A Survey on Cross-domain Recommendation: Taxonomies, Methods, and Future Directions

The first level of the proposed taxonomy is about recommendation scenarios and the classification criteria is the relations between user sets and item sets of two domains. To be more specific, there are two dimensions, that is, the overlap of user sets and the overlap of item sets.

The classification of recommendation scenarios was first proposed by Cremonesi et al. (Cremonesi et al., 2011) in which they identified four different recommendation scenarios (shown in Fig.1 (a)), that is, no overlap, user overlap, item overlap, and full overlap. This classification was widely accepted by subsequent researchers. However, through analysis and summary of recent works, we propose that this classification is coarse-trained and can be further refined. Still considering the relations between user sets and item sets of two domains, we describe these two dimensions in detail as follows.

With these two dimensions, we extend the classification of recommendation scenarios from previous $4$ categories to $9$ categories and show the comparison in Fig. 1. We also present the categorization of existing works according to recommendation scenarios which is shown in Table 1. It is worth noting that there are currently no studies on three scenarios (i.e., user partial overlap $\&$ item partial overlap, user partial overlap $\&$ item full overlap, and user full overlap $\&$ item partial overlap). To ensure the integrity of the tree-structured categorization, we retain these nodes. It should also be pointed out that the recommendation scenario with user non-overlap $\&$ item partial overlap is symmetric to the case with user partial overlap $\&$ item non-overlap. Similarly, the scenario with user non-overlap $\&$ item full overlap is symmetric to the case with user full overlap $\&$ item non-overlap. Most of the approaches proposed for one scenario apply to the other scenario by exchanging users and items. Therefore, we will not discuss in detail the scenarios with user non-overlap $\&$ item partial overlap and user non-overlap $\&$ item full overlap. Moreover, the recommendation scenario with user full overlap $\&$ item full overlap is equivalent to single-domain recommendation and is therefore outside the scope of this paper.

The second level of our proposed taxonomy is about recommendation tasks which also consists of two dimensions. Based on whether the recommended items are in the same domain as the user, cross-domain recommendation can be divided into two categories, that is, intra-domain recommendation and inter-domain recommendation. Considering whether the number of target domains is single or multiple, cross-domain recommendation can be divided into other two categories, i.e., single-target cross-domain recommendation and multi-target cross-domain recommendation. For the convenience of understanding, we elaborate on these two dimensions.

Table 2 shows the categorization of representative cross-domain recommendation studies according to recommendation tasks. As we can see, the most widely studied task is the intra-domain multi-target recommendation followed by the intra-domain single-target recommendation. The inter-domain multi-task recommendation is the least studied, with only two corresponding papers.

The first class of approaches assume that the services of domains are geared towards the general population and users in different domains may have similar preferences while items may share some properties as well. Although there are not overlapping users/items between domains, two domains may share cluster-level rating patterns. Therefore, approaches of this class aim at extracting cluster-level rating patterns from one domain and transfer them to the other domain. Fig. 3 shows the schematic diagram of this method and we describe the details in the following.

The first step is to factorize the rating matrix of the source domain $\textbf{R}_{aux}$ into three latent matrices $\textbf{U}\in\mathbb{R}^{m^{A}\times k}_{+}$, $\textbf{V}\in\mathbb{R}_{+}^{n^{A}\times l}$, and $\textbf{S}\in\mathbb{R}^{k\times l}_{+}$. Specifically, the orthogonal nonnegative matrix tri-factorization (ONMTF) algorithm is a widely used co-clustering algorithm that is proved to be equivalent to a two-way K-means clustering algorithm.

Each row of U and V is the cluster indicator for a user or an item.

The next step is to construct a compact matrix B that encodes the cluster-level rating patterns of $k$ clusters of users and $l$ clusters of items that are shared between domains. The third step is to get the cluster indicator matrices $\textbf{U}_{tgt}$ and $\textbf{V}_{tgt}$ in the target domain by transferring B to the target domain.

where $\circ$ denotes the element-wise product. Finally, the predicted ratings $\tilde{\textbf{X}}_{tgt}$ in the target domain are generated:

The first approach of this method is proposed by Li et al. (Li et al., 2009a). The generated compact matrix B is called a “codebook”. They set the nonnegative entry of U and V in each row to be $1$ and the others to be $0$ getting two indicator matrices $\textbf{U}_{aux}$ and $\textbf{V}_{aux}$. Then the codebook B is constructed by averaging all the ratings in each user-item co-cluster as an entry in the codebook as follows:

The basic paradigm was then widely borrowed, expanded, and improved by many researchers, and some variant approaches have been proposed.

Moreno et al. (Moreno et al., 2012) extended this paradigm by transferring knowledge from multiple source domains with varying levels of relevance and proposed an approach named TALMUD. For each source domain with rating matrix $\textbf{X}_{src_{n}}$, there is a codebook $\textbf{B}_{n}$ representing the transferred knowledge from this domain and a variable $\alpha_{n}$ denoting its relevant degree with the target domain. The target rating matrix is reconstructed by linearly integrating the rating patterns of all source domains, i.e., the equation (2) is changed as follows:

Some researchers proposed that there simultaneously existed common cluster-level rating patterns shared across domains and domain-specific cluster-level rating patterns for each domain. The final predicted rating scores should be the combination of ratings from the perspective of common rating patterns and ratings from the perspective of domain-specific rating patterns. Following this idea, Gao et al. (Gao et al., 2013) proposed a Cluster-Level Latent Factor Model (CLFM) which partitioned the cluster-level rating patterns B in each domain into a common part $\textbf{B}_{0}$ and a domain-specific part $\textbf{B}_{\tau}$, that is $\textbf{B}_{\tau}=[\textbf{B}_{0},\textbf{B}_{\tau}]$. Ren et al. (Ren et al., 2015) proposed a Probabilistic Cluster-level Latent Factor (PCLF) model that jointly learnt a common cluster-level rating matrix and a domain-specific cluster-level rating matrix. Zhang et al. (Zhang et al., 2018) proposed a joint probabilistic model named ProbKT which jointly captured domain-shared group-level knowledge and domain-specific group-level knowledge. The equation (2) of these approaches is changed as follows:

Chen et al. (Chen et al., 2013) extended this paradigm by taking users’ generated tags into consideration and proposed a tensor-factorization-based framework (FUSE). Instead of sharing a cluster-level rating matrix between domains, they constructed a shared three-dimensional cluster-level tensor to transfer knowledge. The matrix factorization process is, therefore, replaced by tensor factorization which maps users, items, and tags into a shared latent feature space. The clustering operation is simultaneously performed on users, items, and tags to obtain clusters of them.

Zhang et al. (Zhang et al., 2017) proposed that there are divergences between domains and directly transferring the cluster-level rating patterns of the source domain to the target domain may result in ”negative transfer”. Therefore, they utilized a domain adaptation technique to ensure the consistency of the transferred knowledge. He et al. (He et al., 2018b) proposed that the orthogonal nonnegative matrix tri-factorization (ONMTF) algorithm adopted by existing approaches requires that the matrix be fully rated which is not easy to be satisfied. They extended the TALMUD (Moreno et al., 2012) approach by applying an incomplete orthogonal nonnegative matrix tri-factorization (IONMTF) algorithm which relaxed the full rating restriction on the rating matrix of ONMTF and was easier to implement on real-world datasets.

Shu et al. (Shu et al., 2018) proposed a cross-media joint friend and item recommendation framework (CrossFire) which aimed to jointly recommend items and friends to users in the target domain. In addition to tri-factorize rating matrices into user feature matrices, item feature matrices, and a shared rating feature matrix as previous works, it also tri-factorized user-user link matrices into user feature matrices and a shared interaction matrix. Besides, CrossFire also utilized item features as auxiliary information. It assumed that items in different domains share a dictionary and factorized feature matrices into the item feature matrices and the dictionary in each domain.

All of the approaches mentioned above are for single-target recommendation as they explicitly extract cluster-level rating patterns in the source domain and then transfer them to the target domain. Some researchers have tried to expand this method to multi-target recommendation.

Li et al. (Li et al., 2009b) proposed a rating-matrix generative model (RMGM) which integrated several sparse domains and assumed that multiple domains share common latent cluster-level patterns. Then they learned the probabilities of each user and item belonging to this shared latent structure. Iwata et al. (Iwata and Takeuchi, 2015) proposed that the latent factors of users/items generated by matrix factorization in each domain were from a common Gaussian distribution. The same mean vector and covariance matrix helped to align the latent factors from different domains.

Wang et al. (Wang et al., 2019) focused on the cross-domain session-based recommendations and proposed a method called cross-domain item embedding method based on co-clustering (CDIE-C). As user information is not available and items differ between domains, we also categorize it to the recommendation scenario where neither user nor item overlaps. The core idea of CDIE-C is to extract cluster-level correlations by exploring cross-domain co-occurrence relations of items based on the co-clustering method. Then, both item-level sequence information within each domain and cluster-level cross-domain correlation information can be captured to generate the final cross-domain recommendation.

This method is based on the assumption that although users and items are different between domains, users may use the same tags to annotate items of interest, and items in different domains may be tagged by the same tags to encode their properties. As shown in Fig. 4, domain A and domain B have different users and items. Users in domain A use tags $\{illustration,sci-friction,romantic\}$ to tag books, and users in domain B use tags $\{scene,sci-friction,romantic\}$ to tag movies, so both tags “sci-friction” and “romantic” exist in both domains. Therefore, this method turns to user-generated tags to establish the linkages between different domains. Specifically, there are two ways to capture tag correlations. On the one hand, tags can be used to simultaneously enhance the profiles of users and items. On the other hand, matrices of similarities between users, items, and tags can be generated based on tags and then be used as constraints to learn better user and item representations.

For enhancing the profiles of users and items, Enrich et al. (Enrich et al., 2013) first proposed to utilize tags as implicit user feedback to enhance item factors. They proposed a tag-based cross-domain collaborative filtering approach based on the SVD++ (Koren, 2008) algorithm with three different adaptations being explored. Fernandez-Tobias et al. (Fernández-Tobías and Cantador, 2014) claimed that the approach proposed in (Enrich et al., 2013) did not fully exploit users’ preferences expressed in their tags assigned to items. They further proposed an approach named TagGSVD++ based on GSVD++ (Manzato, 2013) which simultaneously enriched users’ profiles with tags they used and extended items’ profiles with tags they received.

For constructing similarity matrices between users and items, Shi et al. (Shi et al., 2011) proposed a tag-induced cross-domain collaborative filtering (TagCDCF) algorithm that exploited shared tags to construct cross-domain user-to-user similarity matrix $S^{(U)}$ and item-to-item similarity matrix $S^{(V)}$. The tag-induced similarity matrices were then incorporated into the matrix factorization process as additional constraints by forcing similar users/items to have closer representations. The objective function is generally defined as follows:

Many researchers have proposed improved approaches based on this idea. Hao et al. (Hao et al., 2016) proposed that the number of shared tags between domains was limited and it was a waste to discard domain-dependent tags. They proposed an Enhanced Tag-induced Cross-Domain Collaborative Filtering (ETagiCDCF) algorithm to explore domain-dependent tags. It first grouped domain-dependent tags into clusters based on their co-occurrences with shared tags. The cross-domain user-to-user and item-to-item similarities were computed on these tag clusters. Zhang et al. (Zhang et al., 2019a) proposed that although there were a limited number of shared tags between domains, two non-identical tags in two domains might be semantically related. They proposed a cross-domain recommendation approach with semantic correlations in tagging systems (SCT). It utilized word2vec to analyze all tags and generated continuous vectors to capture contextual information and semantic similarities between tags. Both the intra-domain similarities and inter-domain similarities between users and items can be computed based on tags’ semantic similarities.

Instead of constructing the similarity matrices between users and items, Fang et al. (Fang et al., 2015) proposed to construct a tag co-occurrence matrix that captured the interrelatedness among tags. Then the rating matrix in each domain was tri-factorized into three parts, that is, the tag co-occurrence matrix, the user latent factors for tags, and the item latent factors for tags. The factorization process was optimized by forcing the generated co-occurrence matrix to be as close to the constructed co-occurrence matrix as possible. Liu et al. (Liu et al., 2022) recently extended this method by treating user/item features as bridges to link domains instead of utilizing tags. The rating prediction module jointly combines users’/items’ IDs, historical ratings, and reviews to generate their general embeddings and perform recommendations based on the embeddings. The embedding attribution alignment module treats each dimension of an embedding as a certain kind of attribution. Both vertical and horizontal alignments are equipped to reduce the domain discrepancy and transfer consistent useful knowledge across the source and target domains.

Kumar et al. (Kumar et al., 2014) proposed that the vocabularies of different domains may not match explicitly, but through the use of ontologies, it may be possible to derive semantic relationships between words of distinct domains. They proposed a semantic-clustering-based cross-domain (SCD) recommendation algorithm which first performed semantic clustering to obtain clusters of semantically equivalent words. SCD then got item-based topic distributions and user-based topic distributions. The user profiles were then mapped to the target domain and used to perform inter-domain recommendations.

Yang et al. (Yang et al., 2015) had a similar proposal that different vocabularies were used by different domains so tags should be correlated on semantic level rather than lexical level. Therefore, they utilized online encyclopedias to achieve the semantic matching of tags and built a multi-partite graph to represent the similarities of objects in different domains. Finally, the similarity between a user and an item was measured based on the graph propagation.

This method involves a certain amount of human effort within a fixed budget. For example, at first, there were no explicit entity (i.e., user or item) correspondences between different domains, some users/items are sometimes overlapped. It is expensive or time-consuming to recognize all user correspondences, but the partial mappings of a small number of users or items can be identified within a fixed budget. In addition, more ratings can be obtained through human efforts, which alleviates the problem of data sparsity.

Zhao et al. (Zhao et al., 2013) proposed a margin-based active learning approach that selected the entities in the target domain with low prediction certainty. They first applied a maximum-margin matrix factorization (MMMF) in the target domain to get the original user and item latent factors. They then queried the correspondences of entities with low prediction certainty in the source domain and an extended MMMF was proposed to transfer knowledge from the source domain to refine the user/item latent factors in the target domain. This method was later generalized to a unified framework. Two variants based on regularized low-rank matrix factorization (i.e., RLMF_TL) and probabilistic matrix factorization (i.e., PMF_TL) were proposed in their later works (Zhao et al., 2017).

Zhang et al. (Zhang et al., 2016) incorporated active learning with the previous proposed RMGM (Li et al., 2009b) approach. It first generated the original user and item latent factors as well as shared cluster-level rating patterns using the RMGM algorithm. It added unrated user-item pairs of all domains into a pool and the proposed algorithm iteratively selected the most informative items from the pool to ask for users’ ratings. The selecting criterion measured the global generalization errors which jointly considered domain-specific errors and domain-independent errors. The new rated user-item pairs will be added to the training set and help to re-train the RMGM algorithm.

Collective matrix factorization is a direct extension of the general matrix factorization method for the cross-domain recommendation problem. Fig. 5 shows the schematic diagram of collective matrix factorization. Similar to general matrix factorization, the rating matrix in each domain is factorized into a user latent feature matrix and an item latent feature matrix. The difference is that cross-domain knowledge is utilized to constrain the matrix factorization process within each domain.

Jiang et al. (Jiang et al., 2016) proposed a semi-supervised transfer learning approach called XPTRANS in which they argued that the similarities between overlapped users were consistent across different domains. They first performed nonnegative matrix factorization on two domains. Then the user-based similarities were added as constraints to the matrix factorization process when learning the representations of users and items. Rafailidis et al. (Rafailidis and Crestani, 2016) proposed a joint cross-domain user clustering and similarity learning recommendation algorithm (JCSL) in which they jointly considered cluster-based and user-based cross-domain similarities. The resulting similarity matrices acted as social regularization terms during the matrix factorization process. Rafailidis et al. (Rafailidis and Crestani, 2017) further proposed a cross-domain recommendation approach with collaborative ranking (CDCR) which focused on the ranking performance when generating the recommendation. In this model, they learned the cross-domain user latent matrix to capture correlations of users in two domains and incorporated it as a constraint into the learning process of user/item latent factors.

Zhang et al. extended their previous study (Zhang et al., 2017) to the scenario of user partial overlap and proposed a cross-domain recommender system with kernel-induced knowledge transfer (KerKT) (Zhang et al., 2019b). The overlapping users were utilized to train the domain adaptation function to ensure the consistency of the transferred knowledge. Kernel-induced completion was conducted to measure the user similarities which were integrated into the matrix factorization process as constraints. Yang et al. (Yang et al., 2017) proposed a generative model of Multi-site Probabilistic Factorization (MPF) the basic idea of which was to model cross-site user preferences and site-specific user preferences simultaneously. For multiple-site users, their latent feature vectors $u_{i}^{(s)}$ in site $s$ consist of a common part $\bar{u}_{i}$ and a site-specific part $\vartriangle u_{i}^{(s)}$, i.e., $u_{i}^{(s)}=\bar{u}_{i}+\vartriangle u_{i}^{(s)}$. For an exclusive user in site $s$, $u_{i}^{(s)}=\bar{u}_{i}+0$. In the generative process, each site had a different prior for the site-specific part of users’ latent feature vectors.

Fig. 6 shows the schematic paradigm of this method. We can see, there are typically three layers. The embedding layer generates embeddings for users and items in each domain. In the combination layer, the embeddings of overlapping users from both domains are combined to generate the unified embeddings for overlapping users. Finally, the prediction layer takes both the embeddings of distinct users and overlapping users to train the recommendation model on each domain separately.

Zhu et al. (Zhu et al., 2019) first proposed this paradigm for dual-target cross-domain recommendation (DTCDR) the core idea of which was to share the knowledge of overlapping users across domains. Specifically, in the embedding layer, it generated embeddings for users and items in each domain from both rating and content information. In the combination layer, the embeddings of overlapping users were combined by three different combination operations, i.e., concatenation, max-pooling, and average-pooling. Zhu et al. (Zhu et al., 2020) then proposed a Graphical and Attentional framework for Dual-Target Cross-Domain Recommendation (GA-DTCDR). In the embedding layer, it applied a graph embedding technique (i.e., Node2vec) to generate more representative user and item embeddings in each domain. In the combination layer, it employed an element-wise attention mechanism to more effectively combine the representations of overlapping users. Zhu et al. later extended their proposed framework to support three different recommendation scenarios (Zhu et al., 2021c), that is, dual-target CDR, multi-target CDR, and cross-domain recommendation and cross-system recommendation (CDR+CSR). For different scenarios, personalized training strategies are adopted.

Some approaches of this method focused on capturing the dynamic nature of user preferences. Perera et al. proposed to utilize time-stamped, cross-network information for both new (i.e., distinct users) and existing (i.e., overlapping users) user recommendation (Perera and Zimmermann, 2017). In the embedding layer, they generated users’ topical distribution by topic modeling in each domain. Before the combination, two transfer functions map user preferences from the topical space to the target network user space. In the combination layer, the representations of overlapping users are obtained by fusing user preferences from both domains. Later, they further proposed a time-aware unified cross-network solution (Perera and Zimmermann, 2020) which, in the embedding layer, modeled user preferences under short, long and long short term levels in each domain. Then, in the combination layer, the three-level preference representations in both domains of overlapping users (referred to as existing users in their paper) were integrated to obtain users’ final representations. The distinct users’ (referred to as new users) representations were directly generated by fusing the three representations from the source domain.

This is an inter-domain recommendation method in which one domain is treated as the source domain and the other as the target domain. Fig. 7 shows the schematic diagram of this method. There are three main steps, i.e., latent factor modeling, latent space mapping and cross domain recommendation. During the latent factor modeling process, the aim is to generate user and item latent factors $\{U^{s},V^{s},U^{t},V^{t}\}$ in each domain. During the latent space mapping, the aim is to train a mapping function $f_{U}$. The objective of $f_{U}$ is to establish the relationships between the latent space of domains:

During the cross-domain recommendation process, for a user who only has a latent factor in the source domain, it generates the user’s latent factor in the target domain:

With $\hat{U}_{i}^{t}$, the recommendation in the target domain can be performed to this user.

The embedding and mapping framework for cross-domain recommendation (EMCDR) was first proposed by Man et al. (Man et al., 2017) that aimed at the inter-domain recommendation problem. For latent factor modeling, EMCDR, respectively, applied Matrix Factorization (MF) and Bayesian Personalized Ranking (BPR) to generate user and item latent factors. For latent space mapping, it utilized both a linear function and a nonlinear function based on Multi-Layer Perceptron (MLP) to act as the mapping function. The objective is to approximate the latent factor $U_{i}^{s}$ of overlapping users in the source domain mapped by $f_{U}$ with their corresponding latent factors $U_{i}^{t}$ in the target domain.

This idea was widely improved by many researchers and the improvement is mainly in two aspects, one is the latent factor modeling process, the other is the latent space mapping process.

For latent factor modeling, Wang et al. (Wang et al., 2018) proposed a Cross-Domain Latent Feature Mapping (CDLFM) model. It first defined three similarity measurements on users’ rating behaviors. During latent factor modeling, the similarity values were embedded into the matrix factorization process as constraints. Fu et al. (Fu et al., 2019) proposed a Review and Content-based Deep Fusion Model (RC-DFM). It extended stacked denoising autoencoders to effectively fuse review text and item contents with the rating matrix to generate user and item representations with more semantic information. Bi et al. (Bi et al., 2020b, a) proposed to construct a heterogeneous information network and took into consideration the interaction sequence information to learn effective user/item representations in each domain. The proposed approaches are proved to be effective in the cross-domain insurance recommendation.

For latent space mapping, Zhu et al. (Zhu et al., 2018) proposed a Deep framework for both Cross-Domain and Cross-System Recommendation (DCDCSR) which took into account rating sparsity degrees of individual users/items to generate benchmark factor matrices. The mapping function was trained to map the latent factor matrices of users and items to fit the benchmark factor matrices. Kang et al. (Kang et al., 2019) proposed that in existing EMCDR-based approaches, the training of mapping functions only used overlapping users, so their performance was sensitive to the number of overlapping users. After an in-depth analysis of the Amazon dataset, they proposed that in real-world datasets, the number of overlapping users was always small, which limited the performance of existing approaches. Therefore, they proposed a Semi-Supervised framework for Cross-Domain Recommendation (SSCDR) to utilize both the overlapping users and source-domain items to train the mapping function. Zhu et al. also proposed that the mapping function is biased to the limited overlapping users, which degrades the generalization ability of the model. The proposed transfer-meta framework for CDR (TMCDR) (Zhu et al., 2021a) can replace the training procedure of most existing EMCDR-based methods and has good generalization ability. Zhu et al. later proposed that the complex relationships between user preferences of the source and target domains vary from user to user, which is hard to be captured by a single mapping function. Their proposed framework named Personalized Transfer of User Preferences for Cross-domain Recommendation (PTUPCDR) (Zhu et al., 2022) learns a meta-network to personalize a mapping function for each user. Wang et al. pointed out a similar problem and proposed an approach namely Low-dimensional Alignment for Cross-Domain Recommendation (LACDR) (Wang et al., 2021). Instead of learning a mapping function utilizing overlapping users, LACDR first trains an encoder and a decoder in both the source domain and the target domain utilizing both overlapping users and non-overlapping users. For a cold-start user, the representation in the target domain is obtained by first generating her domain-invariant factor using the encoder of the source domain. Then, the domain-invariant factor is mapped to the latent factor in the target domain using the decoder in the target domain.

The approaches described above are for inter-domain recommendation, as they all learn a mapping function between different domains and map the users’ representation in the source domain to the target domain. Some works have applied this embedding and mapping framework to the intra-domain recommendation.

Zhang et al. proposed that users’ interests and states may vary over time and it was important to quickly capture these changes for timely and accurate recommendations. Therefore, they first divided the sequence of users’ interacted items into itemsets based on timestamps of interactions to denote users’ interests during a period. Instead of capturing the mapping relationships between user representations in different domains like previous EMCDR-based approaches, the proposed cycle generation network (CGN) (Zhang et al., 2020) learned a user’s personalized dual-direction mapping function between the representation of her interaction itemsets in different domains at the same temporal period. Li et al. proposed a Dual Metric Learning (DML) (Li and Tuzhilin, 2021) model which supplemented the dual learning mechanism with the metric learning approach. Through a pre-trained autoencoder network, DML first generate user/item embeddings $W_{u_{A}},W_{u_{B}},W_{i_{A}},W_{i_{B}}$ in each domain. Instead of learning a mapping function from the source domain to the target domain as most EMCDR-based methods, DML aims to learn a transitional metric learning mapping $X$ which is restricted to be an orthogonal mapping. Embeddings of overlapping users $W_{{ou}_{A}}$ and $W_{{ou}_{B}}$ are utilized to learn this metric learning mapping. The objective is to minimize the distance between the mapped user embedding $XW_{{ou}_{A}}$ and the target user embeddings $W_{{ou}_{B}}$ for the same overlapping users, the dual form of which is to minimize the distance between $X^{T}W_{{ou}_{B}}$ and $X_{{ou}_{A}}$. Finally, the recommendation is performed on $XW_{u_{A}}$ and $W_{i_{A}}$ in domain A and $X^{T}W_{u_{B}}$ and $W_{i_{B}}$.

The basic paradigm of this method is building shared graphs to represent the relationships among users, items, attributions, and other factors (i.e., nodes in the graphs), and learn a representation for each node through graph representation learning. The learned representations are proved to be able to capture the high-order and non-linear dependencies between nodes and can be used for subsequent recommendations. Since constructing shared graphs among domains can integrate the information of different domains, through graph representation learning, the representations of nodes from different domains are embedded in the same latent space and, therefore, the cross-domain information can be transferred. Fig. 8 shows the schematic diagram of this method.

Wang et al. (Wang et al., 2017) first applied graph neural networks to the cross-domain social recommendation and proposed a Neural Social Collaborative Ranking (NSCR) approach. It aims to recommend items in an information-oriented domain to users in a social-oriented domain, which can be seen as an inter-domain recommendation. NSCR first utilizes an attributed-aware deep collaborative filtering model in the information-oriented domain to learn user-item interactions. Then embeddings of overlapping users are directly transferred to the social-oriented domain. The cross-domain knowledge is transferred by a multi-layer graph convolution network propagating representations of overlapping users to non-overlapping users. Finally, the embeddings of non-overlapping users in the social-oriented domain and embeddings of items in the information-oriented domain are used for recommendation.

Cui et al. proposed that, in previous works, user behaviors are processed within each domain which is an indirect way to incorporate cross-domain information. They proposed a heterogeneous graph framework (HeroGRAPH) (Cui et al., 2020) that collected user behaviors from all domains to devise a shared graph to directly model users’ cross-domain behaviors. Information within each domain was utilized to conduct within-domain modeling and graph convolution operations with recurrent attention on the shared graph is applied to conduct cross-domain modeling. The within-domain representations and cross-domain representations of users and items are combined to perform the final recommendation. In a similar way, Xu et al. proposed Relation Expansion based Cross-Domain Recommendation (ReCDR) (Xu et al., 2021). The main difference lies in the way of constructing the shared graph. They first applied a graph embedding model (i.e., Node2Vec) to generate pre-trained node embeddings for all nodes in both domains. Nodes with higher similarities will be connected to devise the shared graph. Li et al. (Li et al., 2020) further proposed an embedding content and heterogeneous network (ECHCDR) which creatively incorporated an adversarial learning algorithm. It first utilized Doc2vec to generate content representations of users/items and they are concatenated with adjacency representations to act as initial representations of users/items. It then simultaneously train a generator and a discriminator to learn suitable representations of users and items. Finally, both intra-domain and inter-domain recommendation can be performed based on the inner product of the learned representations.

Apart from the previously introduced embedding and mapping-based approaches, capturing aspect correlations is another method for inter-domain recommendation. It assumes users’ preferences are multi-faceted and aims at modeling fine-grained semantic aspects and exploring their mutual relationships across domains. The score prediction can be performed by matching the aspect features of a user in one domain and an item in the other domain.

Zhao et al. (Zhao et al., 2020) proposed a cross-domain recommendation framework via aspect transfer network (CATN) to capture users’ multi-faceted and fine-grained preferences. It first represents a user by a user document that contains all reviews written by this user, and an item by an item document that contains all reviews it receives. It then generates abstract aspect features for each user and each item from their documents. Aspect features of overlapping users were utilized to identify the global cross-domain aspect correlations. The inter-domain recommendation can be performed by utilizing the user’s review document in the source domain and the item’s review document in the target domain, and vice versa. Specifically, the rating prediction is obtained by aggregating the semantic matching between two aspects in the aspect features of a user and an item.

As described in section 4.1, collective matrix factorization is a direct extension of the traditional matrix factorization method for cross-domain recommendation problem. The difference is that cross-domain knowledge can be utilized to constrain the matrix factorization process within each domain. To some extent, the approaches discussed in section 4.1 are applicable to this recommendation scenario. We omit the schematic diagram as it is the same as Fig. 7. In the following, we discuss approaches that are specially proposed for this recommendation scenario.

Singh et al. (Singh and Gordon, 2008) first proposed the collective matrix factorization (CMF) model which collectively factorized rating matrices $R^{A},R^{B}$ of two domains into user representations $U_{A},U_{B}$ and item representations $V_{A},V_{B}$. The constraint was that the representations of users are shared across different domains which means $U_{A}=U_{B}$. Ma et al. (Ma et al., 2008) proposed a probabilistic matrix factorization approach for social recommendation (SoRec). The rating matrix was factorized into a user feature matrix $U_{A}$ and an item feature matrix $V_{A}$ while the social network matrix was factorized into a user feature matrix $U_{B}$ and a factor feature matrix $Z_{B}$. Similar to CMF, the cross-domain constraint was that the user feature matrix was shared during the process, i.e., $U_{A}=U_{B}$.

However, both of the above two approaches force the same user to have exactly the same representations in different domains, that is, they assume that users’ characteristics and preferences are consistent, which ignores users’ domain-specific characteristics. To overcome this shortcoming, Xin et al. (Xin et al., 2015) proposed a relaxed restriction by putting forward the nonlinear mapping relationships between user representations. They proposed to train two nonlinear mapping functions $f(\cdot),g(\cdot)$ to make $f(U_{A})=U_{B}$ and $g(U_{B})=U_{A}$. Zhao et al. (Zhao et al., 2018; Huang et al., 2019) proposed a low-rank and sparse cross-domain (LSCD) recommendation approach in which the user latent feature matrices $U_{A},U_{B}$ were divided into two parts: domain-shared feature matrix $U^{S}$ and domain-specific feature matrix $H_{A},H_{B}$. The user representation is the sum of these two parts, i.e., $U_{A}=U^{S}+H_{A},U_{B}=U^{S}+H_{B}$.

In essence, tensor factorization is the higher-order generalization of matrix factorization. When only user factors and item factors are considered, the interaction information within each domain can be represented by a matrix. However, when domain factors, time factors, and aspect factors are further considered, the information within each domain will change from a matrix to a tensor. The core idea is to factorize the tensor into user representations, item representations, and other factor representations (i.e., domain, time, and aspect). By multiplying the user representations and domain representations, the domain-specific representations can be obtained. Similarly, time-specific representations and aspect-specific representations can be obtained. The final prediction $\hat{score}$ is derived from the product of multiple related representations. CP model (canonical decomposition/parallel factor analysis (PARAFAC)) is the most widely used tensor factorization algorithm. Fig. 9 shows the schematic diagram of tensor factorization-based approaches.

Hu et al. (Hu et al., 2013) proposed a Cross-Domain Triadic Factorization (CDTF) model which took into consideration the full triadic relation user-item-domain to reveal user preferences on items within various domains in depth. Except for a user-factor matrix $U$ shared among domains and an exclusive item-factor matrix $V_{k}$ for each domain, CDTF also generated a domain-factor matrix $D$ to express the traits of each domain. Then the recommendations are performed based on the results of triadic interactions among user, item, and domain factors. Song et al. proposed to exploit the aspect factors extracted from the review text to improve the performance of cross-domain recommendation. They extracted fine-grained user preferences in aspect-level and concern degrees toward different aspects of items as two tensors. A review-based joint tensor factorization (RB-JTF) approach (Song et al., 2017) was proposed and tensor factorization was applied simultaneously in each domain. The rating matrices were factorized into user, item, and aspect latent factors while knowledge transfer was realized by sharing user latent factors and transferring aspect latent factors.

Liu et al. proposed that previous studies only identified and transferred the linearly correlated knowledge between domains. They proposed a new knowledge transfer technique, called the hyper-structure transfer (HST) (Liu et al., 2015), that captured the non-linear correlations of knowledge between domains. Compared with previous approaches that directly share the cluster-level rating patterns between domains (see section 3.1), HST first generated a more complex structure $\mathcal{H}$ and required the transferred rating pattern matrices in each domain to be projections of $\mathcal{H}$. To get $\mathcal{H}$, canonical polyadic decomposition of tensors is applied.

Factorization Machines (FM) is a machine learning algorithm based on matrix factorization that aims to solve the problem of feature combination in large-scale sparse data. The advantages of FM fit well with the problem scenario of recommendation systems and FM has been proved to be one of the effective algorithms with verified effects. Formula (10) shows a second-order factorization machine model which can be easily extended to multi-order models.

where $n$ represents the dimension of the feature vector. $x_{i}$ denotes the $i$-th feature, and $w_{ij}$ is the combination parameter representing the importance of the combination feature.

FM has been already used for single-domain recommendation, but for cross-domain recommendation, it is necessary to extend FM to allow them to incorporate user interaction patterns from different domains.

Loni et al. (Loni et al., 2014) proposed an extension of FM named FM-MCMC that incorporated user domain-specific interaction patterns from the source domain to expand feature vectors of the target domain. The expanded feature vectors served as input to the general FM model. Specifically, a domain-dependent real-valued function was defined to control the amount of knowledge that was transferred from the source domain. Li et al. (Li et al., 2019) designed coupled factorization machines (CoFM) and proposed that the coupled fields of coupled datasets contained shared characteristics as well as domain-specific uniqueness. CoFM, therefore, allowed the latent vectors of the coupled field between two domains to have a shared part and a domain-specific part.

The schematic diagram of this class of approaches is shown in Fig. 10. The core idea is to first generate users’ initial embeddings $E_{U}$, items’ initial embeddings $E_{I_{A}}$ and $E_{I_{B}}$ in domain $A$ and domain $B$, respectively. Then these initial embeddings, respectively, enter into three separate deep neural network modules $P_{U},P_{I_{A}},P_{I_{B}}$ to learn the latent representations $R_{U},R_{I_{A}},R_{I_{B}}$ of users and items. The module $P_{U}$ that deals with users is shared between two domains to achieve deep sharing of user representations.

Elkahky et al. (Elkahky et al., 2015) proposed a Multi-View Deep Neural Network (MVDNN) in which the initial embeddings were generated from users’ features and items’ attributes. User embeddings were input of one view while item embeddings were input of another two separate views. All the views shared the same structure of multi-layer perception to generate representations of users and items. Two domains shared the same user view, thus achieving the goal of deep sharing of user representations. Following this approach, Lian et al. and He et al., respectively, proposed a cross-domain content-boosted collaborative filtering neural network (CCCFNet) (Lian et al., 2017) and a general cross-domain framework via a bayesian neural network (GCBAN) (He et al., 2018a). The core idea of these two approaches was to incorporate both collaborative filtering and content-based factors into account when generated initial embeddings of users and items in each view. Thus, the initial embeddings consist of two parts: one part generated from features and the other part generated from one-hot encoding. The structure of each view is the same as MVDNN (Elkahky et al., 2015).

Zhao et al. (Zhao et al., 2019) proposed a Preference Propagation GraphNet (PPGN) which constructed a cross-domain preference matrix to model the interactions of different domains as a whole. The high-order user preferences were propagated and integrated through multiple graph convolution and propagation layers. Compared with previous works, the multi-layer perception was replaced by multiple graph convolutional layers. Guo et al. further proposed another graph-based solution, namely Domain-Aware Graph Convolutional Network (DA-GCN) (Guo et al., 2021), for the shared-account cross-domain sequential recommendation. They constructed a cross-domain sequence graph to link different domains and designed two attention mechanisms during the message passing process.

Some researchers improved previous works by jointly considering users’ domain-shared representations and domain-specific representations while only domain-shared representations are shared across domains. Yan et al. (Yan et al., 2019) proposed a model of Deep Attentive Probabilistic Factorization (DeepAPF) in which the user embeddings were initialized into three parts: $P_{U}^{S}$, $P_{U}^{A}$, and $P_{U}^{B}$. $P_{U}^{S}$ was the domain-shared representations capturing cross-domain commonality of user interests and $P_{U}^{A},P_{U}^{B}$ were the domain-specific representations capturing site-peculiarity of user interests. Attention mechanisms were utilized to fuse these two kinds of user representations to generate users’ final representations, i.e., $\hat{P}_{U}^{A}=Attention(P_{U}^{S},P_{U}^{A}),\hat{P}_{U}^{B}=Attention(P_{U}^{S},P_{U}^{B})$. Similarly, Chen et al. (Chen et al., 2019) proposed an efficient adaptive transfer neural network (EATNN) for the social-aware recommendation which jointly performed item recommendation and friend recommendation. It initialized user embeddings into a domain-shared part $\textbf{P}_{U}^{C}$, an item domain-specific part $\textbf{P}_{U}^{I}$, and a social domain-specific part $\textbf{P}_{U}^{S}$. Two attention-based kernels were utilized to automatically estimate the difference of mutual influences between the item domain and the social domain to incorporate the shared and domain-specific representations in each domain. Zhao et al. (Zhao et al., 2022) proposed a Multi-Sparse-Domain Collaborative Recommendation (MSDCR) method which learns user domain-specific and domain-invariant preference in a more fine-grained manner (i.e., aspect-level). A User’s domain-specific preference in a domain is enhanced by transferring the user’s complementary aspect preferences in other domains. Domain adaption is applied to capture users’ domain-invariant aspect preferences that are shared across domains. Li et al. (Li et al., 2021) focused on mitigating domain biases when transferring user information across domains. The debiasing parameters contain the propensity score which solves the bias in single domain by re-weighting each transaction in the observed data. Users’ general preference $\textbf{v}_{u}$ is generated by the nonlinear combination of the domain-specific preference $\textbf{v}_{u}^{d}$ and the propensity score.

Approaches of this class have symmetrical model structures, that is to say, each domain has the same structure and the model structures are in deep structure with multiple hidden layers. As the structures are symmetrical, these methods can simultaneously perform recommendations on multiple domains and are, therefore, for the multi-target recommendation. Fig. 11 shows the schematic diagram of these approaches. Let $S^{A},S^{B}$ denote the deep neural network structure with $L$ layers in the domain $A$ and domain $B$. $r^{A}_{i,l}$ and $r^{A}_{o,l}$ denote the input and output of the $l$-th layer in domain $A$ while $r^{B}_{i,l}$ and $r^{B}_{o,l}$ for domain $B$. The deep dual knowledge transfer is realized by fusing the outputs of the previous layer in this domain and the other domain as the input of the next layer, which can be denoted as $r^{A}_{i,l+1}=Fuze^{A}(r^{A}_{o,l},r^{B}_{o,l})$ and $r^{B}_{i,l+1}=Fuze^{B}(r^{A}_{o,l},r^{B}_{o,l})$. The inputs of the first layer, i.e., $r^{A}_{i,1}$ and $r^{B}_{i,1}$, are the original embeddings of users and items. The outputs of the last layer, i.e., $r^{A}_{o,L}$ and $r^{B}_{o,L}$, are used for recommendation.

Hu et al. (Hu et al., 2018a) first proposed a collaborative cross-network (CoNet) that introduced cross-connections from one base network to another. The inputs of domain $A$ are the one-hot embeddings $x_{u}$ and $x_{i}$ of a user $u$ and an item $i$ while the inputs of domain $B$ are the one-hot embeddings $x_{u}$ and $x_{j}$ of the same user $u$ and another item $j$. The one-hot embeddings in each domain are concatenated as $x_{u,i}$ and $x_{u,j}$ acting as the input of the first layer, that is, $r^{A}_{i,1}=x_{u,i}=[x_{u},x_{i}]$ and $r^{B}_{i,1}=x_{u,j}=[x_{u},x_{j}]$. The deep dual knowledge transfer is achieved in multi-layer feedforward networks by adding dual connections. The formulas are as follows:

where $W^{A}_{l}$ and $W^{B}_{l}$ are domain-specific parameters while $H_{l}$ are domain-shared parameters.

Following CoNet, Liu et al. (Liu et al., 2020b) proposed to capture users’ aesthetic preferences when transferring knowledge between different domains. They proposed a deep aesthetic cross-domain network (ACDN) which utilized a pre-trained deep convolutional neural network to extract aesthetic features $x_{i}^{a}$ and $x_{j}^{a}$ from item images in each domain. The aesthetic features together with one-hot embedding features $x_{u}$, $x_{i}$, $x_{j}$ acted as the input of the first layer, that is, $r^{A}_{i,1}=x_{u,i}=[x_{u},x_{i},x_{i}^{a}]$ and $r^{B}_{i,1}=x_{u,j}=[x_{u},x_{j},x_{j}^{a}]$. The deep dual knowledge transfer is realized in the same way as CoNet which is shown in equation 11.

Li et al. (Li and Tuzhilin, 2020) proposed a Deep Dual Transfer Cross-Domain Recommendation (DDTCDR) model and, compared with CoNet, the improvements mainly lay in three aspects. First, DDTCDR used pre-trained autoencoders which encoded user and item features to generate feature representations as the model input. Second, it learned a latent orthogonal mapping function for transferring user preferences between domains. Third, it jointly modeled users’ within-domain preferences $r_{within}$ and cross-domain preferences $r_{cross}$ to model user preferences and user-item interactions in each domain.

Ma et al. applied this method to the shared-account cross-domain sequential recommendation and proposed a parallel information-sharing network ($\pi$-Net) (Ma et al., [n.d.]). It first utilized separate RNNs in each domain to encode user behavior sequences into a sequence representation $h_{A_{i}}$ and $h_{B_{j}}$. A shared account filter unit and a cross-domain transfer unit are designed to generate transformed representation $h^{CTU}_{{(A\rightarrow B)}_{j}}$ based on $h_{A_{i}}$ (or $h^{CTU}_{{(B\rightarrow A)}_{i}}$ based on $h_{B_{j}}$). The recommendation is performed on the concatenation representation of $h_{A_{i}}$ and $h^{CTU}_{{(B\rightarrow A)}_{i}}$ (or $h_{B_{j}}$ and $h^{CTU}_{{(A\rightarrow B)}_{j}}$).

Liu et al. (Liu et al., 2020a) further incorporated graph neural network into this method and proposed a bi-direction transfer learning approach by using graph collaborative filtering network as the base model (BiTGCF). It constructed a user-item bipartite graph in each domain and the multi-layer feedforward networks in previous works were replaced by multi-layer graph convolutional networks. Features of both users and items were propagated by graph convolution operations. The deep dual knowledge transfer was performed between two graph convolutional networks. Similar to previous works, the user representations of the $l+1$-th layer were a combination of the output of the previous layers in both domains.

Different from the above two classes of approaches that are in symmetrical model structures and aim at the multi-target recommendation, this class of approaches are for the single-target recommendation. As shown in Fig. 12, they treat one domain as the target domain to play a dominant role and the other domains as source domains. The information $R_{A}$ from the source domains is incorporated into the target domain as additional auxiliary information.

Hu et al. (Hu et al., 2018b) proposed an approach based on neural networks named MTNet in which a memory network was utilized to generate high-level representations $\textbf{W}_{o}$ of the context text (i.e., product reviews) in the target domain and a transfer network was utilized to generate representations $\textbf{W}_{c}$ of source domain knowledge. Together with representations $\textbf{W}_{z}$ of the user-item interaction, these three kinds of representations were combined to perform the final recommendation. Ma et al. included users’ content information in social media into rating prediction and proposed a social media content enriched matrix factorization (MF$\_$S) (Ma et al., 2018). It first adopted several different embedding learning algorithms (i.e., word2vector, stacked denoising autoencoder) to generate user embeddings $\vec{D}_{u}$ from the content information. It modified users’ latent vector as $\vec{U}_{u}=[\vec{D}_{u},\vec{B}_{u}]$ where $\vec{B}_{u}$ is randomly initialized. It then applied matrix factorization to train user and item embeddings by keeping $\vec{D}_{u}$ unchanged and only updating $\vec{B}_{u}$. Perera et al. (Perera and Zimmermann, 2018) focused on capturing the dynamic natures of user preferences and providing timely recommendations in the target domain. It first divided user interactions in source domains into several sets according to timestamps of his interactions in the target domain. After topical modeling and sum pooling, each set of interactions in source domains during a time interval was encoded as a high-level latent representation. An improved LSTM with attention mechanisms and time-aware gates were utilized to encode the sequence of the representations and generated the final recommendations.

Some works have proposed to focus on privacy protection. Gao et al. designed a model named Neural Attentive-Transfer Recommendation (NATR) (Gao et al., 2019, 2022) which shares item embeddings between domains rather than user embeddings to reduce the risk of leaking user privacy. It first looked up the embeddings in the source domain of the overlapping items that a user has interacted with within the target domain. An item-level attention unit was designed to aggregate the item embeddings generating an additional user embedding $s_{u}$. A domain-level attention unit was designed to fuse $s_{u}$ with the user embedding $p_{u}$ in the target domain to generate a unified user embedding $z_{u}$. The interaction probability was predicted by the inner product of $z_{u}$ and an item embedding $q_{i}$. Chen et al. proposed a two-stage based privacy-preserving CDR framework (PriCDR) (Chen et al., 2022). In stage one, two methods are proposed for the source domain to publish rating matrix differential privately to the target domain. In stage two, a deep auto-encoder and a deep neural network are utilized to model the published source rating matrix and target rating matrix, respectively, in the target domain. Embeddings of the same users in both domains are aligned.

Movie datasets are favored by a majority of works because they have innate shared movies in different categories which can be treated as different domains to form cross-domain recommendation tasks. Also, as many movies in these datasets are in common, a recommendation scenario based on overlapping items can generate.There are three widely used movie datasets: MovieLens (mov, [n.d.]), Netflix (net, [n.d.]) and EachMovie (eac, [n.d.]).

• •

  The MovieLens dataset is crawled from MovieLens, a well-received movie recommendation website, which contains a group of datasets leveled by a rating scale. Among them three stable benchmark datasets, i.e., MovieLens-100K, MovieLens-1M and MovieLens-20M, are most popular. The differences between them are that they have a distinct volume of interactions. Each interaction in this dataset includes ratings on a scale of $[0.5,5]$ with half-rating increments, attributes of movies, and tags user-generated. Movies are separated into 18 distinct genres including Action, Adventure, Horror, and so on.

• •

  The Netflix dataset, offered by Netflix for a competition, consists of about $100,000,000$ ratings for $17,770$ movies given by $480,189$ users. Each interaction consists of ratings on a scale of $[1,5]$, the interaction time, and attributes of movies.

• •

  The EachMovie dataset is extracted from EachMovie recommendation service compromising $2,811,983$ ratings from $1$ to $6$ entered by $72,916$ users for $1628$ different movies.

The cross-domain book recommendation is another prevalent task. Book-Crossing (boo, [n.d.]) and LibraryThing (lib, [n.d.]) are two majorly adopted datasets for the task.

• •

  The Book-Crossing dataset is crawled from the Book-Crossing community contains $278,858$ users with $1,149,780$ ratings about $271,379$ books. Interactions in this dataset compromise explicit ratings on a scale of $[1,10]$ to books. Demographic information about users including location and age are provided while content-based information of each book, i.e., tile, author, year of publication, and publisher, are given.

• •

  The Library Thing dataset is collected from Library Thing, an online book review website, which publishes information about books and enables users to create their virtual libraries and tag books. It consists of $2,056,487$ tuples with $7,279$ users, $37,232$ books, and $10,559$ tags. In each dataset, a user gives ratings ranged between $1$ and $5$, reviews, tags to a book. In addition, friend relations among users are given which are similar to the trust relations of social networks in Epinions.

Although user identities are not identical across different datasets, each book in these datasets is labeled by a unique ISBN ID. It is possible to match the same book in different domains to build cross-domain recommendation scenarios where users do not overlap and items are fully or partially overlapped.

Music datasets record user-music interactions and Yahoo! Music (yah, [n.d.]) and Last.FM (las, [n.d.]) are two representative music datasets.

• •

  The Yahoo! Music dataset, offered by Yahoo Research, consists of a wealth of information about music. Users give explicit ratings to entities of four different types, i.e., tracks, albums, artists, and genres, constituting four types of interactions. In addition to ratings, each interaction also contains attributes of entities.

• •

  The Last.FM is released by HetRec in $2011$. Different from previously introduced datasets, this dataset contains the number of times a song has been listened to by a user instead of explicit ratings as well as tags generated by the user.

In most instances, social interaction datasets are used as auxiliary information to assist cross-domain recommendation. Twitter (twi, [n.d.]), Youtube (you, [n.d.]), Weibo (wei, [n.d.]) and DBLP (dbl, [n.d.]) are four typically used datasets.

• •

  The Twitter dataset is crawled from one of the most widespread social networks, Twitter. Each interaction includes tweet content, the interaction time, and tags users generated.

• •

  The Youtube dataset, given by Youtube, consists of user-video interactions provided with video ID, video title, label, class, the interaction time, and detailed description.

• •

  The Weibo dataset is crawled from the largest Chinese Twitter Weibo. Each tweet contains tweet content, user identification, interaction time, comments, and tags. Each user owns a profile of gender, name, followers, and followees, which is possible to form a social relation network.

• •

  The DBLP dataset is offered by a famous citation network DBLP. Each interaction compromises paper, abstract, authors, year, venue, title, and citations. Moreover, citations of papers are used to construct a social relation network.

Point-of-interest datasets record the behaviors of users at the Point-of-Interest (POI) which are widely used for cross-domain venue recommendation. The most popular POI datasets include Yelp (yel, [n.d.]) and two check-in datasets, Brightkite (bri, [n.d.]) and Foursquare (fou, [n.d.]).

• •

  The Yelp dataset is offered by the largest review site in the U.S., i.e., Yelp, for a challenge. This dataset consists of ratings on a scale of $[1,5]$, reviews, and tips of each interaction as well as social relation network.

• •

  The Brightkite dataset is extracted from a location-based social networking service provider Brightkite, where users shared their locations by checking-in. Interactions with check-in time and location as well as friendship network are available in this dataset.

• •

  The Foursquare dataset is collected from Foursquare, a location data platform for understanding how people move through the real world. The dataset consists of check-in data for different cities accompanied by timestamps, GPS coordinates, and semantic meaning (represented by fine-grained venue categories).

• •

  The Cheetah Mobile dataset is a mobile dataset collected from Cheetah. It consists of two domains, that is, app installation and news browsing, which makes it naturally fit for cross-domain recommendation scenarios where users overlap but items do not. Each interaction in the news browsing domain contains contents of news, the interaction time, and user profiles, while each interaction of app installation includes app IDs and some metadata about both users and apps.