带有时间上下文的社交推荐（DGRec）、iv) 神经图协同过滤（NGCF、GCCF）、v) 解耦图推荐系统（DGCF、DisenHAN）、vi) 知识感知推荐模型（KGAT）、vii) 用于推荐的异构图表示学习（HAN、HERec、HGT）。

Attentive Social Recommender Systems: Attention mechanisms have been serving as effective techniques to identify important relations for social-aware recommendation.
注意力社交推荐系统：注意力机制一直作为有效技术来识别社交感知推荐中的重要关系。

•

SAMN [4]: it designs a dual-stage attentional model to characterize the user-wise influence and select relevant friends to model user preference. The friend-wise attention is introduced to investigate the social influence among users.
SAMN [ 4]: 它设计了一个双阶段注意力模型来表征用户影响并选择相关朋友来建模用户偏好。引入了朋友注意力来研究用户之间的社会影响。
•

EATNN [5]: it is a transfer learning approach which fuses interaction and social information using attention mechanisms. An optimization scheme is designed to enable the multi-task learning framework.
EATNN [ 5]: 它是一种迁移学习方法，使用注意力机制融合交互和社会信息。设计了一种优化方案来支持多任务学习框架。

GNN-based Social Recommendation Models: Graph neural networks have been utilized to model the graph-based user-item relationships and users’ social ties for recommendation.
基于 GNN 的社会推荐模型：图神经网络已被用于建模基于图的用户-物品关系和用户的社会关系以进行推荐。

•

DiffNet [50]: it uses the graph information propagation paradigm to model social relations with a layer-wise diffusion architecture for users. The dynamic social diffusion simulates the recursive social influence.
DiffNet [ 50]: 它使用图信息传播范式，通过用户的多层扩散架构来建模社会关系。动态社会扩散模拟了递归的社会影响。
•

GraphRec [12]: it is built upon the graph attention network to propagate embeddings over social network, to enhance the representation of users. The social connection and item interactions are aggregated for user latent representations through the attentive combinations.
GraphRec [ 12]: 它基于图注意力网络来在社会网络中传播嵌入，以增强用户的表示。通过注意力组合，社会连接和物品交互被聚合用于用户潜在表示。
•

MHCN [61]: it is a self-supervised learning architecture to capture user relationships using multi-channel hypergraph neural networks. The mutual information between the node-level and sub-graph-level embeddings are maximized, which serve as the auxiliary self-supervised learning task for joint training together with the recommendation loss.
MHCN [ 61]: 它是一种自监督学习架构，使用多通道超图神经网络来捕获用户关系。节点级和子图级嵌入之间的互信息被最大化，这些互信息作为辅助自监督学习任务，与推荐损失一起进行联合训练。

Graph Collaborative Filtering Models: Graph collaborative filtering techniques become the effective recommendation solution by showing their state-of-the-art performance to capture the collaborative effects over user-item interaction graph. For fair comparison, we enhance the graph CF baselines by incorporating the diverse context into the interaction graph.
图协同过滤模型：图协同过滤技术通过展示其在捕获用户-物品交互图上的协同效应方面的最先进性能，成为有效的推荐解决方案。为了进行公平比较，我们通过将多样化的上下文整合到交互图中来增强图 CF 基线模型。

•

GCCF [7]: it is a simplified GNN-based CF model with the utilization of convolution-based message passing. The non-linear transformation is removed from the graph convolutional network to address the overfitting issue.
GCCF [ 7]: 它是一种基于 GNN 的简化 CF 模型，利用基于卷积的消息传递。从图卷积网络中移除了非线性变换，以解决过拟合问题。
•

NGCF [43]: it is a state-of-the-art graph convolution-based collaborative filtering model. In the representation process of users, the high-order connectivity is considered to inject collaborative signals into the user preference learning paradigm with recursively applying graph propagation functions.
NGCF [ 43]: 它是一种基于图卷积的最先进的协同过滤模型。在用户表示过程中，考虑了高阶连接性，通过递归应用图传播函数，将协同信号注入用户偏好学习范式。

Temporal-aware Social Recommendation: Another line of social recommendation lies in the incorporation of temporal context into the modeling of user-wise social influence.
时序感知社交推荐：社交推荐的另一条思路是将时序上下文融入用户社交影响的建模中。

•

DGRec [35]: it incorporates the temporal context into the social recommendation with the integration of recurrent units and graph neural networks. Social connections are incorporated into dynamic interest representations of users.
DGRec [ 35]: 它通过结合循环单元和图神经网络，将时序上下文融入社交推荐中。社交连接被纳入用户的动态兴趣表示中。

Disentangled Graph Recommender Systems: Our DGNN model competes with the representative solutions with disentangled learning techniques for recommendation.
解耦图推荐系统：我们的 DGNN 模型与采用解耦学习技术的推荐代表性解决方案进行竞争。

•

DGCF [46]: this approach first partitions user embeddings into disjoint parts representing disentangled intent of user preference. Then, it perform intent-aware message passing over graph convolutional network for recommendation.
DGCF [ 46]: 该方法首先将用户嵌入划分为不重叠的部分，以表示用户偏好的解耦意图。然后，它在图卷积网络中执行意图感知的消息传递进行推荐。
•

DisenHAN [47]: This model is built over the graph attention model to encode the disentangled embeddings based on different connections among users and items for propagation.
DisenHAN [ 47]: 该模型基于图注意力模型构建，用于根据用户和物品之间的不同连接编码解耦嵌入进行传播。

Knowledge-aware Recommender System:We also compare our proposed DGNN framework with the recommendation algorithm which utilizes the knowledge graph as the item side information to learn the item semantic relatedness.
知识感知推荐系统：我们还比较了我们提出的 DGNN 框架与利用知识图谱作为物品侧信息的推荐算法，以学习物品语义相关性。

•

KGAT [42]: it is a knowledge-enhanced model using attention to aggregate information from both user-item interactions and item knowledge graph. The weights of neighboring nodes and entities are learned through the attention layer.
KGAT [ 42]: 它是一个知识增强模型，使用注意力机制从用户-物品交互和物品知识图谱中聚合信息。相邻节点和实体的权重通过注意力层学习。

Heterogeneous Graph Representation for Recommendation: In the performance comparison, we include two state-of-the-art heterogeneous graph embedding techniques to model the different relationships in recommender systems.
推荐系统的异构图表示：在性能比较中，我们包含了两种最先进的异构图嵌入技术来建模推荐系统中的不同关系。

•

HAN [45]: it encodes the heterogeneity of graph with a meta-path-guided hierarchical attention model consisting of node- and semantic-level attention. We apply this method to encode the node representations in our collaborative heterogeneous graph $\mathcal{G}$ , to preserve both the social-aware user dependencies and knowledge-aware item correlations.
HAN [45]: 它使用一个元路径引导的分层注意力模型来编码图的异构性，该模型包含节点级和语义级注意力。我们将此方法应用于编码我们协作异构图 $\mathcal{G}$ 中的节点表示，以保留社会感知的用户依赖性和知识感知的项目相关性。
•

HGT [45]: this method is a graph transformer architecture for heterogeneous graph representation learning. It calculates edge-specific transformation and attention for graph message passing with heterogeneity encoding.
HGT [45]: 该方法是一种用于异构图表示学习的图 Transformer 架构。它计算边特定的转换和注意力，用于异构性编码的图消息传递。
•

HERec [34]: it is a heterogeneous network embedding method which integrates various fusion functions with meta-path random walk strategy, to incorporate various side information into the user preference learning.
HERec [34]: 它是一种异构网络嵌入方法，集成了多种融合函数和元路径随机游走策略，以将各种侧信息整合到用户偏好学习中。

Table III: Performance evaluation with varying Top-N in terms of HR@N and NDCG@N.
表 III：不同 Top-N 下基于 HR@N 和 NDCG@N 的性能评估。

Model	Ciao@5		Ciao@20		Epinions@5		Epinions@20		Yelp@5		Yelp@20
Model	HR	NDCG	HR	NDCG	HR	NDCG	HR	NDCG	HR	NDCG	HR	NDCG
SAMN	0.3468	0.2460	0.6251	0.3223	0.5176	0.3860	0.7491	0.4553	0.6359	0.4662	0.9009	0.5407
EATNN	0.2969	0.2124	0.5222	0.2819	0.5283	0.3924	0.7501	0.4557	0.6425	0.4866	0.8066	0.5468
DiffNet	0.3941	0.2816	0.6647	0.3573	0.5106	0.3820	0.7367	0.4476	0.6701	0.5127	0.9053	0.5701
GraphRec	0.3058	0.2235	0.5976	0.3042	0.5683	0.4325	0.8001	0.5011	0.6631	0.4903	0.8944	0.5650
NGCF	0.3570	0.2360	0.5937	0.3188	0.5612	0.4316	0.8010	0.5006	0.6748	0.5192	0.9011	0.5684
GCCF	0.3685	0.2668	0.6289	0.3414	0.5538	0.4161	0.7906	0.4852	0.6703	0.5130	0.9011	0.5503
DGRec	0.3724	0.2647	0.6219	0.3277	0.5053	0.3775	0.7308	0.4429	0.6511	0.4897	0.8824	0.5611
KGAT	0.3391	0.2422	0.6052	0.3326	0.5483	0.4139	0.7880	0.4837	0.6503	0.4901	0.8795	0.5521
DGCF	0.3871	0.2782	0.6775	0.3604	0.5479	0.4144	0.7770	0.4811	0.6565	0.4958	0.9010	0.5678
DisenHAN	0.3493	0.2482	0.6161	0.3248	0.5609	0.4247	0.7890	0.4911	0.6511	0.4944	0.9040	0.5650
HAN	0.2937	0.1897	0.6513	0.2821	0.5403	0.4106	0.7761	0.4802	0.6635	0.5080	0.8977	0.5529
HGT	0.3415	0.2372	0.6128	0.3229	0.5757	0.4360	0.8053	0.5029	0.6888	0.5136	0.9060	0.5802
HERec	0.3832	0.2679	0.6846	0.3641	0.5519	0.4179	0.7792	0.4839	0.5833	0.4501	0.8125	0.5034
MHCN	0.3864	0.2799	0.6321	0.3453	0.5199	0.3883	0.7496	0.4551	0.6607	0.4911	0.8958	0.5670
DGNN	0.4120	0.2890	0.6942	0.3726	0.6142	0.4794	0.8281	0.5387	0.7052	0.5378	0.9293	0.6043

V-A3 Evaluation Metrics V-A3 评估指标

We focus on top- $N$ item recommendation and use two widely adopted metrics for evaluation: Hit Rate (HR)@ $N$ and Normalized Discounted Cumulative Gain (NDCG)@ $N$ with the top- $N$ ranked positions [9, 43], to measure the recommendation accuracy of each evaluated method. For individual target user, we select 100 non-interacted items as negative samples and combine them with the interacted item (as positive instances) in the evaluation procedure. Formally, the metrics are calculated as follows:
我们关注 Top- $N$ 项目推荐，并使用两种广泛采用的指标进行评估：命中率（HR）@ $N$ 和归一化折扣累积增益（NDCG）@ $N$ ，以 Top- $N$ 排名位置 [9, 43] 来衡量每种评估方法的推荐准确性。对于单个目标用户，我们选择 100 个未交互项目作为负样本，并将它们与评估过程中的交互项目（作为正实例）结合。形式上，这些指标的计算如下：

	$\displaystyle HR@N$	$\displaystyle=\frac{\sum_{i=1}^{M}\sum_{j=1}^{N}r_{i,j}}{M}$
	$\displaystyle NDCG@N$	$\displaystyle=\sum_{i=1}^{M}\frac{\sum_{j=1}^{N}r_{i,j}/\log_{2}(j+1)}{M\cdot IDCG_{i}}$		(12)

where $M$ denotes the number of tested users. $r_{i,j}=1$ if the $j$ -th item in the ranked list of the $i$ -th user is the positive item, and $r_{i,j}=0$ otherwise. The numerator of NDCG@ $N$ is the discounted cumulative gain (DCG)@ $N$ , and $IDCG_{i}$ denotes the possible maximum DCG@ $N$ value for the $i$ -th tested user.
其中 $M$ 表示测试用户数量。如果 $j$ -th 项目在 $i$ -th 用户的排名列表中是正项目，则为 $r_{i,j}=1$ ，否则为 $r_{i,j}=0$ 。NDCG@ $N$ 的分子是折扣累积增益（DCG）@ $N$ ， $IDCG_{i}$ 表示第 $i$ 个测试用户的可能最大 DCG@ $N$ 值。

V-A4 Hyperparameter Settings
V-A4 超参数设置

We implement the proposed DGNN framework based on Pytorch and perform the model optimization with Adam. For our DGNN method, the dimensionality of embedding is tuned from the range [4, 8, 16, 32]. The learning rate is set as $0.01$ and the batch size is searched between 512 and 4096. The coefficient $\lambda$ of regularization term is tuned in { $10^{-3},10^{-4},10^{-5}$ }. In our experiments, we set the number of latent memory units as 8. Other hyperparameter details can be found in our release source code.
我们基于 Pytorch 实现了所提出的 DGNN 框架，并使用 Adam 进行模型优化。对于我们的 DGNN 方法，嵌入的维度从[4, 8, 16, 32]范围内进行调整。学习率设置为 $0.01$ ，批大小在 512 到 4096 之间进行搜索。正则化项的系数 $\lambda$ 在{ $10^{-3},10^{-4},10^{-5}$ }中进行调整。在我们的实验中，我们将潜在记忆单元的数量设置为 8。其他超参数的详细信息可以在我们的发布源代码中找到。

V-B Performance Comparison (RQ1)
V-B 性能比较 (RQ1)

The empirical results of all compared methods on three different datasets (i.e., Ciao, Epinions, Yelp) are reported in Table II. We summarize the following major observations:
在三个不同数据集（即 Ciao、Epinions、Yelp）上所有比较方法的实证结果如表 II 所示。我们总结了以下主要观察结果：

Our DGNN achieves the best performance as compared to all baselines across three different datasets, which demonstrates the performance superiority of DGNN. Such performance improvements are attributed to the following model design: i) Benefiting from our heterogeneous graph memory network, DGNN could preserve the comprehensive relation semantics with latent factor disentanglement, which results in the effectively integration of disentangled social- and knowledge-aware collaborative signals. i) By incorporating knowledge-aware item relations into social recommendation framework, DGNN can better characterize the heterogeneous relationships among users and items, which enhances the representation paradigm of user-item interactions.
我们的 DGNN 在三个不同数据集上相较于所有基线模型都取得了最佳性能，这证明了 DGNN 的性能优越性。这种性能提升归因于以下模型设计：i) 借助我们的异构图记忆网络，DGNN 能够保存具有潜在因子解耦的全面关系语义，这导致了解耦的社会和知识感知协同信号的有效整合。ii) 通过将知识感知的项目关系融入社会推荐框架，DGNN 能够更好地表征用户和项目之间的异构关系，这增强了用户-项目交互的表示范式。

GNN-based social recommendation models perform better than the attentional solutions, which suggests the rationality of performing the embedding propagation with multi-hop graph structures for social relation transformation. In addition, although the design of transforming various relationships via heterogeneous graph encoders in HAN and HERec, they are limited by the generation of meta-path-guided relations with data-specific domain knowledge. To address this issue, DGNN learns more powerful node- and edge-type dependent representations by avoiding customized meta paths in the embedding function of relation heterogeneity.
基于 GNN 的社交推荐模型比注意力解决方案表现更好，这表明使用多跳图结构进行嵌入传播以实现社交关系转换的合理性。此外，尽管 HAN 和 HERec 通过异构图编码器设计来转换各种关系，但它们受限于数据特定领域知识生成的元路径引导关系。为解决这个问题，DGNN 通过在关系异质性的嵌入函数中避免定制元路径来学习更强大的节点和边类型相关表示。

The performance gap between DGNN and GNN-based methods (e.g., DiffNet, GraphRec, DGRec), indicates that leaving the knowledge-aware item relations untapped will limit the performance of social-aware recommender systems. Such observation also suggests that DGNN is good at fulfilling the potentials of learning latent factors from both user and item domains, with the designed memory-enhanced graph neural architecture. From Table III, we can observe the performance gain achieved by DGNN over other competitors with different ranked top- $N$ positions, which further justifies the superior ranking performance of our framework. The recommendation accuracy improves with larger $N$ values.
DGNN 与基于 GNN 的方法（例如 DiffNet、GraphRec、DGRec）之间的性能差距表明，若不充分利用知识感知的项目关系，将限制社交感知推荐系统的性能。这一观察结果也表明，DGNN 擅长利用其设计的记忆增强图神经网络架构，从用户和项目领域学习潜在因素。从表 III 中，我们可以观察到 DGNN 在与其他竞争者在不同排名的 Top- $N$ 位置上取得的性能提升，这进一步证明了我们框架的优越排名性能。推荐准确度随着更大的 $N$ 值而提高。

V-C Module Ablation Analyses (RQ2)
V-C 模块消融分析（RQ2）

In this section, we investigate the design rationality of sub-networks in our DGNN framework. Towards this end, we remove each of key modules and implement three model variants of DGNN corresponding to three technical points of our DGNN: i) “-M”: DGNN without the disentangled memory-enhanced relation heterogeneity encoder. ii) “- $\tau$ ”: DGNN without the incorporation of user-specific social influence with the representation recalibration function $\tau(\cdot)$ . iii) “-LN”: DGNN without the layer normalization in each propagation layer for stable node embedding training.
在本节中，我们研究了我们 DGNN 框架中子网络的设计合理性。为此，我们移除每个关键模块，并实现了三个对应于我们 DGNN 三个技术点的模型变体：i) “-M”：没有解耦记忆增强关系异构编码器的 DGNN。ii) “- $\tau$ ”：没有结合用户特定社交影响和表示重校准函数 $\tau(\cdot)$ 的 DGNN。iii) “-LN”：没有在每层传播中应用层归一化以实现稳定节点嵌入训练的 DGNN。

We evaluate the performance of the above variants as well as DGNN on three experimental data. The results are shown in Figure 4. DGNN consistently achieves best performance in comparison to the three variants. By inspecting the results in detail, we have the following observations: i) Removing the memory-enhanced relation heterogeneity encoder (i.e., “-M”) causes significant performance degradation. This validates the effectiveness of disentangling latent factors pertinent to each type of relations. ii) The performance gap between the “- $\tau$ ” variant and DGNN indicates that using local structures in social relations benefits the user representation learning through explicitly involving heterogeneous relation data. iii) By comparing “-LN” with DGNN, we can conclude that the layer normalization technique has contribution to the model training of DGNN. We ascribe the improvements to its ability to generate stable gradients through normalization.
我们评估了上述变体以及 DGNN 在三个实验数据集上的性能。结果如图 4 所示。与三个变体相比，DGNN 始终取得了最佳性能。通过详细检查结果，我们得出以下观察：i) 移除记忆增强关系异构性编码器（即，“-M”）会导致性能显著下降。这验证了将与每种关系相关的潜在因素解耦的有效性。ii) “- $\tau$ ”变体与 DGNN 之间的性能差距表明，在社交关系中使用局部结构通过明确涉及异构关系数据有利于用户表示学习。iii) 通过比较“-LN”与 DGNN，我们可以得出层归一化技术对 DGNN 模型训练有贡献的结论。我们将改进归因于其通过归一化生成稳定梯度的能力。

V-D Effect of Heterogeneous Relationships (RQ3)
V-D 异构关系的影响（RQ3）

We further investigate the influence of different auxiliary relational data (i.e., social connections and item-wise relatedness) on the performance of our DGNN. In specific, the following three model variants are considered: i) “-T”: DGNN removes the item relation matrix $\textbf{T}\in\mathbb{R}^{J\times|R|}$ . ii) “-S”: DGNN without the user-user social relation matrix $\textbf{S}\in\mathbb{R}^{I\times I}$ in the joint adjacent matrix. iii) “-ST”: both user-wise social relations and item-wise relations are removed from the input.
我们进一步研究了不同辅助关系数据（即社交连接和物品间关联性）对 DGNN 性能的影响。具体而言，考虑了以下三种模型变体：i) “-T”：DGNN 移除了物品关系矩阵 $\textbf{T}\in\mathbb{R}^{J\times|R|}$ 。ii) “-S”：DGNN 在联合邻接矩阵中移除了用户-用户社交关系矩阵 $\textbf{S}\in\mathbb{R}^{I\times I}$ 。iii) “-ST”：从输入中移除了用户间社交关系和物品间关系。

The evaluation is conducted on Ciao data and Yelp data, with varying top-N settings. The results are shown in Figure 5. Major conclusions can be drawn as follows: 1) The auxiliary heterogeneous relations consistently bring positive effects to the model performance, which can be attributed to the benefit of incorporated heterogeneous semantics into the representations. 2) The suboptimal performance of “-S” suggests the helpfulness of leveraging social contextual signals to assist user preference learning. 3) DGNN performs better than “-T” in all cases. We ascribe the improvements to excavating the rich item-wise dependencies with our memory-enhanced relation heterogeneity encoder. 4) The “-ST” variant always produces the worst performance in both datasets, which further indicates that incorporating the heterogeneous relations from either user or item domains can improve the accuracy.
评估在 Ciao 数据和 Yelp 数据上进行，设置了不同的 top-N 参数。结果如图 5 所示。主要结论如下：1) 辅助异构关系始终对模型性能产生积极影响，这归因于将异构语义融入表示中的好处。2) “-S”的次优性能表明利用社交上下文信号有助于用户偏好学习。3) 在所有情况下，DGNN 的表现均优于“-T”。我们将改进归因于我们记忆增强关系异构编码器挖掘了丰富的项级依赖关系。4) “-ST”变体在两个数据集上始终表现最差，这进一步表明，从用户或物品域中引入异构关系可以提高准确性。

V-E Performance on Alleviating Data Sparsity (RQ4)
V-E 在缓解数据稀疏性方面的表现 (RQ4)

In this subsection, we perform experiments to demonstrate the advantage of our DGNN in incorporating heterogeneous side information from both user and item domain, in order to alleviate the sparsity issue of recommendation. We first rank all users in terms of their interaction densities and partition them into four different groups which contains equal number of users (as shown in x-axis of Figure 6: 0-25%; 25%-50%, etc). In Figure 6, we calculate the average number of interactions for each user group as shown in left side of y-axis. The recommendation performance of each compared method is presented in the right side of y-axis. From the results, we can observe that DGNN performs best compared with baselines on different datasets, which shows the robustness of our recommender system in dealing with the sparsity of user behavior data. This again further confirms that the effectiveness of DGNN for enabling external knowledge from both user and item domain to guide the user preference embedding with cross-relational context under data scarcity.
在本小节中，我们通过实验验证了我们的 DGNN 在整合用户和物品领域的异构边信息以缓解推荐数据稀疏性问题方面的优势。我们首先根据用户的交互密度对所有用户进行排序，并将他们分为四个包含相同数量用户的组（如图 6 的 x 轴所示：0-25%；25%-50%，等）。在图 6 中，我们计算了每个用户组的平均交互次数，如图表左侧的 y 轴所示。每个对比方法的推荐性能则显示在右侧的 y 轴上。从结果中可以看出，与基线方法相比，DGNN 在不同数据集上表现最佳，这显示了我们的推荐系统在处理用户行为数据稀疏性方面的鲁棒性。这再次进一步证实了 DGNN 在数据稀缺的情况下，能够有效利用用户和物品领域的知识来指导用户偏好嵌入，并考虑跨关系上下文。

We further show the evaluation results w.r.t two different factors (social and interaction dimensions). As shown in Figure 6, we can observe that DGNN consistently outperforms competitive methods with different data sparsity levels, which justifies the effectiveness of DGNN in alleviating the sparsity from the perspectives of both social relations and user-item interactions. Overall, this property of our DGNN method in alleviating the data sparsity problem is important, for the recommendation scenarios, in which there are few user-item interactions compared with the entire interaction space.
我们进一步展示了关于两个不同因素（社交和交互维度）的评估结果。如图 6 所示，我们可以观察到 DGNN 在不同数据稀疏性水平下始终优于竞争方法，这从社交关系和用户-物品交互的角度证明了 DGNN 在缓解稀疏性方面的有效性。总体而言，我们 DGNN 方法在缓解数据稀疏性问题方面的这一特性非常重要，因为在推荐场景中，与整个交互空间相比，用户-物品交互较少。

V-F Hyperparameter Study (RQ5)
V-F 超参数研究 (RQ5)

This section studies how the hyperparameter settings affect the performance, by exploring the influences of hidden state dimension size $d$ , graph layer numbers $L$ , and latent memory unit numbers $\mathcal{M}$ . To save space, we present the evaluation results (with different value scales) on different datasets in a unified figure. The y-axis of Figure 7 indicates the performance degradation ratio as compared to the best accuracy.
本节研究了超参数设置如何影响性能，通过探索隐藏状态维度大小 $d$ 、图层数量 $L$ 和潜在记忆单元数量 $\mathcal{M}$ 的影响。为节省空间，我们在同一图表中展示了不同数据集上的评估结果（具有不同的值尺度）。图 7 的 y 轴表示与最佳准确率相比的性能退化率。

Hidden State Size $d$ . We plot the performance curve of our DGNN by varying $d$ in range { $2^{2}$ , $2^{3}$ , $2^{4}$ , $2^{5}$ }. With the incorporation of semantic relatedness from both user and item domains, we can notice that the embedding dimensionality of 16 is sufficient to bring good performance to our DGNN framework. In addition, the model suffers from the performance degradation with the larger embedding dimensionality. In summary, the strong performance of our model with smaller hidden state dimensionality is beneficial for practical recommender systems, in which the model computational cost is directly influenced by the embedding dimension.
隐藏状态大小 $d$ 。我们通过在范围 { $2^{2}$ , $2^{3}$ , $2^{4}$ , $2^{5}$ } 中变化 $d$ 来绘制我们 DGNN 的性能曲线。随着用户和物品域中语义相关性的结合，我们注意到 16 的嵌入维度足以为我们 DGNN 框架带来良好的性能。此外，随着嵌入维度的增大，模型性能会退化。总之，我们模型在较小隐藏状态维度下的优异性能有利于实际推荐系统，其中模型的计算成本直接受嵌入维度影响。

Graph Layer Numbers $L$ . We perform the context-aware message passing on the collaborative heterogeneous graph $\mathcal{G}$ . Now, we investigate the model performance through stacking more graph layers ( $1\leq L\leq 3$ ). We can observe that propagating embeddings across two-hop neighboring nodes brings performance improvement. We also compare our method with the non-propagation variant ( $L=0$ ). The results on three datasets show the effectiveness of encoding high-order relationships between users and items. We also see that by stacking more graph layers, the performance will slightly drop due to the over-smoothing problem of graph neural networks.
图层数量 $L$ 。我们在协同异构图 $\mathcal{G}$ 上进行上下文感知的消息传递。现在，我们通过堆叠更多图层（ $1\leq L\leq 3$ ）来研究模型性能。我们可以观察到，在两跳邻居节点之间传播嵌入能够带来性能提升。我们还将我们的方法与非传播变体（ $L=0$ ）进行了比较。在三个数据集上的结果表明，编码用户和物品之间的高阶关系是有效的。我们还发现，通过堆叠更多图层，由于图神经网络的过平滑问题，性能会略有下降。

Memory Unit Numbers $|\mathcal{M}|$ . In our experiments, the number of memory units $\mathcal{M}$ is searched from { $2^{1}$ , $2^{2}$ , $2^{3}$ , $2^{4}$ }. We can observe that the best performance can be achieved with 8 memory units for encoding relation heterogeneity. Our method leverages the multi-dimensional representation space to capture the semantics of heterogeneous connections by disentangling the implicit factors.
记忆单元数量 $|\mathcal{M}|$ 。在我们的实验中，记忆单元数量 $\mathcal{M}$ 是从 { $2^{1}$ , $2^{2}$ , $2^{3}$ , $2^{4}$ } 中搜索得到的。我们可以观察到，在编码关系异质性的最佳性能下，使用 8 个记忆单元。我们的方法利用多维表示空间，通过解耦隐含因素来捕获异构连接的语义。

Figure 7: Hyper-parameter study on important parametric configurations of DGNN (i.e. the hidden state dimensionality

d

, the number of graph neural iterations

L

, and the number of memory units

|\mathcal{M}|

), in terms of HR@10 and NDCG@10, on Ciao, Epinions, and Yelp datasets.
图 7：在 Ciao、Epinions 和 Yelp 数据集上，关于 DGNN 的重要参数配置（即隐藏状态维度

d

、图神经迭代次数

L

和记忆单元数量

|\mathcal{M}|

）的超参数研究，以 HR@10 和 NDCG@10 为指标。

V-G Model Efficiency Study (RQ6)
V-G 模型效率研究 (RQ6)

We evaluate the model efficiency from two aspects, i.e., the computational cost measured by running time as well as the convergence w.r.t epochs. Two state-of-the-art baselines (i.e., DGCF and HGT) are experimentally compared.
我们从两个方面评估模型效率，即通过运行时间测量的计算成本以及相对于训练轮次的收敛性。实验中比较了两种当前最先进的基线模型（即 DGCF 和 HGT）。

V-G1 Running Time per Epoch
V-G1 每轮训练的运行时间

As shown in Table IV, we can observe that our DGNN can achieve better efficiency compared with the disentangled recommender system (i.e., DGCF) and heterogeneous GNN-based method (i.e., HGT). To be specific, HGT employs the transformer-like multi-head dot-product attention mechanism, which is time-consuming. The larger graph size will result in the increased training time of HGT enormously. In addition, for the method DGCF, the cost associated with the design of recursive routing mechanism is huge, which leads to the heavy computational burden for performing the propagation among multiple user embeddings.
如表 IV 所示，我们可以观察到我们的 DGNN 与解耦推荐系统（即 DGCF）和异构 GNN 方法（即 HGT）相比，能够实现更高的效率。具体来说，HGT 采用了类似 Transformer 的多头点积注意力机制，这非常耗时。更大的图规模会导致 HGT 的训练时间大幅增加。此外，对于 DGCF 方法，与递归路由机制设计相关的成本很高，这导致在多个用户嵌入之间进行传播时计算负担沉重。

Table IV: Running time (seconds) in one epoch for different models.
表 IV：不同模型在一个 epoch 中的运行时间（秒）。

Model	Traning 训练			Testing 测试
Model	Ciao	Epinions	Yelp	Ciao	Epinions	Yelp
DGCF	2.56	63.52	81.15	0.87	14.77	66.57
HGT	4.21	525.94	728.23	0.77	13.55	79.74
DGNN	2.47	31.60	39.50	0.71	7.39	25.57

V-G2 Performance v.s. Number of Epochs
V-G2 性能 v.s. 训练轮数

We evaluate the model performance in terms of HR@10 and NDCG@10 after each training epoch, which shows the performance improvement with the parameter optimization process. We show the results in Figure 8, from which we have the following observations: i) DGNN achieves best performance in all epochs compared to HGT and DGCF. This indicates the effectiveness of our model optimization for parameter inference. The architecture of DGNN not only produces better recommendation accuracy, but also are easier to be optimized. We ascribe this to mapping edge relations into multiple latent spaces with the consideration of relation heterogeneity. ii) Compared to DGCF, the performance of HGT increases faster in the early epochs. This implies the advantages of heterogeneous graph transformer over vanilla GCNs in handling heterogeneous graph structures. The reason for such superiority may be the modeling of heterogeneous semantics and the utilization of multi-head dot-product attention technique.
我们在每个训练轮后评估模型在 HR@10 和 NDCG@10 方面的性能，这显示了随着参数优化过程的性能提升。我们在图 8 中展示了结果，从中我们可以得出以下观察：i) 与 HGT 和 DGCF 相比，DGNN 在所有轮次中均实现了最佳性能。这表明我们模型优化参数推理的有效性。DGNN 的架构不仅产生了更好的推荐准确率，而且更容易进行优化。我们将此归因于将边关系映射到多个潜在空间，并考虑了关系异构性。ii) 与 DGCF 相比，HGT 在早期轮次中的性能提升更快。这表明异构图转换器在处理异构图结构方面优于普通的 GCN。这种优越性的原因可能是对异构语义的建模以及多头点积注意力技术的利用。

V-H Case Study (RQ7)
V-H 案例研究 (RQ7)

In this section, we conduct case study from two aspects, to investigate the representation ability of DGNN for encoding heterogeneous semantic with disentangled representations.
在本节中，我们从两个方面进行案例研究，以调查 DGNN 对编码异构语义的表示能力，使用解耦表示。

V-H1 Embedding Visualization
V-H1 嵌入可视化

In this part, we project the learned user/item feature vectors into low-dimensional latent space using t-SNE [38]. The embedding visualization results are presented in Figure 9. Different colors in this figure show different users (stars) and their interacted items (circles). The user embeddings encoded by KGAT, HAN and our DGNN method are shown in Figure 9 (a)-(c), respectively. From the results, we summarize the following observations:
在本部分，我们使用 t-SNE [ 38]将学习到的用户/物品特征向量投影到低维潜在空间。嵌入可视化结果展示在图 9 中。该图中的不同颜色表示不同的用户（星号）及其交互的物品（圆圈）。KGAT、HAN 和我们的 DGNN 方法的用户嵌入分别展示在图 9 (a)-(c)中。从结果中，我们总结了以下观察：

•

The better node separation phenomenon of heterogeneous graph neural network (HAN) as compared to knowledge-aware recommender (KGAT), indicating that the exploration of item-wise relationships with social effects will improve the discriminative ability of user preference embeddings.
与知识感知推荐器（KGAT）相比，异构图神经网络（HAN）表现出更好的节点分离现象，表明探索物品间具有社交效应的关系将提高用户偏好嵌入的判别能力。
•

Given interaction patterns over different items of those sampled users, it is obvious that our DGNN separates users better than other baselines. Also, the item nodes with same colors are commonly distributed around the related user in the center. The low-dimensional representation clearly shows the better ability of DGNN in preserving the user-item relatedness. This superior representation ability should be attributed to the joint modeling of user-user and item-item dependencies, as well as the multi-channel disentangled projection via disentangled graph neural networks.
通过分析这些采样用户在不同物品上的交互模式，可以明显看出我们的 DGNN 比其他基线模型更好地分离用户。此外，具有相同颜色的物品节点通常分布在中心相关用户周围。低维表示清晰地展示了 DGNN 在保留用户-物品相关性的能力上表现更优。这种优越的表示能力应归因于用户-用户和物品-物品依赖的联合建模，以及通过解耦图神经网络实现的多通道解耦投影。

V-H2 Memory Attention Visualization
V-H2 Memory Attention 可视化

Next, we visualize the learned attention weights over different memory units for different heterogeneous relations, to validate if the edge-type-specific memory attention of users reflect the corresponding user-wise relations. Specifically, we train a neural network to map the attention vectors $[\eta(\textbf{H}^{(L)}[u_{i}],1),...,\eta(\textbf{H}^{(L)}[u_{i}],m),...,\eta(\textbf{H}^{(L)}[u_{i}],M)]$ into three-dimensional vectors corresponding to RGB color values. The mapping function is trained with self-discrimination task, so that the memory attention weights can be visualized with the original user-memory connections preserved. We randomly pick two closely-connected user-wise subgraphs from Ciao data, one of which contains only social ties, and another one contains only co-interaction relations. The subgraphs are shown in Figure 10, where circles represents users with their color denoting the learned memory attention weights. The lines denote the heterogeneous user-wise connections. The embedding visualization is conducted for both the user-user relations, and the user-item relations.
接下来，我们可视化不同异构关系下不同记忆单元的学习到的注意力权重，以验证用户特定边型的记忆注意力是否反映了相应的用户关系。具体来说，我们训练一个神经网络将注意力向量 $[\eta(\textbf{H}^{(L)}[u_{i}],1),...,\eta(\textbf{H}^{(L)}[u_{i}],m),...,\eta(\textbf{H}^{(L)}[u_{i}],M)]$ 映射为对应 RGB 颜色值的三维向量。该映射函数通过自判别任务进行训练，以便在保留原始用户-记忆连接的同时可视化记忆注意力权重。我们从 Ciao 数据中随机挑选两个紧密连接的用户子图，其中一个只包含社交关系，另一个只包含共同交互关系。这些子图显示在图 10 中，其中圆圈代表用户，颜色表示学习到的记忆注意力权重。线条表示异构用户连接。用户-用户关系和用户-物品关系的嵌入可视化均进行了处理。

From the results, we can clearly observe that users connected by social ties have close user-user memory-unit weights, while they usually have very different user-item memory weights. This pattern also holds for the co-interaction subgraph, where users having co-interactions have similar user-item memory weights, and have very different user-user memory weights. This observation between relation-specific memory weights and relation-specific graph structures, validates the capability of the memory-augmented heterogeneity encoder of our DGNN in capturing node/edge-type-specific semantics by disentangling diverse relational factors.
从结果中，我们可以清晰地观察到，通过社交关系连接的用户具有相近的用户-用户记忆单元权重，而他们通常具有非常不同的用户-物品记忆权重。这种模式也适用于共同交互子图，其中具有共同交互的用户具有相似的用户-物品记忆权重，而具有非常不同的用户-用户记忆权重。这种关于特定关系记忆权重和特定关系图结构的观察，验证了我们 DGNN 的记忆增强异构编码器在通过分离多样化的关系因素来捕获节点/边类型特定语义方面的能力。

VI Conclusion VI 结论

In this paper, we develop a novel Disentangled Graph Neural Network (DGNN) to improve social recommendation with the disentanglement over heterogeneous relations from both user and item domains. Specifically, by integrating the latent memory units into the graph neural network, DGNN could automatically captures heterogeneous structural dependency with disentangled representations. The model differentiates the relation-aware information propagation and aggregation among the correlated users and items over the collaborative heterogeneous graph. Experimental results show that DGNN can lead to significantly better performance compared to state-of-the-arts on several real-world recommendation datasets. In the future, we would like to endow our DGNN with the power of cross-domain knowledge transfer, so as to further improve the model performance for cold-start recommendations. In addition, another potential direction is to explore the heterogeneous relational data under a pre-trained framework to augment the side knowledge learning.
在本文中，我们开发了一种新的解耦图神经网络（DGNN），通过从用户和物品域中解耦异构关系来改进社交推荐。具体而言，通过将潜在记忆单元集成到图神经网络中，DGNN 能够自动捕获具有解耦表示的异构结构依赖。该模型区分了在协同异构图上相关用户和物品之间关系感知信息传播和聚合。实验结果表明，与当前最先进技术相比，DGNN 在多个真实世界推荐数据集上能够显著提高性能。未来，我们希望赋予 DGNN 跨域知识迁移的能力，以进一步提高模型在冷启动推荐中的性能。此外，另一个潜在方向是探索在预训练框架下异构关系数据，以增强侧知识学习。

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	$\displaystyle\xi(u_{i},v_{j})=(\textbf{H}^{}[u_{i}]+\tau(\textbf{H}^{}[u_{i}]))^{\top}\cdot\textbf{H}^{*}[v_{j}]$
	$\displaystyle=\textbf{H}^{\top}[u_{i}]\cdot\textbf{H}^{}[v_{j}]$		(10)
	$\displaystyle+\frac{\textbf{H}^{\top}[v_{j}]}{\|N_{u_{i}}^{S}\|+1}\Bigm{(}\sum_{u_{i}^{\prime}\in N_{u_{i}}^{S}}\textbf{H}^{}[u_{i}^{\prime}]+\textbf{H}^{*}[u_{i}]\Bigm{)}$

Disentangled Graph Social Recommendation ††thanks: †Equal contribution. *Corresponding author: Chao Huang.解耦图社交推荐 ††thanks: †Equal contribution. *Corresponding author: Chao Huang.

Abstract 摘要

I Introduction I 引言

II Related Work II 相关工作

II-A Social-aware Recommendation MethodsII-A 社会感知推荐方法

II-B Graph Neural Network for RecommendationII-B 用于推荐的图神经网络

II-C Disentangled Learning for RecommendationII-C 推荐的解耦学习

II-D Context-aware Recommender SystemsII-D 基于上下文的推荐系统

III Preliminaries III 预备知识

IV Methodology IV 方法论

IV-A Collaborative Heterogeneous GraphIV-A 协同异构图

IV-B Disentangled Heterogeneous Graph Memory NetworkIV-B 解耦异构图记忆网络

IV-B1 Memory-Augmented Relation Heterogeneity EncoderIV-B1 增强记忆关系异构编码器

IV-B2 Message Aggregation with Relation HeterogeneityIV-B2 基于关系异构的消息聚合

IV-C Model Forecasting PhaseIV-C 模型预测阶段

IV-D Model Efficiency AnalysisIV-D 模型效率分析

IV-D1 Time Complexity AnalysisIV-D1 时间复杂度分析

IV-D2 Space Complexity AnalysisIV-D2 空间复杂度分析