A Survey on Cross-Domain Sequential Recommendation

1 Introduction

In real life, people always leave interaction traces in multiple scenarios (e.g., shopping scenarios, reading scenarios, etc.), multiple platforms (e.g., Amazon, Taobao, etc.), and even multiple boards (e.g., books and movies in Douban, etc.). Considering all these as different domains, combining in-depth information across domains is a critical step for the development of recommender systems. It makes the data of user preferences no longer fragmented and shifts the modeling from flat to stereoscopic. As shown in Table 1, recommender systems focus on information that is becoming deeper and more comprehensive, starting from traditional one-class collaborative filtering (OCCF), further progressing to sequential one-class collaborative filtering (SOCCF) and to crossdomain one-class collaborative filtering (CD-OCCF), and finally to cross-domain sequential one-class collaborative filtering (CD-SOCCF, also called cross-domain sequential recommendation, CDSR).

∗Corresponding author

In the case of OCCF [Rendle et al., 2012], the available information is limited to whether a user interacts with an item. As illustrated in Figure 1, we only know all the items that User 1 and User 2 have interacted with in a single domain, without considering the sequential pattern among successive items. SOCCF [Lin et al., 2020], building upon OCCF, places greater emphasis on the order relationships between items within a sequence, i.e., the information of intra-sequence in a single domain, which enables the model to capture the user's long-term and short-term preferences. At a large granularity, expanding from a single domain to multiple domains offers a fresh perspective to address the data sparsity issue in recommender systems, thus constituting CD-OCCF [Hu et al., 2018]. For instance, as shown in Figure 1, users have interactions not only in the book domain but also in the closely related movie domain. In a cross-domain scenario, we must meet the following challenges: how to transfer or aggregate interaction records from multiple domains and how to align representations of users or items across different domains [Zhu et al., 2021b].

Indeed, CDSR combines all of the aforementioned directions and further incorporates sequential information based on CD-OCCF and cross-domain information based on SOCCF. As indicated by the purple arrows in Figure 1, CDSR necessitates the precise capturing of sequential relationships between items across different domains. For example, User 1, after reading two books in the Harry Potter series, chooses to watch the corresponding Harry Potter movie. Similarly, User 2 who enjoys watching romantic movies also reads the original novels after watching the Pride and Prejudice movie. Besides, it is also worth considering in CDSR how to fuse sequential information from different domains as well as how to distinguish between users' specific preferences within a single domain and global preferences shared across multiple domains.

In this survey, we first formulate the CDSR problem and modeling tasks, considering various dimensionality reductions and different input representations. Then we adopt both macro and micro views to summarize the existing works in CDSR. From a macro view, we present an overview of multilevel fusion structures, discussing how to fuse information across different domains and exploring bridges for crossdomain fusion. From a micro view, we conduct a detailed analysis of various technologies employed by existing works that are categorized into basic and auxiliary learning technologies. Based on this analysis, we obtain a comprehensive classification (shown in Table 2) and framework figure of the key technologies (shown in Figure 5). Furthermore, we list the datasets commonly used in CDSR and the representative experimental results as well as provide some insights into potential future directions.

2 Formulation

In this section, we first present the problem definition of CDSR using a four-dimensional tensor. Then, referring to Figure 2, we delve into the various directions of dimensionality reduction that are often adopted in practical modeling and the corresponding multi-type input representations.

2.1 ProblemDefinition

As temporal information and cross-domain information are incorporated, the interaction data between users and items in CDSR undergoes a gradual expansion into a four-dimensional data tensor, consisting of dimensions about users, items, time, and domains. We denote this four-dimensional tensor with Γ ∈ Rn×m×s×k , where n and m is the number of users and items in all domain, s is the discrete time intervals, and k is the number of domains. Each element γ(u,i,t,d) in it signifies whether there is an interaction between user u and item i at time t in domain d. The goal of CDSR is to estimate the probability for all candidate items in each domain, and then to recommend the most probable next item to each user. The estimated probability can be formalized as follows,

where ˆi denotes the candidate item of each user in each domain, Γ is the four-dimensional tensor containing all interaction information, and f( Γ ) indicates the learned function to estimate P( ˆi | Γ ).

Notice that most existing works in CDSR are primarily established on two domains, i.e., k = 2. Therefore, for the subsequent discussion, we take two domains as an example and represent them as domain A and domain B, respectively. In fact, some researchers [Bi et al., 2020; Xu et al., 2023c] also refer to the two domains as a source domain and a target domain. Moreover, some works [Ma et al., 2019; Sun et al., 2023; Guo et al., 2021; Guo et al., 2023c] introduce an additional assumption with a shared account. They assume that within a real account, there are q virtual users (uj, j ≤ q) simultaneously active. Regarding the shared account issue, it is applicable not only in cross-domain scenarios but also in single-domain scenarios.

2.2 Multidirectional Dimensionality Reduction

For computational and modeling convenience, the fourdimensional tensor is often reduced to some threedimensional tensors from various directions (as shown in Figure 2). Below, we explain dimensionality reduction from three directions:

W/o User Dimension. For a user, his or her interactions in chronological order can form a sequence in each domain. These sequences reflect the user's personalization as well as long and short-term preferences in different domains, and can further serve as the basis for constructing a local graph in subsequent work.

W/o Time Dimension. Mapping the tensor along the temporal dimension and aggregating interactions within a time lays the groundwork for a global graph. It allows models to learn user-to-user and user-to-item connections, which are more skewed toward users' global preferences.

W/o Domain Dimension. Blending two or more domains into a hybrid domain, a model can clarify the passing relationships between items originally in different domains. Many existing studies treat the hybrid domain as an independent domain, and design model fusion structures that incorporate all three domains in parallel, which is shown in Section 3.1.

Indeed, these dimensionality reduction directions are often combined and used in conjunction rather than being treated as independent. Adopting only one reduction direction may result in missing information to a certain degree. Next, we visualize these reduction processes on different input representations.

2.3 Multi-Type Input Representations

Researchers' considerations on dimensionality reduction directions in CDSR are first reflected in the input representations. Here, we categorize conventional input representations into pure sequential representation and graph-encoded sequential representation. Subsequently, we analyze unconventional inputs, including side information and pre-trained features.

Pure Sequential Representation

Arranging the interacted items of a user in chronological order yields a sequence. For each user u, we define SA u = {iA1 , iA2 , . . . } and SB u = {iB1 , iB2 , . . . } as his or her interaction sequences in domain A and domain B, respectively. If u is an overlapping user who has interactions both in domain A and domain B, we can mix SA u and SB u to a hybrid sequence in chronological order (e.g., Shybrid u = {iA1 , iB1 , iA2 , iA3 , iB2 , . . . }), which is viewed as a sequence of the hybrid domain. From a pure sequential perspective, we can substitute the four-dimensional tensor in Eq.(1) with the set of sequences in each domain, as follows,

Graph-Encoded Sequential Representation

Some researchers [Guo et al., 2021; Zheng et al., 2022; Cao et al., 2022; Zhang et al., 2023b] turn to construct directed graphs G = {V,E} to model sequential information, where V is a set of items that have been interacted with and E is the edges that represent relations of the serial relationship from item to item. Constructing a user's sequence within a domain or a sequence within a session as a local graph is a common practice [Zheng et al., 2022; Chen et al., 2021]. In the global graph construction scenario, E is also utilized to denote the relations between users and items [Xu et al., 2023c]. We represent the raw data in its graph-encoded form to extend Eq.(1), where Gl denotes all local graphs and Gg denotes the global graph, as follows,

Side Information

More and more researchers consider incorporating side information to enrich the semantic representation of users' historical behaviors. In this section, we divide the most common side information into three categories: time, text (e.g., user/item contexts and reviews), and knowledge graph.

Time. Previously the timestamps are only used to order the items, but some researchers [Xiao et al., 2023; Wang et al., 2022; Guo et al., 2022] define tij = |ti - tj| to model the time interval and apply it to the subsequent learning of model, where ti and tj are the timestamps that the item i and the item j are interacted with, respectively. Besides, we can also mine more information about time, such as periodicity and the duration of the interaction, etc.

User/ItemContexts and Reviews. Except for the user ID, triples composed of multiple contextual information (e.g., ("UserID", "City", "Age", · · · )) are utilized as a basis for finding user-user relationships [Ouyang et al., 2020]. Similarly, the context information that consists of categories, tags, keywords, etc, is used as a supplement to item ID [Xiao et al., 2023; Ouyang et al., 2020; Zhuang et al., 2020]. Review as a type of available text message can associate users and items well. A common way to encode these texts is through some pre-trained models, such as BERT [Devlin et al., 2018].

Knowledge Graph. Knowledge graphs [Bi et al., 2020; Ma et al., 2022] deal with information from both entity and relationship views. It not only contains structural information between nodes but also implies some relationship description. A knowledge graph defines an entity set EKG and a relation set RKG, which consists of multiple entity-relation-entity triples < ei, r, ej > (e.g., < eiA1 , Is the same category, eiB1 > meaning that the entity eiA1 from domain A has the same category as entity eiB1 from domain B).

Considering the aforementioned side information, we can extend Eq.(1) as follows,

where D is the side information mentioned above and often serves as supplementary data to conventional inputs.

Pre-trained Features

Considering the privacy issues in two or more domains, some works [Ding et al., 2023; Zhang et al., 2023a; Lei et al., 2021] use model-trained features as the input from the source domain, instead of raw data. [Ding et al., 2023] directly combines the pre-trained user features from one domain with another domain. [Zhang et al., 2023a] utilizes federated learning to fetch the global representation from the server, and then injects it into the local model.

We take domain A as an example and revise Eq.(1) as follows,

where M B are the features of domain B after pre-training and ΓA denotes the interaction data exclusively within domain A. Notice that in domain B, the equation is P( ˆi | ΓB ,M A) ∼ f( ΓB ,M A).

3 Macro-View: What Structure Is Used to Fuse the CDSR Information?

In CDSR, the fusion structure serves as the primary skeleton of a model, providing pathways for the separation and aggregation of these features. In this section, we first describe multi-level fusion structures and then elaborate on the bridge for inter-domain fusion.

3.1 Multi-Level Cross-Domain Fusion Structures

For cross-domain fusion, researchers employ various structures to aggregate information from different domains. In this section, we overview the various multi-level fusion structures shown in Figure 3. Specifically, we introduce those structures from two parts, i.e., the one-level fusion structures and the two/three-level fusion structures.

One-Level Fusion Structures

In earlier works, to combine the cross-domain information, there are a lot of works that first learn user preferences from domain A and domain B separately, and then fuse the representations of the two domains using various operations (as shown in Figure 3(a)). These operations include, but are not limited to, concatenation [Lei et al., 2021; Guo et al., 2023c], summation [Alharbi and Caragea, 2021; Ding et al., 2023], multi-layer perceptron (MLP) [Bi et al., 2020], and some attention mechanisms [Ouyang et al., 2020; Li et al., 2021].

Additionally, some works employ transfer learning to transfer knowledge from a source domain to a target domain [Chen et al., 2021; Liu and Zhu, 2021], or train a discriminator to bridge the representations of two domains with the idea of adversarial learning [Li et al., 2022], as shown in Figure 3(b).

In contrast to the above-juxtaposed structures, there are also works utilizing a tandem structure to fuse information [Alharbi and Caragea, 2022] (i.e., Figure 3(c)), or directly tackling the problem from the perspective of a hybrid-domain view (i.e., Figure 3(d)). For instance, some works [Guo et al., 2021; Guo et al., 2022] construct a global graph for the hybrid domain to combine the cross-domain knowledge. And others like [Ma et al., 2019; Sun et al., 2023] choose to learn the item transition patterns in the hybrid sequences Shybrid .

Two/Three-Level Fusion Structures

Considering the potential for further exploration and advancement in fusion structures, some works combine the single domain and the hybrid domain with a multi-level fusion structure. As shown in Figure 3(e), in order to predict the next item in a separate domain, the hybrid domain is utilized as the main sharer [Cao et al., 2022; Wang et al., 2022] or the bridge [Zheng et al., 2022] to transfer knowledge from another domain. There are also some works [Ye et al., 2023] that choose to combine the domain A and domain B first and then fuse the hybrid information (i.e., Figure 3(f)).

To delve further into the fusion structures, some researchers continue to extend the hierarchy, as illustrated in Figure 3(g) [Xu et al., 2023c] which aggregates the representations again after combining the hybrid domain information on the basis of Figure 3(e). Figure 3(h) [Zhang et al., 2023b] proposes a more complex structure, which shares the coarsegrained representations of the target domain A and the hybrid domain with each other domain.

Discussion

Although there are various multi-level fusion structures, it does not mean that a more complex structure will perform better. Limited by the degree of fusion, the simple fusion structures, i.e., one-level fusion structures, are easy to implement but may not comprehensively model the domainspecific and domain-generic features. While improving effectiveness, multi-level fusion structures bring increased complexity and reduced interpretability.

Considering the symmetry and asymmetry of the structures, which the researchers focus on each domain greatly affects the design of a cross-domain fusion structure. For example, some researchers [Ouyang et al., 2020; Bi et al., 2020; Xu et al., 2023c] consider the two domains as source and target domains and leverage the data-rich source domain to assist the data-sparse target domain, which makes the target domain dominant in the fusion structure. Other researchers [Guo et al., 2021; Li et al., 2021; Ma et al., 2022] aim to improve the recommendation performance of both domains simultaneously, making the fusion structure designed tend to be more symmetric.

3.2 Bridges for Cross-Domain Fusion

When comes to cross-domain fusion, it is vital to clarify the bridges for information sharing between domains. We divide those bridges into three categories: same users, contexts, and clusters/groups, as shown in Figure 4. The first is prevalent in scenarios with overlapping users, while the latter two are applied in scenarios without overlapping users.

Same Users. If some same users exist, then they are often the first choice as the bridge. Some works only focus on the fully overlapping users, neglecting non-overlapping users, while others [Li et al., 2022] consider both cases.

Contexts. If there are no common users, it is feasible to leverage the semantic similarity of natural language. For instance, we can replace traditional item IDs with item contexts to explore similarities between items of different domains [Liu et al., 2023].

Clusters/Groups. Further restricting the condition to no overlapping users and no side information, the clusters/groups are another entry point since a specific group of users could have similar preferences [Lin et al., 2023a].

Works relying on overlapping users often perform well but their application scenarios may face limitations due to the sparse real-world data. Conversely, works built on nonoverlapping users can be applied to a broader range of scenarios but may have limited performance. In fact, cross-domain can be built on more than one type of bridge.

4 Micro-View: What Technologies Are Used to Address the CDSR Problem?

In this section, we take a more tangible perspective to summarize the technologies adopted by the existing models in addressing the challenges in CDSR. In conjunction with Table 2 and Figure 5, we elaborate on the basic technologies and the auxiliary learning technologies, respectively.

4.1 Basic Technologies

According to Section 2.3, the cross-domain information is always considered as a pure sequential representation or a graph-encoded sequential representation. So we illustrate the utilization of sequence modeling technologies (i.e., recurrent neural networks and attention mechanisms) and graph structure modeling technologies (i.e., graph neural networks) in CDSR, respectively. Moreover, from Figure 5, we can observe that the three basic technologies are not independent entities and can be applied interchangeably or in parallel based on the characteristics of different technologies. Notice that multi-layer perceptron (MLP) is used in almost all existing models for non-linear feature mapping or to simply aggregate cross-domain information [Xu et al., 2023b; Hong and Jung, 2023], so we do not describe it separately.

Recurrent Neural Networks in CDSR

Recurrent neural networks (RNNs) model sequences, by taking the current time step's representation and the hidden features from the previous time step as input, and generating the output and hidden features for the current time step. Due to the issues of vanishing and exploding gradients, its variants, i.e., gated recurrent unit (GRU) and long short-term memory (LSTM) [Yang et al., 2020], are more widely adopted. In CDSR, some works [Li et al., 2021; Chen et al., 2021; Zang et al., 2023] directly employ GRUs as encoders of sequences to get sequential representations. While some works incorporate a shared unit into each step of RNNs to transfer cross-domain information. The shared unit could be a shared-account filter unit [Ma et al., 2019; Sun et al., 2023] or the common representations of the overlapping users [Wang et al., 2020]. While RNNs are easy to implement and are capable of modeling the temporal relationships in sequences, they still suffer from issues such as vanishing and exploding gradients during training.

Attention Mechanisms in CDSR

Attention mechanisms can selectively focus on the importance of different parts and weight their contributions accordingly, enabling effective aggregation. Attention mechanisms are utilized in two main ways in CDSR. One is to use an attention-based encoder (e.g., Transformer [Vaswani et al., 2017], SASRec [Kang and McAuley, 2018] or multihead attention blocks, etc.), replacing RNNs as a sequence encoder [Ye et al., 2023; Xu et al., 2023c; Alharbi and Caragea, 2022; Ding et al., 2023; Park et al., 2023]. The other is to obtain learnable attention weights thus aggregating cross-domain information at multiple levels. For instance, MiNet [Ouyang et al., 2020] designs item-level attention and interest-level attention to learn which items are more important and which of these items better matches a certain interest of the user. With representation-level attention, C2DSR [Cao et al., 2022] fuses the sequential representation and the graph representation together. By adopting domain-level attention, Tri-CDR [Ma et al., 2023] learns the weights of the features from different domains and then aggregates them. And MAN [Lin et al., 2023a] also proposes a group-level attention to bridge the not-aligned information. In fact, attention strategies need to be designed from multiple levels which poses a challenge to researchers.

However, it needs to use the interaction of all the positions when calculating the weights, so it contains a large number of parameters and may suffer from the issue of data sparsity.

Graph Neural Networks in CDSR

Aware of the structural relationships of item-item and itemuser in a sequence, graph neural networks are used to model such information. Some works construct a graph per session [Chen et al., 2021] or per domain [Cao et al., 2022; Xu et al., 2023c], or just construct a global graph [Guo et al., 2021; Zhang et al., 2023b] based on the hybrid domain of all users. Apart from that, DCDIR [Bi et al., 2020] and MIFN [Ma et al., 2022] construct a knowledge graph to encompass more semantic information. Most works combine graph encoders (i.e., GNNs) and sequence encoders (i.e., RNNs or attention mechanisms) as complementary parts in CDSR. For instance, DA-GCN [Guo et al., 2021] utilizes graph convolutional networks to learn latent user representations and user-specific item representations and then carries the weights from the item and user neighbors to the target item in each domain with an attention matrix. C2DSR [Cao et al., 2022] combines the encoded representations from GNNs with the original sequences and feeds them into the attention encoder for further modeling. It supplementally learns complex information about nodes and edges to capture more comprehensive preferences of users. However, when GNNs are applied to a large-scale data, the huge computational and storage overhead is a major drawback in most cases.

4.2 Auxiliary Learning

In addition to the aforementioned key technologies, the utilization of auxiliary learning technologies to facilitate the integration of cross-domain information garners significant attention.

Transfer Learning

Transfer learning (TL) [Pan and Yang, 2009] is primarily employed to transfer knowledge learned from one task to another task. For instance, CDNST [Zhuang et al., 2020] transfers the novelty-seeking trait learned from a source domain to a target domain. SATLR [Liu and Zhu, 2021] considers transferring knowledge by multiplying the independently learned representations from one domain with an orthogonal mapping matrix. Some works adopt dual transfer learning to improve the ability to transfer knowledge. DAT-MDI [Chen et al., 2021] combines a dual transfer model with slot attention to selfadapt item embedding from different domains. DASL [Li et al., 2021] applies a dual embedding component to unify the learning process of user representations and then proposes a dual attention component to incorporate user behaviors in multiple domains.

Contrastive Learning

Contrastive learning (CL) [Jing et al., 2023] is also a widely applied technique that leverages the similarities and differences between samples to extract useful information. In the case of Tri-CDR [Ma et al., 2023], it designs two contrastive learning tasks, i.e., coarse-grained similarity modeling and fine-grained distinction modeling. Coarse-grained similarity modeling closes three domains' sequence representations of the same user, and fine-grained distinction modeling assumes the distance between domain A and domain B should be larger than the distance between domain B and the hybrid domain. MGCL [Xu et al., 2023c] views the local and global item representations of a user as the positive samples and the representations from different users as the negative samples. Additionally, some works aggregate the sequences and then combine those processed sequences with CL. DREAM [Ye et al., 2023] proposes supervised contrastive learning to minimize the relevance among inter-sequences with different preferences.

Other Auxiliary Learning Technologies

In addition to transfer learning and contrastive learning, there are other auxiliary learning technologies. For instance, RecGURU [Li et al., 2022] and TPUF [Ding et al., 2023] train a discriminator until it is unable to distinguish whether a feature belongs to domain A or domain B, thereby achieving the goal of adversarial feature alignment. FedDCSR [Zhang et al., 2023a] leverages federated learning [Yang et al., 2019]

to preserve data privacy. RL-ISN [Guo et al., 2023c] utilizes rewards in reinforcement learning to determine whether to revise the whole transferred sequence and selects which interactions should be retained, thus alleviating the noise introduced by transferring cross-domain information. PLCR [Guo et al., 2023b] treats domain-specific contexts as the prompt and feeds them with domain-agnostic contexts and label features into self-attention blocks to learn prompt embedding.

Discussion

Incorporating auxiliary learning technologies aims to enhance a model's ability to capture cross-domain information. Contrastive learning can make learned representations more discriminative and robust, but it is sensitive to the designed contrastive strategy. Transfer learning enables the sharing of information across domains, but the effectiveness of knowledge transfer is affected by the correlation between domains, i.e., there is vulnerability to negative transfer [Zhang et al., 2023c]. Moreover, adversarial learning can unify representations from different domains but its training process is more complex.

5 Datasets and Experimental Results

In this section, we summarize a list of commonly used datasets of CDSR, including their corresponding domains, data types, and scales shown in Table 3.

In order to more fully represent the advantage in CDSR compared to other issues in Table 1 and the performance of models with different technologies in CDSR, we quote the results of representative models from [Cao et al., 2022; Xiao et al., 2023; Ye et al., 2023] in Table 4. Notice that these three papers are consistent in their treatment of this dataset. The results show that with the increase in information and advancements in methods, the results gradually improve.

6 Future Directions

In this section, we provide several promising directions in CDSR for potential developments from different aspects.

Multi-Domain Simultaneous Improvement. As mentioned in Section 3.1 and shown in Figure 3, most existing models are primarily established on two domains. In realworld applications, users tend to have interactions in multiple domains.Exploring how to integrate information from multiple domains (e.g., dozens of domains) and simultaneously improve the performance of each domain is a crucial research direction for the future of CDSR.

Heterogeneous Information Fusion. Apart from the side information mentioned in Section 2.3, there is a large amount of relevant heterogeneous information in real-world applications. For example, users are likely to transfer from browsing short videos to purchasing items mentioned in the videos. Therefore, it is worth investigating effective methods that combine heterogeneous information (e.g., image, video, etc.) and traditional ID-based information, to address the challenges in cross-domain recommendation. Moreover, it is also worth considering introducing heterogeneous sequential behaviors into cross-domain scenarios.

Deep Utilization of Non-overlapping Information. Indeed, the majority of current models rely on overlapping users to bridge different domains, but non-overlapping data also contain rich semantic information that is worth exploring and extracting [Liu et al., 2023]. So researchers can conduct deeper studies on non-aligned information.

Privacy Preservation. When it comes to sensitive user information, encryption and protection of data is crucial. Particularly within the realm of CDSR, there is a greater inclusion of user data. Therefore, designing effective federated learning methods to ensure privacy while minimizing the loss of valuable information in the cross-domain scenario is a meaningful but less studied area [Lin et al., 2023b].

Fairness and Interpretability. Fairness and interpretability are crucial research topics in recommender systems. In CDSR, it is essential to reduce the bias between different domains and to interpret cross-domain sequential recommendation results to users.

More Advanced Technologies. In Section 4, we analyze the technologies used in existing CDSR models from a micro view. However, achieving greater leaps in performance demands more advanced technologies. For instance, exploring the application of large language models (LLMs) [Wu et al., 2023] in the CDSR scenario is also a promising direction.

7 Conclusions

Cross-domain sequential recommendation (CDSR) extends traditional recommender systems by incorporating sequential and cross-domain information, aiming to address the data sparsity issue. In this survey, we approach CDSR with a fourdimensional tensor and offer a comprehensive overview from macro and micro views. From a macro view, we summarize the existing models by abstracting multi-level fusion structures and discuss the bridges for cross-domain fusion. From a micro view, we analyze and summarize the employed basic and auxiliary learning technologies. Finally, we include some public datasets and experimental results for CDSR, and provide some promising future research directions.

Acknowledgments

We thank the support of National Natural Science Foundation of China (Nos. 62172283 and 62272315), Guangdong Basic and Applied Basic Research Foundation (No. 2024A1515010122) and National Key Research and Development Program of China (No. 2023YFF0725100).