A Survey on Recommendation Methods Based on Social Relationships

Abstract

With the rapid development of online social networks recently, more and more online users have participated in social network activities and rich social relationships are formed accordingly. These social relationships provide a rich data source and research basis for in-depth study on recommender systems (RSs), while also promoting the development of RSs based on social networks. To solve the problems of cold start and sparsity in RSs, many recommendation algorithms are constantly being proposed. Motivated by the availability of rich social connections in today’s RSs, a large number of recommendation techniques based on social relationships have been proposed recently, achieving good recommendation results, and have become the mainstream research direction in the field of RSs, attracting more and more researchers to engage in this research. In this study, we mainly review and summarize the social relationship-based recommendation methods and techniques in RSs, and study some recent deep social relationship recommendation methods and techniques based on deep learning (DL), including the latest social matrix factorization (MF)-based recommendation methods and graph neural network (GNN)-based recommendation methods. Finally, we discuss the potential impact that may improve the RS and future direction. In this article, we aim to introduce the recent recommendation techniques integrating social relationships to solve data sparsity and cold start, and provide a new perspective for improving the performance of RSs, thereby providing useful resources in the state-of-the-art research results for future researchers.

1. Introduction

As a major filtering tool to solve information overload, RSs can quickly and accurately provide users with items that they may be interested in, greatly reducing their time consumption. They are widely used in fields such as e-commerce, news, education, and online video, bringing great convenience to people’s work and life.

Despite the tremendous success of RSs, a major challenge that still exists is issues of data sparsity and cold start. Faced with extremely sparse data, RSs find it difficult to effectively learn user preferences and therefore cannot effectively recommend items to users. Cold start is an extreme case of sparse data, where new users have little or no feedback on the item, and RSs are unable to learn the users’ true preferences and effectively recommend the items. This has become a major issue in the field of RSs, and many algorithms have been proposed for this purpose, such as collaborative filtering (CF), MF, content-based recommendation, and hybrid recommendation [1,2,3,4].

Traditional recommendation models are usually based on a single factor, such as user rating or user behavior, which often result in inaccurate recommendations due to sparse data or cold start [4,5,6]. Recently, recommendation based on social relationships has become an important development direction in the field of RSs [7]. This is because social relationships not only alleviate the problem of data sparsity, but also can greatly improve recommendation quality by introducing recommendation models as an important factor affecting user behavior. For example, memory-based recommendation methods can predict ratings by balancing the similarity and user trust obtained from ratings, resulting in recommendations [8]. Social MF-based methods integrate trust and friend relationships into matrix decomposition process for recommendations [9,10,11]. DL-based recommendations use social relationships, user features and item features as embedding layers to establish a deep neural network model for prediction and achieve recommendations [12,13,14,15,16,17,18,19,20,21,22].

In this article, we conduct a comprehensive literature survey on social relationship-based RSs, and aim to help researchers understand the development of RSs based on social relationships and the characteristics of various recommendation algorithms, and understand how to solve problems of data sparsity and cold start using social relationships in RSs, providing research ideas for future research work. In this work, we make the following contributions:

• We outline traditional techniques and modern approaches used to alleviate data sparsity and cold start issues.
• When there is a lack of user rating information, we focus on how to use social relationships to create recommendation models based on social relationships.
• We summarize various recommendation methods for integrating social relationships, including MF, factorization machine (FM), DL, and GNN.

The remainder of this survey is organized as follows: in Section 2 we conduct a literature review. Section 3 provides an basic framework of a social relationship-based RS and the formal definition of a social relationship-based RS. Section 4 discusses the recommendation technology based on social relationships. Section 5 discusses the future research directions. Section 6 provides a discussion. Section 7 concludes this survey article.

2. Literature Review

In this section, we provide a brief historical overview of social relationship-based RSs, including the key milestones and developments, and related technological development on social relationship-based RSs. In addition, we compare this article with other surveys, and introduce our survey method in this article.

2.1. The Overview of Social Relationship-Based RSs

The recommendation algorithm was first proposed by Xerox’s Paraoto Research Center in 1992, which is an RS based on CF algorithms for spam filtering. In 2003, Amazon truly applied recommendation algorithms to the commercial field. Netflix proposed MF technology in 2006, effectively solving the above problems. MF has a strong generalization ability, but it requires a large amount of computation and is not suitable for dealing with large-scale sparse matrices. In 2007, a trust-aware CF recommendation algorithm was proposed, which is a memory-based CF recommendation algorithm that integrates the user’s trust propagation mechanism into the CF recommendation algorithm [23]. In 2009, a probability factor factorization model was proposed, which fuses user interests with the preferences of trusted friends. Osaka University proposed the FM model in 2010, which can capture second-order features well, and has some mathematical skills. The algorithm has a relatively low time complexity. After 2012, FM gradually became the mainstream algorithm in the recommendation field, until gradient boosting decision tree was applied in the recommendation field [24,25]. In 2019, a new GNN framework for social recommendation was proposed to jointly capture interactions and opinions in user–item graphs, which consistently models two graphs and heterogeneous strengths [26]. The key milestones and developments of social relationship-based RSs is shown in Figure 1. Figure 1 shows representative social relationship-based recommendation techniques from different periods and which publication or conference they were published in. These recommendation techniques are arranged in chronological order.

2.2. Related Technological Development and Related Surveys

To solve the problems of data sparsity and cold start in RSs, a series of recommendation algorithms have been proposed, and the development of RSs has gone through stages such as CF-based RSs, Content-based RSs, Hybrid RSs, and Social relationship-based RSs [6,7,8,9]. Due to the ability of social relationships to alleviate issues of data sparsity and cold start, recommendation based on social relationships dominates. According to the adopted technology, RSs can be divided into following categories [10,11,23].

(1) Recommendation technology based on social MF. Traditional recommendation algorithms suffer from severe impact on recommendation quality due to data sparsity and inconsistency between their assumption of mutual independence among users and the actual situation. With the development of social networks and the introduction of social relationships into MF models, social MF recommendation methods have emerged since 2008. Jamali et al. [27] propose a social network recommendation model based on trust propagation by establishing trust relationships between users and constraining their feature vectors. Ma et al. [28] propose a typical representative of the weighted ensemble method, which considers both the user’s direct predictive ratings of the item and the user’s trusted friend’s ratings of the items. Chen et al. [29] analyze the impact of user cognitive behavior on user preferences from the perspective of social relationship context, and propose an enhanced social recommendation method based on a social relationship context by establishing a social factor enhancement model, namely EnSocialMF. Yang [30] obtained implicit user similarity through explicit user ratings and trust relationships to approximate more accurate user features, thereby improving recommendation accuracy. This method improves prediction accuracy to a certain extent, but does not take into account the negative impact of extremely sparse user trust relationships on user social relationships, as well as the positive impacts of the implicit evaluation of user–item (such as social tags) relationships and the approximate relationship estimation of item–item relationships on recommendation quality.

(2) Recommendation technology based on FM. Although MF can fuse user implicit feedback into the social MF model, which can alleviate the problem of data sparsity to some extent and improve recommendation accuracy, it is difficult to integrate user statistical information (age, gender, region, income, etc.), and its scalability and interpretability are insufficient, limiting its generalization ability to a certain extent. FM can integrate more dimensional features well, resulting in a stronger generalization ability of the learned model. Rendle [24] proposes a new classification and prediction method, which has good prediction performance in sparse data and linear time complexity. Huang [25] proposes feature–over-field interaction FM (FIFM) by fusing feature vectors and class vectors, and pairing the fused vectors to obtain richer interactive semantic information. Starting from the perspective of feature interaction, category interaction, and the interaction between feature-class interaction factor decomposers in sparse scenario prediction in feature-class RSs, FIFM comprehensively obtains various types of interactive information in sparse scenarios, further improving prediction performance. Yan et al. [31] summarize the methods, strategies, and key technologies of the model in terms of width expansion, and compare and analyze the integration methods and characteristics of the FM model with other models, especially the integration with DL models, providing ideas for the deep expansion of traditional models.

(3) Recommendation technology based on DL. FM has good training results and fast training speed when the data are sparse, but its ability to cross-feature is limited, which will limit the mining of deeper data patterns. DL technology can automatically learn and extract data features, and can process large-scale data. Its huge success in computer vision and image processing inevitably affects recommendation systems. Since 2015, recommendation systems based on DL have emerged. In 2016, Google proposed the Wide&Deep [32], marking the beginning of the large-scale application of DL in the field of ctr prediction. The Wide&Deep model is a hybrid model composed of single-layer Wide parts and multi-layer Deep parts. The model can quickly process and remember a large number of historical behavioral features, and has strong expressive ability. It not only quickly became the mainstream model in the industry at that time, Moreover, a large number of hybrid models based on the Wide&Deep model have been derived, and their influence has continued to this day. In 2017, the Huawei Ruoya Ark team proposed a DeepFM [32] model that effectively combines FM with a deep-learning neural network (DNN). It mainly draws on the ideas of Google’s Wide&Deep paper and makes appropriate improvements, replacing the wide part (logistic regression) with FM and DNN for feature intersection. The Wide and Deep parts share the original input feature vectors, which allows DeepFM to directly learn the intersection of low- and high-order features from the original features. In 2017, researchers from the National University of Singapore proposed the NeuralCF [33] model based on DL. NeuralCF is based on two embedding layers, user vector and item vector, and utilizes different interoperability layers for feature cross combination. It can flexibly concatenate different interoperability layers, reducing the complexity of the model.

(4) Recommendation technology based on GNN. The ability of DL to extract complex patterns at the bottom of data is widely recognized. However, it is difficult to learn from graphs that are commonly present in the real world. The graph convolutional network (GCN) [34] is a DL model for graph signals, which has been widely used due to its powerful feature representation ability. In the field of RSs, users and items can be viewed as graph vertices, user ratings of products can be viewed as edges (links), and user and item features can be viewed as signals distributed on the vertex set (graph). This transforms the recommendation problem into a graph link prediction problem. Graph convolutional neural networks have shown more powerful capabilities in learning graph structured data. Due to its superior performance in graph learning, GNN is widely used in RSs. In addition, it has also been applied to many fields, such as text classification, natural language processing, disease prediction, feature relationship extraction, etc. Fan et al. [26] propose a new GNN framework, namely GraphRec, for social recommendation. In particular, a principled method for jointly capturing interactions and opinions in user–item graphs is proposed, which consistently models the strength of two graphs and heterogeneity. Wu et al. [35] propose a deep impact propagation model to simulate how users are influenced by the recursive social diffusion process of social recommendations. For each user, the diffusion process starts with the initial embedding of relevant features and the free user potential vector that captures potential behavioral preferences.

2.3. Recommendation Based on Social Relationships

In real life, people prefer to obtain information or listen to suggestions from users such as friends with similar interests and preferences or friends they trust. Social relationship-based recommendations can generally be divided into friendship-based recommendations and trust relationship-based recommendations.

2.3.1. Friendship-Based Recommendation

Friendship-based recommendations mainly utilize interpersonal relationships on social networks to obtain the strength of friend relationships, namely friendship strength, by discovering potential indirect relationships between users through direct connections or interactions between users and items. Generally, users with strong connections have a greater impact than those with weak connections, which is very useful for improving recommendation quality. The main method is to calculate friendship strength through various implicit data, which is different from the similarity measurement based on rating in CF. For example, Seo et al. [36] propose a personalized RS based on friendship strength by calculating the closeness between users in social networks. Ma [33] proposes a social RS based on social friend interest similarities, and verifies its effectiveness on the Douban dataset and Epinins dataset.

2.3.2. Trust-Based Recommendation

The trust relationship between users is an important social relationship, which is a measure of credibility made by users based on their surrounding environment and historical interaction experience, reflecting to some extent the degree of correlation between users’ interests and preferences. In general, users are likely to be willing to listen to the suggestions of trusted users. The recommendation algorithm based on trust relationships can improve the effectiveness of recommendations to some extent by modeling the impact of user trust relationships on user behavior. Massa et al. propose a trust aware CF-based recommendation method, which comprehensively evaluates user similarity and trust values, and then make recommendations through CF technology. Yang et al. propose a social matrix recommendation method based on user trust relationships by analyzing the relationship between users’ trustors and trustees, mapping user features to a shared space based on user ratings and trust relationships. In addition, Moradi et al. [33] propose a reliability-based trust perception CF-based recommendation method, which utilizes reliability evaluation methods to evaluate the reliability of rating predictions to ensure the accuracy of recommendations.

2.4. Methodology

RSs have been developed since 1992, and there have been many surveys on RSs. In contrast, these surveys have focused on different types of RSs, such as a literature survey on CF-based recommendations [37], survey on MF-based RSs [38], and survey on DL-based recommendations [39]. In addition, there are also some RS surveys that investigate a specific application, such as literature reviews on CF-based RSs for mobile applications.

In this article, we provide a literature survey on RSs on social relationships, which does not appear in current publications on this topic. This article aims to help researchers understand the development of social relationship-based recommendation technology and the characteristics of various technologies, and understand how to integrate various social relationships into recommendation models to solve data sparsity and cold start problems in RSs.

The selection of relevant publications in social relationship-based RSs was conducted from the Science Direct Electronic Journal Full Text Database and Springer electronic Journal database by using the keywords “social recommendation” and “recommender systems”. Moreover, our survey of the literature also included the latest popular social recommendation methods based on GNN. We collected these publications from famous journals and conferences such as SIGIR, RecSys, WWW, KDD, WSDM, IJCAI, CIKM, and DLRS. This process resulted in a selection of 85 articles from 2007 to 2023 for our literature review. These two major journal databases and important conferences have covered most of the high-quality papers in the field of RSs. The articles we selected are mainly SCI papers and important conference papers. We selected articles based on their JCR partition, publication year, and keyword, and the criteria for inclusion of studies are shown in

Table 1. The criteria for the inclusion of studies.

Inclusion Criteria	Inclusion Contents
JCR partition	JCR Q1~Q 4
Important conferences	SIGIR, RecSys, WWW, KDD, WSDM, IJCAI, CIKM, DLRS
Year of publication	2007~2023
Keywords	social recommendation, recommender systems

. Furthermore, we have reviewed related articles in the area of social relationship-based RSs in detail in Section 2.2, and provided details of representative recommendation technology based on social relationships in Section 4.

3. The Basic Framework and the Formal Definition of Social Relationship-Based RSs

3.1. The Basic Framework of Social Relationship-Based RSs

In recent years, domestic and foreign researchers have conducted extensive research on RSs based on social networks and proposed many effective recommendation algorithms. Although these recommendation algorithms use different technologies, the recommendation framework models are all based on the structural characteristics of social networks, the popularity of items in social groups, and the impact of social relationship information between users on recommendation quality [6,8,23,40]. The basic framework of a social network RS is shown in Figure 2, which includes four steps [9,10,32,41]:

(1) Data collection: Attribute information of users and items is obtained, as well as interaction data between users and items (including explicit ratings and implicit interaction information such as clicks, purchases, and favorites), to form a dataset of user and item attributes, as well as a dataset of user–item relationships. At the same time, user social tags, social activity logs, and contextual information are analyzed to form a social relationship dataset.

(2) Data preprocessing: After collecting various user social relationship data, it is necessary to preprocess the data through denoising, dimensionality reduction, and pre-filling, and then input the processed information into the social recommendation model for learning and training to complete the recommendation task. For some pseudo-preference behavior data, correction strategies such as deletion and behavior compensation are used to ensure the reliability of input information [10,36]. For extremely sparse user–item rating matrices, it is necessary to pre-fill missing values using algorithms such as the mean and median [33,42]. For data without explicit ratings, it is necessary to quantify user ratings using user interaction information (such as the Tencent dataset) [34]. Using the user trust relationship dataset to construct a topological structure, sometimes it is necessary to evaluate the reliability of trust relationships and filter out untrusted relationships between users [6,10,43].

(3) The establishment of a recommendation model based on social networks: This is a key aspect of an RS based on social networks. Its main task is to analyze user preference behavior from two aspects: the user–item rating matrix and user social relationships, and consider selecting appropriate recommendation techniques to integrate the impact of user social relationships on recommendation results into the RS. Currently, commonly used recommendation techniques based on social relationships include MF, FM, DL, and GCN. TidalTrust [8] and Reliability-based Trust Perceived CF Recommendation Algorithm (RTCF) [44] are memory-based recommendation methods for social relationships, and MF-based models for recommendation in social networks (SocialMF) and role preferences for trust aware recommendation (RoRec) are MF-based recommendation methods [34,44,45,46].

Social network analysis is a very popular social science research method that studies social phenomena and structures from the perspective of social relationships. Its results are widely applied in recommendation systems based on social relationships, including the currently popular GNN-based RSs.

(4) Presentation and evaluation of recommendation results. The task at this stage is not only to use social recommendation models to predict missing items and recommend items that may be of interest to users based on the prediction results, but also to improve recommendation strategies and methods with the recommendation results based on implicit feedback from users. The evaluation indicators include recommendation accuracy, diversity, coverage, and the availability of RSs [30,42].

3.2. The Formal Definition for Social Relationship-Based RSs

At the 20th International Internet Conference in 2011, the concept of social relationship-based RSs was officially proposed: social network-based recommendation is a recommendation method that primarily processes social media data [47]. The data resources that RSs can utilize not only include user–item rating data that reflect user behavior, but also various user interaction data from social media, such as user clicks, favorites, purchases, shares, user trust relationships, and social tags.

According to the formal definition of traditional RSs, combined with the influencing factors of social relationships, RSs based on social networks can be formally described as follows [48]:

Definition 1. 

An RS based on social networks [23,49]. An RS based on social networks can be represented by a five tuple, i.e., RS = (U, I, S, $\phi$, R), where U, I, and S denotes the user set, item set, and the user social relationship matrix, respectively. Mapping relationship $\phi$: U × I → R represents the evaluation utility function of recommendation results, and R is the recommended utility value, which is a set of non-negative real numbers within a certain range. N = |U|, M = |I|, Y = $\left|\left\{u_y|u_y\in U,s_{xy}\ne 0,{x\ne y,s}_{xy}\in S\right\}\right|$ represents the total number of users who have social relationships with the user. The content of its research is described as follows: in a user group with known social relationships, based on the evaluation of all items in the user group, it actively recommends the item set I* that meets the user’s preference needs and has the highest utility, namely,

$$\forall u_x\in U,I^{*}=\arg {\max }_{i\in I}({\mu }_i+\alpha \phi (u_x,i)+(1-\alpha )\frac{1}{Y}{\displaystyle \sum _y^Y\phi (u_y,i))}$$

(1)

where $\forall \alpha \in \left[0,1\right]$, ${\mu }_i$ represents a bias variable, the larger its value, the more the attention the item has in the user community, and  $\phi$ represents a mapping. The formal description is based on the interaction between the user u_x and the item i, as well as the interaction between the user u_y and the item i to obtain the maximum utility value, thus recommending the corresponding items.

4. Recommendation Technology Based on Social Relationships

According to recommendation strategies, social relationship-based recommendation techniques are divided into memory-based social relationship recommendation methods and model-based social relationship recommendation methods [35,36,50].

4.1. Memory-Based Social Relationship Recommendation Technology

Memory-based social network recommendation, also known as heuristic social network recommendation, mainly combines traditional memory-based CF recommendation technology with social network information, establishes user weight relationships through user rating information and user social relationships, and predicts user preferences for items. Among them, TidalTrust and RTCF are the most representative algorithms.

(1) TidalTrust model [8,11]: This model introduces trust propagation theory into the process of measuring user trust relationships to predict unrated items. The trust relationship is expressed as follows:

$$S_{uv}=\frac{{\displaystyle {\sum }_{w\in F_u^{+}}{S}_{uw}{S}_{wv}}}{{\displaystyle {\sum }_{w\in F_u^{+}}{S}_{uw}}}$$

(2)

Among them, $F_u^{+}$ represents the set of users that user $u_u$ directly trust, and $S_{uw}$ represents the level of trust that user w by user u. The predicted rating of the item i by the user u can be obtained through the following formula:

$${\widehat{r}}_{ui}=\frac{{\displaystyle {\sum }_{v\in D}{s}_{uv}{r}_{vi}}}{{\displaystyle {\sum }_{v\in D}{s}_{uv}}}$$

(3)

Here, $r_{vi}$ denotes the rating of user u on item i, and D denotes the maximum depth set of user trust relationships.

(2) Trust-aware-based recommendation algorithm (TAR) [11]: this algorithm proposes a weighted measure that combines rating similarity and user trust relationships:

$$w_{uv}=\alpha \cdot si{m}_{uv}+(1-\alpha )\cdot T_{uv}$$

(4)

where $\alpha \in [0,1]$, T_uv represents the degree to which the user v is trusted by the user u.

(3) RTCF [44]: This method first estimates missing user trust relationships based on the trust propagation mechanism, then uses rating information and trust relationships to obtain weights between users, predicts user ratings, evaluates the reliability of the predicted ratings, and finally reconstructs the trust network for rating prediction. The weight calculation formula between two users is as follows:

$$w_{uv}=\{\begin{array}{ll}\frac{2·s_{uv}·t_{uv}}{s_{uv}+t_{uv}},& if s_{uv}+t_{uv}\ne 0, and s_{uv}·t_{uv}\ne 0\\ s_{uv},& else if s_{uv}\ne 0,and t_{uv}=0\\ t_{uv},& else if s_{uv}=0,and t_{uv}\ne 0\\ 0,& else\end{array}$$

(5)

Among them, $s_{uv}$ represents the degree to which the user v is trusted by the user u, and $t_{uv}$ represents the range of values for both is [0, 1].

4.2. Model-Based Social Relationship Recommendation Technology

Due to the excellent performance of MF models in RSs, many scholars incorporate social relationships into MF models and use MF technology to map user–item historical rating information and user social relationships to a shared user feature space. This enables the more accurate prediction of missing rating information through the obtained user potential feature matrix and item potential feature matrix [31,33,35,37,50]. For example, in order to improve the accuracy of recommendations, references [10,11,32,34,42,44] consider factors such as user trust, friend relationships, and the mutual influence of interest preferences in the modeling process to obtain accurate user and item features. Since Ma et al. proposed a social recommendation using probabilistic factor analysis (SoRec) in 2008, domestic and foreign scholars have successively proposed a series of recommendation models based on social networks [8,9,10,11,33,45,47,49,51,52,53,54].

4.2.1. MF Technology Based on Social Relationships for Recommendation

The MF recommendation method that integrates social relationships not only considers the preferences and interests of neighboring users on the item, but also considers the impact of users’ social network information (such as trust relationships, friend relationships, and colleague relationships) on user preferences and behaviors. It integrates various social network information into the optimization process of the matrix, learns user historical behavior and social association information, and optimizes the potential feature vectors of users to obtain more accurate prediction scores and improve recommendation quality. This recommendation method can be formalized as [11,51,55]

$$\underset{U,V,\Omega }{\min }{‖W\Theta (R-U^{T}V‖}_F^2+\alpha Social(S,C,\Omega )+\lambda ({‖U‖}_F^2+{‖V‖}_F^2+{‖\Omega ‖}_F^2)$$

(6)

where $Social(S,C,\Omega )$ describes the various social relationship network information of users, S is the user preference similarity matrix obtained based on user–item rating information, and C is the user social relationship matrix, which is a set of parameters learned from social networks. W is used to control the weight matrix of rating information in the model, Θ represents the Hadamard inner product of two matrices, $\alpha$ is used to control the contribution of social information, λ denotes a regular term parameter, and ${‖·‖}_F^2$ represents the Frobenius norm.

According to the different methods of optimizing and solving latent feature vectors based on social network information, MF methods based on social networks can be divided into the following three categories [8,32]: the weighted integration, collaborative factorization, and regularization methods.

(1) Weighted integration method: The integration method is to use the linear superposition of user ratings with the same preferences and ratings with trusted users to predict unrated items. For example, the Recommended Social Trust Ensemble (RSTE) proposed in reference [28] is a typical representative of the weighted ensemble method, which considers both the user’s direct predictive rating of the item and the user’s trusted friend’s rating of the item. The conditional probability distribution of existing ratings is as follows:

$$p(R|S,U,V,{\sigma }_R^2)={\displaystyle \prod _{u=1}^N{\displaystyle \prod _{i=1}^M{\left[N(r_{ui}|g({\displaystyle \sum _{k\in T(u)}{S}_{uk}{U}_k^T{V}_i),{\sigma }_R^2}\right]}^{I_{ui}^R}}}$$

(7)

where $T(u)$ represents the set of friends trusted by user u, and $S_{uk}$ represents the trust relationship between user u and his friend k. By comprehensively considering the rating information of user u and trusted friend k on item i, the final predicted rating of user u on item i is as follows:

$${\widehat{r}}_{ui}=\alpha U_u^T{V}_i+(1-\alpha ){\displaystyle \sum _{k\in T(u)}{S}_{uk}{U}_k^T}{V}_i$$

(8)

Here, $\alpha$ is used to control the current user’s rating of the item and the degree of influence of the rating of the item from their trusted friends.

Reference [56] combines trust propagation mechanisms with traditional user–item rating and trust relationships, and proposes a personalized recommendation model fusing trust relationship based on comprehensive evaluation (CETrust). This model weights the similarity of users’ ratings and trust relationships, and considers users with higher rating and trust values as close neighbors. The CETrust algorithm predicts users’ ratings for items as follows:

$${\widehat{r}}_{ui}=\alpha U_u^T{V}_i+(1-\alpha )\frac{{\displaystyle \sum _{k\in T(u)}{T}_{uk}^{*}{U}_k^T}{V}_i}{{\displaystyle \sum _{k\in T(u)}{T}_{uk}^{*}}}$$

(9)

where $T_{uk}^{\ast }$ represents the comprehensive trust degree between user u and user v in social networks.

Reference [57] utilizes trust relationships between users to optimize user characteristics and user–item rating space, and proposes a context-aware social recommendation using individual trust (CSIT) based on trust relationships:

$$\begin{array}{l}L(R,U,V,T)=\frac{1}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{i=1}^M{I}_{ui}^R}}{(r_{ui}-g(\alpha U_u^T{V}_i+(1-\alpha ){\displaystyle \sum _{\left\{f\right|f\in N_u\}}{T}_{uf}{U}_f^T{V}_i}))}^2\\ +\frac{{\lambda }_f}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{\left\{f\right|f\in N_u\}}{T}_{uf}}(U_u}-U_f{)}^2+\frac{{\lambda }_U}{2}{‖U‖}_F^2+\frac{{\lambda }_U}{2}{‖V‖}_F^2\end{array}$$

(10)

(2) Collaborative factorization method: Collaborative factorization is the use of user rating information and social relationships to jointly optimize the shared user feature space, thereby obtaining more accurate user preferences. The most representative ones are the MF models based on trust propagation proposed by Yao and Ma et al.: RoRec [46] and SoRec [47].

Yao et al. divided users into trustor users and trusted users, modeled users’ predictive ratings for items from the perspectives of their trustors and trusted users, and proposed the RoRec model based on user role preferences [46]:

$$\begin{array}{l}L(R,T,W,E,V)=\frac{1}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{i=1}^M{I}_{ui}^R}}{(r_{ui}-g(\alpha W_u^T{V}_i+(1-\alpha )E_u^T{V}_i))}^2\\ +\frac{1}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{k=1}^N{I}_{uk}^S}}{(S_{uk}-{\widehat{S}}_{uk})}^2+\frac{{\lambda }_W}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{j=1}^N{C}_{uj}^{(W)}}(W_u}-W_j{)}^2\\ +\frac{{\lambda }_E}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{j=1}^N{C}_{uj}^{(E)}}(E_u}-E_j{)}^2 +\frac{\lambda }{2}({\displaystyle \sum _{u=1}^N{W}_u^T{W}_u}+{\displaystyle \sum _{k=1}^N{E}_k^T{E}_k}+{\displaystyle \sum _{i=1}^M{V}_i^T{V}_i})\end{array}$$

(11)

where ${\widehat{S}}_{uk}=g(W_u^T{E}_k)$. $W_u\in R^K$ and $E_u\in R^K$ are the preference feature vectors of the trustor and the trustee with the user’s dimension k, respectively. $C_{uj}^{(W)}$ represents the preference similarity between two trusted users, and $C_{uj}^{(E)}$ represents the preference similarity between two trusted users.

Ma et al. combined users’ social networks with user–item rating information and proposed the SoRec model based on user social relationships [47]:

$$\begin{array}{l}L(R,C,U,V,Z)=\frac{1}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{i=1}^M{I}_{ui}^R}}{(r_{ui}-g(U_u^T{V}_i))}^2+\frac{{\lambda }_C}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{k=1}^N{I}_{uk}^C}}{(C_{uk}-g(U_u^T{Z}_k))}^2\\ +\frac{{\lambda }_U}{2}{\displaystyle \sum _{u=1}^N{U}_u^T{U}_u}+\frac{{\lambda }_V}{2}{\displaystyle \sum _{i=1}^M{V}_i^T{V}_i}+\frac{{\lambda }_Z}{2}{\displaystyle \sum _{k=1}^N{Z}_k^T{Z}_k}\end{array}$$

(12)

where $C_{uk}$ denotes the social network relationship between users u and k, and $Z_k$ denotes the feature vector of user k auxiliary factors.

(3) Regularization method [8,11,29,58]: The regularization method constrains the preferences of user features in social networks by utilizing the approximation degree of two user or item features to approximate real user features. SocialMF [27], Average-based Social Regulation (ASR), and Individually based Social Regularization (ISR) are typical representatives of recommendation methods based on social networks. Considering the impact of social networks on user preferences, Ma et al. proposed the ASR method based on social relationship regularization, which utilizes the average preference influence of friends in social networks to constrain the matrix decomposition process, based on the viewpoint that user decisions are likely to come from valuable suggestions from friends.

$$\begin{array}{l}L(R,T,U,V)=\frac{1}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{i=1}^M{I}_{ui}^R}}{(r_{ui}-g(U_u^T{V}_i))}^2+\frac{{\lambda }_U}{2}{\displaystyle \sum _{u=1}^N{U}_u^T{U}_u}+\frac{{\lambda }_V}{2}{\displaystyle \sum _{i=1}^M{V}_i^T{V}_i}\\ +\frac{{\lambda }_F}{2}{{\displaystyle \sum _{u=1}^N‖U_u-\frac{{\displaystyle \sum _{f\in F^{+}(u)}sim(u,f)*U_f}}{{\displaystyle \sum _{f\in F^{+}(u)}sim(u,f)}}‖}}_F^2\end{array}$$

(13)

Here, $F^{+}(u)$ denotes the set of friends of user u; $sim(u,f)$ is the similarity function, and denotes the similarity between users u and v.

To reflect user personalized preferences, Ma proposed the ISR method based on individual user interests:

$$\frac{{\lambda }_F}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{f\in F^{+}(u)}sim(u,f)}||U_u-U_f|{|}_F^2}$$

(14)

Jamali et al. proposed the SocialMF model based on trust propagation by establishing trust relationships between users and constraining their feature vectors [27]:

$$\begin{array}{l}L(R,T,U,V)=\frac{1}{2}{\displaystyle \sum _{u=1}^N{\displaystyle \sum _{i=1}^M{I}_{ui}^R}}{(r_{ui}-g(U_u^T{V}_i))}^2+\frac{{\lambda }_U}{2}{\displaystyle \sum _{u=1}^N{U}_u^T{U}_u}+\frac{{\lambda }_V}{2}{\displaystyle \sum _{i=1}^M{V}_i^T{V}_i}\\ +\frac{{\lambda }_F}{2}{\displaystyle \sum _{u=1}^N((U_u-{\displaystyle \sum _{v\in N_u}{T}_{uk}{U}_k{)}^T(}}{U}_u-{\displaystyle \sum _{v\in N_u}{T}_{uk}{U}_k}))\end{array}$$

(15)

where $T_{uk}$ represents the degree to which user v is trusted by user u, and ${\displaystyle \sum _{k=1}^N{T}_{uk}=1}$.

Subsequently, some improved social MF recommendation algorithm models have been successively proposed, such as SocialIMF [59], EnSocialMF [29], and TrustPMF [30]. Among them, SocialMF obtains implicit user similarity through explicit user ratings and trust relationships to obtain more accurate user features. EnSocialMF incorporates social factor enhancement models into MF models by establishing them. TrustPMF introduces user ratings and trust relationships into the social relationship MF model, and introduces the influence of regularization factors.

4.2.2. FM Technology Based on Social Relationship for Recommendation

FM is one of the important models for predicting the click-through rate (CTR). Since its proposal in 2010, it has received large-scale support and is also one of the methods used by Meituan and Toutiao to make recommendations and CTR estimates. The FM was first proposed by Steffen Rendle at the Industrial Conference on Data Mining in 2010. It is a universal prediction method that can estimate reliable parameters and make predictions even when data are very sparse [24].

The logistic regression (LR) model is the earliest and most successful model in the field of CTR estimation. Most industrial recommendation ranking systems integrate artificial nonlinear features. However, the biggest drawback of the LR model is that it requires manual feature design and consumes a lot of human resources to filter and combine nonlinear features. By adding second-order features to the calculation formula of the linear model, any two features are paired and added to the linear model to obtain the following model:

$$\widehat{y}(x)=w_0+{\displaystyle \sum _{i=1}^n{w}_i{x}_i}+{\displaystyle \sum _{i=1}^{n-1}{\displaystyle \sum _{j=i+1}^n<p_i,p_j>x_i{x}_j}}$$

(16)

In the above model, any two features intersect in pairs, where n denotes the number of features, x_i represents the i-th feature value, and p_i and p_j represent the inner product of the item’s feature vectors, respectively.

FM can be seen as a special case of Field-aware FM (FFM), which refers to the FFM model where all features belong to one field. Based on the field sensitivity of FFM, its model equation can be derived [24]:

$$\widehat{y}(x)=w_0+{\displaystyle \sum _{i=1}^n{w}_i{x}_i}+{\displaystyle \sum _{i=1}^{n-1}{\displaystyle \sum _{j=i+1}^n<p_{i,f_j},p_{j,f_i}>x_i{x}_j}}$$

(17)

where f_j is the field to which the jth feature belongs. If the length of the hidden vector is k, then there are nfk quadratic parameters in FFM, far more than nk in the FM model.

DeepFM [32] is a deep model proposed by Huawei for solving CTR problems. DeepFM is based on Google’s Wide&Deep model and introduces the FM algorithm to the Wide side, replacing the LR model in the original Wide&Deep model. It can achieve end-to-end-learning feature crossover without the involvement of artificial feature engineering.

DeepFM consists of two parts: a neural network and a FM machine, which are responsible for extracting low-order features and high-order features, respectively.

$$y_{DNN}=\sigma (W^{\left|H\right|+1}\cdot a^H+b^{\left|H\right|+1})$$

(18)

The final output of DeepFM is as follows:

$$\widehat{y}=sigmoid(y_{FM}+y_{DNN})$$

(19)

4.2.3. DL Technology Based on Social Relationship for Recommendation

DL combines low-level features to form more dense high-level semantic abstractions, automatically discovering distributed feature representations of data, solving the problem of manually designing features in traditional machine learning. The DL-based RS usually takes various types of users and items as input, uses DL models to learn implicit representations of users and items, and generates item recommendations for users. The DL-Based recommendation framework integrating social relationships is shown in Figure 3.

Overall, DL-Based recommendation models are constructed by the cross-fusion of high-order and low-order features, which can be roughly divided into two methods: serial structure and parallel structure. Typical representatives of serial structures include Product-based Neural Networks (PNN) [51], Neural FM (NFM) [42], and FM models that combine Attention networks (AFM) [35], while typical representatives of parallel structures include Wide&Deep, DeepFM, Deep&Cross Network (DCN), NeuMF, and NeuralCF.

(1) Serial structures

• PNN

The PNN model includes an embedding layer to learn the distributed representation of category data, a product layer to capture feature interaction patterns between fields, and a fully connected layer to mine higher-order feature interactions.

The innovation of the PNN model in the DL structure is mainly reflected in the introduction of the Product layer, which is composed of l_Z and l_p. The inner product operation of vectors is as follows:

$$\mathrm{A}\odot \mathrm{B}\triangleq \sum _{i,j}{A}_{ij}{B}_{ij}$$

(20)

Calculate ${\mathrm{l}}_z$ and ${\mathrm{l}}_p$ through z and $\mathrm{p}$ as follows:

$$l_{z=}{W}_z\odot \mathrm{Z}$$

(21)

$$l_{p=}{W}_p\odot \mathrm{p}$$

(22)

where ${\mathrm{W}}_z$ and ${\mathrm{W}}_p$ are the weight parameters of the product layer, respectively, and their shape depends on z and p, respectively.

The outputs of the hidden layers l₁ and l₂ are obtained by the following formulas, respectively:

$$l_{1=}relu(l_z+l_p+b_1)$$

(23)

$$l_{2=}relu({W_{2}l}_1+b_2)$$

(24)

At the output layer, the output of the PNN model is a real number in the range of (0, 1), representing the click through rate. The calculation method is as follows:

$$\widehat{y}=\sigma ({W_{3}l}_2+b_3)$$

(25)

Among them, $W_3$ and $b_3$ are the parameters of the output layer, and $l_2$ is the output of the second hidden layer.

• NFM

NFM is used to solve the problem of sparse prediction. It is mainly applied in scenarios where input data are particularly sparse and feature combinations are crucial for predicting results.

NFM can be formalized as follows [42]:

$${\widehat{y}}_{NFM}\left(x\right)=w_0+\sum _{i=1}^n{w}_i{x}_i+f\left(x\right)$$

(26)

where $f\left(x\right)$ is the core of NFM, used to learn second-order combined features and higher-order combined feature patterns.

Considering the weight matrices of the hidden layers in the previous layers, f (x) is formalized as follows:

$${\widehat{y}}_{NFM}\left(x\right)=w_0+{\sum }_{i=1}^n{w}_i{x}_i + h^T{\sigma }_L(W_L\left(\dots {\sigma }_1\left(W_1{f}_{BI}\left(V_x\right)+b_1\right)\dots \right)+b_L)$$

(27)

• AFM

The essence of AFM model design is that FM models that combine attention networks can learn the weight coefficients of second-order cross features. The purpose of the pair-wise interaction layer is to express the computational logic of FM in neural networks [35,60]:

$$\widehat{y}=p^T{\sum }_{(i,j)\in R_x}\left\{(v_i\odot v_j)x_i{x}_j\right\}+b$$

(28)

Here, p and b represent the weight and bias values of the prediction network, respectively.

The output of the attention-based pooling layer is a k-dimensional vector that compresses all feature interactions by distinguishing their respective importance in the embedded space, and then maps these to the final prediction result. The complete formula of the AFM model is as follows:

$${\widehat{y}}_{AFM}\left(x\right)=w_0+\sum _{i=1}^n{w}_i{x}_i+p^T\sum _{i=1}^n\sum _{j=i+1}^n{a}_{ij}\left(v_i{\odot v}_j\right)x_i{x}_j$$

(29)

The previous part is a linear part, and the latter part performs element-wise product on every two embedded vectors to obtain the interacted vector. Then, the attention mechanism is used to obtain the attention score for each combined feature.

(2) Parallel structures

• Wide&Deep

The Wide&Deep [36] model achieves both memory and generalization in a single model through the collaborative training of a linear model module and a neural network module. Wide exhibits good memory ability, while Deep exhibits good generalization ability. Wide&Deep combines the advantages of both.

The final prediction output is as follows [36]:

$$p(y=1|x)=\sigma (w_{wide}^T[x,\varphi (x)]+w_{deep}^T{a}^{l_f}+b)$$

(30)

Among them, $y$ represents the binary class label, $\sigma$ represents the sigmoid function, $\phi \left(x\right)$ represents the cross product transformation of the original feature, b is the deviation term, and $a^{l_f}$ represents the activation value of the last layer of NN. ${\mathrm{w}}_{wide}$ is the weight vector of all wide models, and $w_{deep}$ is the weight of $a^{l_f}$.

• DCN

The advantage of the DNN model in ctr estimation algorithm lies in its powerful learning ability, which can learn feature combinations to a certain extent. The implementation of the cross network is calculated by the following formula [31]:

$$x_{l+1}=x_0{x}_l^T{w}_l+b_l+x_l=f\left(x_l,w_l,b_l\right)+x_l$$

(31)

Like FM, DCN is also based on parameter sharing mechanism.

• NeuralCF

NeuralCF [33] uses the embedding layer to simulate MF, obtain hidden vectors for users and items, then cross the hidden vectors through the fully connected layer for features, and finally output predicted values.

It concatenates the hidden vectors of users and items, inputs them into the fully connected layer for feature crossover, and the specific forward propagation process is as follows [33]:

$$z_1={\mathrm{\varnothing }}_1\left(p_u,q_i\right)=\left[\begin{array}{c}{p}_u\\ q_i\end{array}\right]$$

(32)

$${\mathrm{\varnothing }}_2\left(z_1\right)={a_2(W}_2^T{z}_1+b_2)$$

(33)

$${\mathrm{\varnothing }}_L\left(z_{L-1}\right)={a_L(W}_L^T{z}_{L-1}+b_L)$$

(34)

$${\widehat{y}}_{ui}=\sigma \left(h^T{\mathrm{\varnothing }}_L\right(z_{L-1}\left)\right)$$

(35)

Among them, $a_L$ and h are the activation functions of the output layer.

• NeuMF

NeuMF is obtained by combining GMF and MLP, which concatenates the output results of GMF and MLP, and then the concatenated results are further processed through a fully connected layer for more sufficient feature crossing. Finally, the activation function is used to output the final prediction result. The forward propagation process is as follows [58,61]:

$${\mathrm{\varnothing }}^{GMF}=p_u^G\odot q_i^G$$

(36)

$${\mathrm{\varnothing }}^{MLP}={a_L(W}_L^T{(a}_{L-1}(\dots {(a}_2(W_2^T\left[\begin{array}{c}{p}_u^T\\ q_i^T\end{array}\right]+b_2)\dots ))+b_L)$$

(37)

$${\widehat{y}}_{ui}=\sigma \left(h^T\left[\begin{array}{c}{\mathrm{\varnothing }}^{GMF}\\ {\mathrm{\varnothing }}^{MLP}\end{array}\right]\right)$$

(38)

4.2.4. GNN Technology Based on Social Relationship for Recommendation

In recommendation algorithms based on graph convolutional neural networks, some algorithms do not directly use the GCN method, but instead integrate GCN with graph embedding, thereby improving the efficiency of the entire model.

The principle of GNNs is mainly as follows: firstly, a graph structure model is constructed to reflect the relationship between entities; then, specific methods are used to describe the nodes and obtain nodes that contain the final neighbor-node information and topology characteristic states. This node has undergone continuous updating iterations. Finally, the representation of these nodes will be output in a specific way and the required information will be obtained.

• GraphRec

GraphRec provides a principled approach to jointly capture interactions and opinions in user–item graphs, and introduces a mathematical approach that considers the heterogeneous strength of social relationships.

The model contains three components: user modeling, item modeling, and rating prediction [43,56]. Among them, the user model aims to learn implicit features of users from user relationship diagrams and user–item relationship diagrams. The item model aims to learn the implicit features of items from their relationship diagrams. The rating prediction is achieved by integrating user modeling and item modeling.

$$h_i^S=\sigma \left(W·\left\{\sum _{o\in N\left(i\right)}{\beta }_{io}{h}_o^I\right\}+b\right)$$

(39)

$$z_j=\sigma \left(W·\left\{\sum _{t\in B\left(j\right)}{\mu }_{jt}{f}_{jt}\right\}+b\right)$$

(40)

$${\widehat{r}}_{ij}=w^T·g_{l-1}$$

(41)

Here, the βio denotes the strengths between users, ${\mu }_{jt}$ denotes the user attention, and ${\widehat{r}}_{ij}$ denotes the predicted rating from the user u_i to the item v_j.

• GDSRec

GDSRec [43] is a novel GNN-based social recommendation model to solve user and item bias problems. It is learned on the decentralized graph with distinct differentiable social connection strengths.

$${\mathrm{h}}_{ui}=Tanh\left(W·\left\{\sum _{v_l\in R\left(u_i\right)}{\rho }_{il}{x}_{il}\right\}+b\right)$$

(42)

$${\mathrm{h}}_{vj}=Tanh\left(W·\left\{\sum _{u_k\in R\left(v_j\right)}{\epsilon }_{jk}{y}_{jk}\right\}+b\right)$$

(43)

$${\mathrm{z}}_k=Tanh\left(W_1·\left[h_{ui}{\odot h}_{vj}\right]+b\right)$$

(44)

$${\widehat{r}}_{ij}=w^T·z_k$$

(45)

Among them, ${\mathrm{h}}_{ui}$ represents the latent factor offset for the user u_i, and ${\mathrm{h}}_{vj}$ represents the latent factor offset of the item v_j.

• HeteGraph

For processing and training complex large-scale heterogeneous graph data, Tran et al. proposed a novel framework based on the GCN principle—recommendation framework for heterogeneous graph structured data (HeteGraph) [62,63,64]. It learns node embedding of high-quality graphs through a sampling technique and a graph convolution operation. This is different from traditional GCN, which requires a complete graph adjacency matrix for embedding learning. The framework designs two models to evaluate RS tasks, namely rating prediction and diversified item recommendation.

The HeteGraph recommendation framework is divided into three stages: node neighborhood sampling, graph convolutional operation, and embedding learning strategy [62,63].

$${\mathrm{f}}_{{PO}_n}=mean\left(\sigma (W^{pool}·f_{{NB}_n})\right)$$

(46)

$$mean\left(\left[\begin{array}{ccc}{x}_{11}& \cdots & x_{1m}\\ ⋮& \ddots & ⋮\\ x_{n1}& \dots & x_{nm}\end{array}\right]\right)=\left[\begin{array}{ccc}\frac{\sum _{i=1}^n{x}_{i1}}{n}& \dots & \frac{\sum _{i=1}^n{x}_{im}}{n}\end{array}\right]$$

(47)

Here, $W^{pool}$ denotes the weight parameter, and $f_{{PO}_n}$ denotes the aggregated neighborhood tensor.

4.2.5. Comparison of Several Recommendation Methods Based on Social Relationships

Overall, among the five types of RS methods based on social relationships mentioned above, graph convolutional neural networks have better performance by integrating the advantages of several methods.

Table 2. The comparative analysis of several representative recommendation methods based on social relationships.

Category	Model	Problems	Solutions	Advantages	Disadvantages
Basic MF	PMF [56]	large-scale, sparse, and imbalanced data	Optimize Regularized MF	PMF perfectly solves the shortcomings of SVD with smaller errors.	The training of the model is quite time-consuming
	NMF [39]	Not handling missing values	Constrain the decomposed factors to be non-negative	NMF has high interpretability and is particularly suitable for implicit feedback matrices that represent positive preferences in ratings.	This model may increase the error of unobserved items.
MF for social relationships	SocialMF [27]	Cold start	Incorporate the influence of trust propagation to connect user vectors with their neighbors’ feature vectors	SocialMF can significantly reduce recommendation errors (RMSE), especially for cold start users	The model requires explicit trust relationships
	SoRec [47]	Data sparsity	Propose a factor analysis method based on PMF	SoRec solves the problems of sparse data and inaccurate predictions, and can be applied to very large datasets	This model is prone to overfitting
	RSTE [28]	Data sparsity. The assumption that all users are independent and identically distributed ignores the connections between users	Integrate the tastes of users and the preferences of trusted friends	RSTE blends the preferences of users with those of trusted friends.	This model finds it difficult to balance the weights of ratings and trust relationships
FM	FM [24]	Data sparsity, Independent independence of coefficients	Automatically integrate second-order (higher-order) cross features, eliminating the need for manual feature engineering	FM can perform parameter estimation well in sparse data, and the parameters and operation time are linear	FM cannot perform deep cross over of features
DL	NFM [42]	Sparse features	Combine DNN and FM to learn higher-order features and nonlinear feature crossover	NFM can learn higher-order non-linear feature intersections.	High computational complexity
	NeuralCF [33]	Data sparsity	The multi-layer neural network and output layer replace the inner product operation in MF	NeuralCF improves the model’s expression ability, and has stronger feature combination and nonlinear ability	High computational complexity
	Wide&Deep [36]	Sparse features	Combine shallow and deep models to balance the memory and generalization abilities of the model	Wide&Deep can quickly process and memorize a large number of historical behaviors, and has strong expressive ability	The model has poor generalization ability
GCN	GraphRec [26]	Heterogeneity of user social relationships	Introduce principled methods and attention mechanisms	GraphRec combines heterogeneous graphs to capture the interaction between users and items.	Problems may arise when processing graphics with complex adjacency relationships.
	HeteGraph [63]	Data sparsity, and heterogeneous graphs	propose a sampling technique and graph convolution operation to learn high-quality node embedding	HeteGraph can represent complex interactions in real systems	A large amount of computing resources are required.
	GCN [34]	Interpretability of graphical network decisions	Gradient-based and decomposition-based techniques	GCN can effectively handle heterogeneous graph data	This model is only applicable for handling two entities, namely users and items

presents a comparative analysis of several representative recommendation methods based on social relationships, including model categories, model names, proposed problems, solutions, and advantages and disadvantages of the model.

5. Future Research Directions

Although a series of recommendation technologies such as social MF, FM, and DL have been proposed, and greatly improve recommendation quality, current research still faces challenges such as complex social relationships and dynamic trust. The following are some future research directions and potential solutions.

5.1. The Fusion of Complex Social Relationships with Other Information

With the continuous emergence of complex network data such as social networks and transportation networks, traditional DL methods have gradually exposed limitations in processing graph data. It is a challenge to use DL technology to organically integrate heterogeneous information such as user ratings, social relationships, and comments for interaction [9,10,11]. GNN has a strong representational learning ability for the irregularity and dynamism of graph data. It can capture higher-order interaction relationships in user–item relationships through iterative propagation. Therefore, a hybrid recommendation model that combines MF, DL, and GNN may effectively improve data sparsity and cold start issues in RSs.

5.2. Dynamic Social Relationships in RSs

Traditional recommendation algorithms often consider static relationships between users, while in the real world, social relationships between users change over time. For example, at different times, we may have different groups of friends. In addition, the preferences of different users may change over time. A potential solution is to incorporate temporal factors into recommendation algorithms based on social relationships, and sequence models such as recurrent neural networks can store trust perception information and dynamically update themselves with changes.

5.3. Recommendations That Integrate User Comment Information

User comments contain rich semantic information, which may include users’ evaluations of various aspects such as the color, quality, and price of an item. However, user ratings and social relationships are only the final outcome, from which we find it difficult to know the true preferences of users. For example, does a user like to watch a movie because he/she likes the plot or because he/she likes the actors in the movie? This can only be known through comments. At present, some articles on RSs based on DL have begun to use comment text as a data source for recommendations. In the future, integrating user comments and social relationships will be a mainstream research direction. There is still much work to be done in the application of text mining and sentiment analysis technology for user comments in personalized RSs.

5.4. Privacy Protection in RSs

User attributes and interaction records contain rich personal privacy, and traditional RSs inevitably bring the risk of user privacy leakage. Due to the protection of user privacy by law, social networks and historical orders may not be available [65,66,67,68,69]. The RS based on GNN utilizes higher-order information on the user–item interaction graph for recommendation, but the extraction of higher-order information often comes with a greater risk of privacy leakage. Potential privacy protection technologies can solve the problem of privacy leakage: cryptographic methods (typically using homomorphic encryption (HE) and secure multiparty computation (MPC) techniques to protect intermediate transmission parameters) and the confusion method (adding noise to updated parameters) [70,71,72,73].

5.5. Explainable Recommendation

Although RSs have been successfully applied in many fields, the interpretability of algorithms seriously restricts the promotion of RSs. In particular, the inexplicability of DL makes it difficult for recommendation algorithms based on DL to be applied in broader fields such as healthcare and finance [74,75,76]. Interpretable recommendation systems not only provide recommendations to users, but also increase people’s trust in machine learning algorithms, improving the effectiveness, efficiency, persuasiveness, and user satisfaction of RSs [65].

6. Discussion

Compared with other survey articles, this article is a comprehensive survey article based on social relationship recommendation. The advantage of our work is that it classifies and surveys recommendation methods for social relationships, provides a framework and formal definition of social relationship recommendation systems, summarizes various recommendation techniques for integrating social relationships, and provides representative examples. Although there have been previous review articles on RSs based on social relationships, such as [77], which only reviewed memory-based social relationships and social MF, their introduction was not comprehensive enough and their scope was very limited. Other review articles mainly focused on a specific technology or application for review. The main techniques used in other surveys are shown in

Table 3. The main technical detail in other surveys.

Author	Reference	Technical Details
Yong Zheng	[78]	Provide a comprehensive literature review of the multi-objective RSs.
Manqing Dong	[79]	Provide a systematic summary of three categories of trust issues in RSs.
Xiwang yang	[77]	Introduce two RSs: MF-based social recommendation algorithms and neighborhood-based social recommendation algorithms.
Robin Burke	[80]	Survey the different recommendation techniques, and discuss how adding a hybrid with CF.
Xiaoyuan Su	[81]	Introduce three major categories of CF technologies, memory-based, model-based, and hybrid CF algorithms, with examples for representative algorithms of each category.
He Chen	[82]	Present an interactive visualization framework to solve user control and transparency.
Jiliang Tang	[83]	Provide narrow and broad definitions of social recommendation, and review representative RSs for each category in detail.
Ivens Portugal	[82]	Conduct a systematic review of the literature and analyze the use of various algorithms in RSs.
Liwei Huang	[83]	Analyze the differences and advantages between DL-based RSs and traditional RSs, and compare and analyze their main research directions and application progress.
Guangshang Gao	[84]	Summarize and analyze key strategies, algorithms, or techniques to calculate the weight of the current input data.
Elahi Mehdi	[85]	Survey recent strategies by grouping active learning strategies: personalization and hybridization.

. Our deficiency is that due to space limitations, each social relationship recommendation method was not fully elaborated upon, which is also one aim of our next research work.

7. Conclusions

In this survey, we investigated the state of the art of RSs based on social relationships, and highlighted several important recommendation technologies that integrate social relationships to solve data sparsity and cold start issues, including MF, FM, DL, and GNN. We summarized the related technological development and concluded a literature review on social relationship-based recommendation. For the convenience of readers’ understanding, we provided a basic framework and formal definition of an RS based on social relationships. We classified social recommendation systems based on technology and summarized various social recommendation methods by category, providing representative examples. Based on current research progress, this article provides future research directions, difficulties, and potential solutions for social relationship-based RSs. Finally, there was the discussion section, which included the methods of this survey, the advantages of this survey, and the technical details of other surveys. We believe that the classification and systematization of this research can help us to better understand and use these social recommendation technologies.