Dual cross-domain session-based recommendation with multi-channel integration

Abstract

Session-based recommendation aims at predicting the next behavior when the current interaction sequence is given. Recent advances evaluate the effectiveness of dual cross-domain information for the session-based recommendation. However, we discover that accurately modeling the session representations is still a challenging problem due to the complexity of preference interactions in the cross-domain, and various methods are proposed to only model the common features of cross-domain, while ignoring the specific features and enhanced features for the dual cross-domain. Without modeling the complete features, the existing methods suffer from poor recommendation accuracy. Therefore, we propose an end-to-end dual cross-domain with multi-channel interaction model (DCMI), which utilizes dual cross-domain session information and multiple preference interaction encoders, for session-based recommendation. In DCMI, we apply a graph neural network to generate the session global preference and local preference. Then, we design a cross-preference interaction module to capture the common, specific, and enhanced features for cross-domain sessions with local preferences and global preferences. Finally, we combine multiple preferences with a bilinear fusion mechanism to characterize and make recommendations. Experimental results on the Amazon dataset demonstrate the superiority of the DCMI model over the state-of-the-art methods.

Keywords

Session-based recommendation dual cross-domain cross-preference interaction module bilinear fusion mechanism

1. Introduction

Session-based recommendation (SR) is to predict which item a user will click next, only based on his/her current sequential session data and without user identification [25]. It plays a significant role in recommendation systems, such as e-commerce and search, because it helps users alleviate the problem of information overload in many web applications.

Due to the highly practical value in both industry and academia, many approaches have been proposed till the present moment. The classic approaches model the session representation are either similarity-based or chain-based categories. The former heavily depends on the co-occurrence of items while ignore the sequential information in the session. The latter models the single way transitions between adjacent items in a session, such as Markov Chain (MC) [24], and Item-KNN [23]. However, these methods ignore the complex transitions among distant items. More recent solutions employ deep-learning-based methods, such as graph neural networks and memory networks, to efficiently model complex item transitions in SR. Such methods learn the session representation utilizing the relevance of the last item to the user preference of the current session. However, the problem of data sparsity remains the challenge of session-based recommendation. Recently, with the development of neural networks, methods with either auxiliary information or self-supervised learning [30] have been proposed to alleviate the data sparsity issue. Despite the achievements, these approaches focus on a single domain where users may have a short behavior history, affecting user preference learning and leading to sub-optimal recommendation performance.

Cross-domain recommendation has been proposed to alleviate the data sparsity issue by mapping the user preference from one domain to the target domain. Inspired by its great success in the areas of cold start recommendation, some session-based recommendation utilize cross-domain information achieving state-of-the-art performance [1] by leveraging and combining information from different domains, such as finding a movie from the movie domain with the help of a certain style in the book domain. However, these methods introduce information in other domain by mapping user representation from one domain to another by capturing common features, which cannot make recommendations for two domains simultaneously. Furthermore, to exploit the duality between the two domains and improve the transfer ability, the dual transfer learning mechansism for a session-based recommendation has been proposed to learn marginal distribution. One of the key challgenges in dual cross-domain session-based recommendation is to capture and transfer complex and useful information about related preferences across different domains. Zheng et al. [35] integrate information from other domains to improve recommendation performance using dual dynamic graph modeling and hybrid metric learning. Ma et al. [17] design a mixed information flow network for the cross-domain sequential recommendation that considers behavioral information and the knowledge flow by incorporating the behavior transfer unit and knowledge transfer unit. However, the above modeling methods only learn the mapped shared subspace’s features while ignoring the complex interaction between cross-domain for session-based recommendation tasks. In the real world, users in different domains have different preferences, with the feature interaction between cross-domain including common preferences, specific preferences, and enhanced preferences. For example, as illustrated in Fig. 1, the sessions of a user in domain Movie and domain Book are session A and session B. Suppose we use the cross-domain session B as the collaborative information of session A. In that case, the movies of Heidi and Zootopia in domain A are considered noisy since the common science-fiction features in both domains generate the recommendation results. However, this ignores the specific preferences of the kind of self-improvement in domain A since the interactions of Heidi and Zootopia are integral parts. Additionally, the potential features of the enhanced preference in cross-domain are also not effectively captured. The items of $v_{1}^{B}$ , $v_{3}^{B}$ , $v_{5}^{B}$ are remapped into movies $v_{2}^{A}$ , $v_{3}^{A}$ , $v_{5}^{A}$ , which are also clicked by a user. This indicates that the user prefers to read books made into movies or watch movies published as a book. Therefore, building a framework that can make session-based recommendations for the dual cross-domain simultaneously is meaningful, and building the session preference from the multiple-channel interactions is also necessary.

Fig. 1.

Cross-domain sessions of a user.

Spurred by the above findings, we propose a novel end-to-end approach to exploit session representation over the cross-domain recommendation in a more subtle manner for better inferring the user preference for session-based recommendation, which is named dual cross-domain with multi-channel interaction for session-based recommendation (DCMI). In DCMI, it first uses the graph neural network to generate the session global preference and local preference based on current session for each domain. Second, it employs a cross-preference interaction module to update the three preferences of each domain with the help of cross-domain information, which captures the complex interaction patterns and derives common, specific, and enhanced preferences. It proves significantly effective. Then, it introduces adversarial mechanism to encourage divergence between the two encodes, which can prevent the two models become very similar and suggest the similar item. Finally, we combine multiple preferences with bilinear fusion mechanism as each session representation, and further compute the recommendation score for each candidate item based on the session representation in each domain. Meanwhile, since improving recommendation performance in one domain could also lead to an improved recommendation performance in the other domain, transferring the preferences from the target domain back to the source domain is more desirable.

We implement experiments on three public datasets. The experimental results show our model obviously outperforms other state-of-the-art methods on Amazon dataset. The main contributions of our method can be summarized as follows:

To the best of our knowledge, we are the first to introduce the thought of learning the complexity of cross features for dual cross-domain session-based recommendation. Additionally, we design a cross-preference interaction module that models cross-domain feature interactions that effectively build complete and rich enhanced features.

We build an efficient adversarial mechanism that uses the divergence constraint to make the two encoders differ to some degree. This strategy exploits different aspects of connectivity information.

For better learning of the session representation, we introduce a bilinear fusion mechanism to improve session representation. With selectively combining information from current session and cross-domain, a better representation can be achieved and further helping SR.

The experimental results demonstrate that our model achieves obvious and consistent improvements compared with all state-of-the-art methods. Some analysis parts also validate the effectiveness of our proposal.

2. Related work

The proposed method stems from three research directions: session-based recommendation, cross-domain recommendation, dual learning.

2.1. Session-based recommendation

The conventional methods for SR are mainly based on the idea of item-to-item or co-occurrences of items in sessions. Linden et al. [14] use item-to-item collaborative filtering for recommendation. Rendle et al. [21] combine Matrix Factorization and MC to model sequential behaviors for next basket recommendation. However, these methods do not make full use of the whole sequence simultaneously. To enhance the capability of capturing high-dimensional features, deep learning based method is introduced into SR methods, and Recurrent neural network (RNN) and GNN are two typical networks for session-based recommendation. RNN has received great attention since its capabilities in modeling the sequential behavior. Hidasi et al. [7] are the first research to apply RNN into SR, in which the item sequences in a session are treated as the input of RNN. Tan et al. [26] improve the RNN-based model performance by data augmentation and a method to account for shifts in the input data distribution. Li et al. [10] design a model called NARM which takes the last item’s hidden state as global interest and applies item-level attention mechanism to build the main purpose. Liu et al. [15] propose a method called STAMP which captures long-term and short-term interest to generate the global interest and main purpose. Wang et al. [28] introduce a hybrid framework CSRM which uses ongoing session information and collaborative neighborhood information to improve recommendation performance. Pan et al. [19] consider the importance of the items in terms of their relevance to user’s main intent to improve the recommendation performance. However, these methods focus on modeling the sequential transitions of adjacent items to build user preference by modeling the chronology of the given sequence, and they put a poor show in modeling complex transition patterns. Later GNN is increasingly used in SR recently. Qiu et al. [20] propose a weighted attention graph layer and a readout function to learn embeddings of items and sessions for recommendation. Yu et al. [32] design a model called TAGNN which incorporates graph-structured data and target-aware attention module for SR. However, these methods model the user preference only based on the current session, and they cannot model the good quality embedding of user preference for the problem of data sparsity due to the very limited short-term interactions. To alleviate the problem of data sparsity, Xia et al. [31] combine self-supervised learning with co-training processes for SR recommendation, which preserves the complete session information and fulfills genuine data augmentation. Pang et al. [8] propose a mirror graph enhanced neural model for SB recommendation to exploit item attribute information. Wang et al. [27] consider time intervals and introduce the graph transformer into SR recommendation. Li et al. [13] incorporates the information of user’s location and the current time for modeling user preference in session-based recommendation. However, all these methods mainly focus on capturing the sequential characteristic in a single domain. In contrast, our proposed model learns the item-transition information over dual cross-domain strategy to enhance the learning from the two sessions.

2.2. Cross-domain recommendation

Cross-domain recommendation has ability to alleviate data sparsity issues since it can introduce auxiliary information from other domains. Zhao et al. [34] consider the process of user preference propagate in the graph and propose a preference propagation graphnet to alleviate high sparsity. Li and Tuzhilin [11] explicity model information of user and item features for cross domain recommendation. Li et al. [9] introduce the thought of cross domain to sequential recommendation scenario and propose a RecGURU method. Li et al. [12] design a gromov-wassertein guided cross-domain recommendation framework for the cross-domain recommendation where no explicit overlap between the source and target domains in terms of users/items. However, these methods only improve the recommendation accuracy on a target domain with the help of a source domain, and do not consider the dual cross-domain recommendation scenario. Moreover, applying them into dual cross-domain recommendation scenario immediately is not proper, which may further amplify noise interactions.

2.3. Dual learning

To improve the accuracy of recommendation performance on both domains simultaneously, recent studies pay attention to dual cross-domain recommendation. Zhang et al. [33] propose a cycle generation networks to construct the dual-direction personalized itemset mapping between a user’s behaviors in two different domains. Zhu et al. [36] propse a graphical and attentional framework, which uses element-wise attention mechanism to effectively combine the embeddings of common users learned from both domains. However, they ignores the sequence transition patterns. Recently, Ma et al. [16] take hybrid interaction sequence and extra knowledge into sequential representation modeling for across domains. However, mixing different domain sequential information is easily to bring noise information since different domain has different data distribution. Moreover, some studies give attention to shared-account cross-domain sequential recommendation. Ma et al. [18] propose a dual cross-domain sequential recommendation framework which simultaneously yields recommendations for two domains. Guo et al. [4] employ graph structure into modeling sequential patterns and explicit cross-main information for shared-account cross-domain sequential recommendation. Guo et al. [5] propose a reinforcement learning-based solution to model sequential patterns for shared-account cross-domain sequential recommendation. Although these studies begin to explore dual cross-domain recommendation, they do not focus on the integrating it with session-based recommendation task, and neglect to explore the complex interactions across domains. In contrast, our proposed method considers the collaborative information in dual directions simultaneously, it can improve the recommendation performance in all domains simultaneously: we use the item embedding and session preference in other sessions to enrich the item embeddings of current session and session preference in current session and vice versa, and then build session representation by selectively integrating them. In recent years, Chen et al. [1] introduce session information in other domain by mapping user representation from one domain to another by capturing common features, which can make recommendations for two domains simultaneously. However, it ignores the mixed feature interactions between cross domain, which includes common features, specific features, and enhanced features. Comparing with the above methods, our proposed model not only captures the item-transition information through different domains simultaneously to improve the representation learning, but also the complete and informative information can be derieved.

3. The proposed algorithm

In this section, we first give a formulation of the dual cross-domain session-based recommendation problem. Then, we give a high-level introduction to the framework of DCMI. Finally, we describe each component of DCMI in detail.

3.1. Task definition

Dual cross-domain session-based recommendation aims to simultaneously predict what the user may click next based on the anonymous current sequential data of each domain without accessing to the long-term preference profile. The main differences between dual cross-domain session-based recommendation and traditional session-based recommendation is that the former considers bidirectional latent information of user preferences across source-target domain pairs. At the same time, the latter only improves the recommendation performance in one domain.

To effectively extract latent user preferences and efficiently model the session representations, let $A = {v_{1}^{A}, v_{2}^{A}, \dots, v_{i}^{A}, \dots}$ denote the set of unique items in all sessions of domain A and $B = {v_{1}^{B}, v_{2}^{B}, \dots, v_{j}^{B}, \dots}$ denote the set of unique items in all sessions of domain B in a dual cross-domain session-based recommendation task. For sessions in different domain of a user, the sequences of m and n clicked actions by the user are denoted as $s_{A} = {v_{1}^{A}, v_{i}^{A}, \dots, v_{m}^{A}}$ and $s_{B} = {v_{1}^{B}, v_{j}^{B}, \dots, v_{n}^{B}}$ in time order, where $v_{i}^{A} \in A$ is the i-th index of one clicked item in domain A, $v_{j}^{B} \in B$ is the j-th index of one clicked item in domain B, The goal of our model is to predict the next clicked item $v_{m + 1}^{A}$ and $v_{n + 1}^{B}$ based on information extracted from $s_{A}$ , $s_{B}$ , and their dual interactions. Formally, our model aims to form a ranked list of all candidate items of each domain, which are denoted by ${\hat{y}}_{A} = {{\hat{y}}_{1}^{A}, {\hat{y}}_{2}^{A}, \dots, {\hat{y}}_{| V |}^{A}}$ and ${\hat{y}}_{B} = {{\hat{y}}_{1}^{B}, {\hat{y}}_{2}^{B}, \dots, {\hat{y}}_{| S |}^{B}}$ , where ${\hat{y}}_{m}^{A}$ refers to the score of item $v_{m}^{A}$ and ${\hat{y}}_{n}^{B}$ refers to the score of item $v_{n}^{B}$ . The prediction scores in each domain are ranked in the descending order, and the items ranked in the top-k are used for each session recommendation. The symbol table of this paper is shown in Table 1.

Table 1
Symbol definition descriptions

Symobol definition Descriptions

A Session A

B Session B

$v_{i}^{A}$ i-th index of one clicked item in domain A

$v_{j}^{B}$ j-th index of one clicked item in domain B

${\hat{y}}_{m}^{A}$ the score of item $v_{m}^{A}$

${\hat{y}}_{n}^{B}$ the score of item $v_{n}^{B}$

$v_{i}^{A}$ item embedding of $v_{i}^{A}$

$v_{j}^{B}$ item embedding of $v_{j}^{B}$

$l^{A}$ local preference of session A

$g^{A}$ global preference of session A

$l^{B}$ local preference of session B

$g^{B}$ global preference of session B

$L_{C L}$ contrastive learning loss

$L_{diff}$ divergence constraint loss

$s^{A}$ final session representation of session A

$s^{B}$ final session representation of session B

Symobol definition	Descriptions
A	Session A
B	Session B
$v_{i}^{A}$	i-th index of one clicked item in domain A
$v_{j}^{B}$	j-th index of one clicked item in domain B
${\hat{y}}_{m}^{A}$	the score of item $v_{m}^{A}$
${\hat{y}}_{n}^{B}$	the score of item $v_{n}^{B}$
$v_{i}^{A}$	item embedding of $v_{i}^{A}$
$v_{j}^{B}$	item embedding of $v_{j}^{B}$
$l^{A}$	local preference of session A
$g^{A}$	global preference of session A
$l^{B}$	local preference of session B
$g^{B}$	global preference of session B
$L_{C L}$	contrastive learning loss
$L_{diff}$	divergence constraint loss
$s^{A}$	final session representation of session A
$s^{B}$	final session representation of session B

3.2. Model overview

In the following subsections, we will describe DCMI, our proposed solution for dual cross-domain session-based recommendation, in detail. The key idea of DCMI is to learn a recommendation model that can first extract local preference and global preference from the domain A session, then transfer these preferences and the session representation to domain B, and combine it with the preference information in domain B to improve the session-based recommendation for domain B, and vice versa. This process is achieved in an end-to-end and parallel way, which means the information from both domains of a same user are shared.

Fig. 2.

The architecture of dual cross-domain with multi-channel interaction model (DCMI) for session-based recommendation.

Figure 2 shows an overview of DCMI, which comprises four main components: a session encoder, a cross-preference interaction module, an adversarial mechanism and a bilinear fusion mechanism. The session encoder encodes the session sequences of each domain into high-dimensional hidden representations. The cross-preference interaction module takes each domain preferences as input and tries to extract common, specific, enhanced features for building session representation. The adversarial mechanism keeps the encodes differ somewhat and prevents the model from collapsing. Finally, the bilinear fusion mechanism integrates the information from both domains and generates a list of recommended item for each domain session simultaneously. The details on DCMI are presented in the following sections.

3.3. Session encoder

For the session in domain A and given an input session $s_{A} = {v_{1}^{A}, v_{i}^{A}, \dots, v_{m}^{A}}$ , we firstly model this session as a direct graph where each item $v_{i}^{A}$ is denoted as a node, and each edge $(v_{i}^{A}, v_{i + 1}^{A})$ represents the item $v_{i + 1}^{A}$ that is clicked after the item $v_{i}^{A}$ in this session. Because several items may appear in a session repeatedly, each edge is computed by the occurrence of the edge divided by the outdegree of that edge’s start node. Therefore, we can build the adjacent matrix according to the connection edges. Then, we directly take the embeddings of the unique items in the session as the nodes representation: $\begin{matrix} (1) & v_{i}^{A} = (e_{1}^{A}, e_{2}^{A}, \dots, e_{d}^{A}) \end{matrix}$ where $v_{i}^{A}$ is a d-dimensional embedding of node in the graph. Since gated GNN can extract features of session graph with considerations of rich node connections, we utilize gated GNN as encoder to learn node vectors in a session graph [13,20,27,32]. Formally, for each item embedding $v_{i}^{A}$ at time i in a graph session and adjacent matrix, the information propagation between different nodes is computed as: $\begin{matrix} (2) & \begin{array}{c} a_{i}^{A} = M_{i}^{A} {[v_{1}^{A}, \dots, v_{m}^{A}]}^{T} H + b \\ z_{i}^{A} = σ (W_{z}^{A} a_{i}^{A} + U_{z}^{A} v_{i - 1}^{A}) \\ r_{i}^{A} = σ (W_{r}^{A} a_{i}^{A} + U_{r}^{A} v_{i - 1}^{A}) \\ {\tilde{v}}_{i}^{A} = tanh (W_{o}^{A} a_{i}^{A} + U_{o}^{A} (r_{i}^{A} ⊙ v_{i - 1}^{A})) \\ v_{i}^{A} = (1 - z_{i}^{A}) ⊙ v_{i - 1}^{A} + z_{i}^{A} ⊙ {\tilde{v}}_{i}^{A} \end{array} \end{matrix}$ where $H \in R^{d \times 2 d}$ controls the weight, $z_{i}^{A}$ is the update gate, and $r_{i}^{A}$ is the reset gate. ${\tilde{v}}_{i}^{A}$ is candidate activation function. $W_{z}^{A}$ , $U_{z}^{A}$ , $W_{r}^{A}$ , $U_{r}^{A}$ , $W_{o}^{A}$ and $U_{o}^{A} \in R^{d \times d}$ are learnable parameters. ⊙ denotes element-wise multiplication. $σ (\cdot)$ is the sigmoid function. $a_{i}^{A}$ and $z_{i}^{A}$ are the update gate and the reset gate, which controls how much information of the previous state should be written in the candidate activation ${\tilde{v}}_{i}^{A}$ , respectively. The adjacent matrix $M^{A} \in R^{d \times 2 d}$ determines how nodes in the graph communication with each other and $M_{i}^{A} \in R^{1 \times 2 d}$ are the two columns of blocks in $M^{A}$ corresponding to node $v_{i}^{A}$ . In this way, information from adjacent items can be propagated in the graph neural network. Finally, we can obtain all the node vectors $[v_{1}^{A}, v_{2}^{A}, \dots, v_{m}^{A}]$ after updating all nodes in a session into gated GNN. Through the session encoder, we use the last clicked item $v_{m}^{A}$ as the embedding of local preference $l^{A} \in R^{d}$ : $\begin{matrix} (3) & l^{A} = v_{m}^{A} \end{matrix}$

Since different node vectors have different priority levels for modeling the global preference, we use the soft-attention mechanism to intensify the relative preference’s effect and weaken the disturbance nodes. We assign a higher weight to relatively more important nodes. Specifically, the weighting factor $α_{i}^{A}$ models the relationship between the last-clicked node vector $v_{m}^{A}$ and the previous clicked node vector $v_{i}^{A}$ by computing their similarity: $\begin{matrix} (4) & α_{i}^{A} = q^{T} σ (W_{1}^{A} v_{m}^{A} + W_{2}^{A} v_{i}^{A}) \end{matrix}$ where parameters $q \in R^{d}$ , and $q^{T}$ is the transpose of $q$ . $W_{1}^{A} \in R^{d \times d}$ and $W_{2}^{A} \in R^{d \times d}$ control the weights of item embedding vectors and transform $v_{m}^{A}$ and $v_{i}^{A}$ into latent space, respectively. Then, we can build the global preference of the session by adaptively focusing on more important items: $\begin{matrix} (5) & g^{A} = \sum_{i = 1}^{m} α_{i}^{A} v_{i}^{A} \end{matrix}$

Thus, the representation $S_{u}^{A} \in R^{2 d}$ of session A is formulated as: $\begin{matrix} (6) & S_{u}^{A} = (l^{A} : g^{A}) \end{matrix}$

Similarly, given behavior session of user in domain B, the local preference $l^{B}$ and global preference $g^{B}$ of session in domain B are obtained formulated as: $\begin{array}{c} (7) & l^{B} = v_{n}^{B} \\ (8) & α_{j}^{B} = q^{T} σ (W_{1}^{B} v_{n}^{B} + W_{2}^{B} v_{j}^{B}) \\ (9) & g^{B} = \sum_{j = 1}^{n} α_{j}^{B} v_{j}^{B} \end{array}$ where $α_{j}^{B}$ models the relationship between the last-clicked node vector $v_{n}^{B}$ and the previous clicked node vector $v_{j}^{B}$ by computing their similarity. Therefore, the representation $S_{u}^{B} \in R^{2 d}$ of session B is described as: $\begin{matrix} (10) & S_{u}^{B} = (l^{B} : g^{B}) \end{matrix}$

3.4. Cross-preference interaction module

Following the session encoder, we only models the flow of behavior information of current session in each domain. To make dual cross-domain session-based recommendation, we need to introduce the preference information from domain B to domain A or from domain A to domain B, and then combine it with the preferences in domain A and domain B to improve the recommendation, and we call it as transfer preferences. Actually, inherent characteristics remain unchanged for each user in any case, and user often makes decision after the contrast and the analysis. It indicates that transfer preferences are composed of multiple categories of features, and the transfer preferences of cross-domain has complementary and dependency relationships for modeling user preference. Thus, we design a cross-preference interaction module, as illustrated in Fig. 3, which takes contrastive learning for modeling common features, uses adversarial mechanism for learning specific features, and adopts a parallel attention mechanism for building enhanced features.

Fig. 3.

Framework of cross-preference interaction module.

In order to capture the common features, we feed cross-domain session representations into contrastive learning to generate the common features shared in different domains. Contrastive learning ensures that the representations derived from different domains of the same user are similar. Thus, an auxiliary learning objective is developed to distinguish whether two features are derived from the same user in different domains. Specifically, the views of the same user are used as positive pairs, and the views of different users are used as negative pairs. Then, we use the following contrastive objective to distinguish the features of the same user from others. $\begin{matrix} (11) & L_{C L} = \sum - log \frac{exp (cos (s_{u}^{A}, s_{u}^{B}) / τ)}{\sum exp (cos (s_{u}^{A}, s_{u^{'}}^{B}) / τ)} \end{matrix}$ where $s_{u}^{A}$ is session representation and is defined as $s_{u}^{A} = [l^{A} : g^{A}]$ . $cos (\cdot, \cdot)$ is the cosine similarity function, and τ is a hyper-parameter that is empirically set to 0.5 in the experiments.

In order to capture the specific features, we design a divergence constraint on the two domains by integrating adversarial examples into the training, which can prevent the model from collapsing. Theoretically, the adversarial examples targeting one domain would mislead the encoder to form wrong predictions. However, if the encoders for cross-domain are trained to be resistant to the adversarial examples formed by each other and still output the correct predictions, we can manage to achieve the goal of keeping them different and build specific features. We define the divergence constraint as follows: $\begin{matrix} (12) & L_{diff} = KL ({prob}_{A} (v_{c}), {prob}_{B} (v_{d})) + sim (v_{c}, v_{d}) \end{matrix}$ where ${prob}_{A} (v_{c})$ and ${prob}_{B} (v_{d}))$ denote the probabilities of candidate item to be recommended to the given cross-domain sessions, which are computed by the encoders. $KL (\cdot)$ represent the KL divergence. $sim (\cdot)$ represent the similarity of candidate $v_{c}$ and $v_{d}$ .

In order to capture the enhanced features, given all the item vectors $[v_{1}^{A}, v_{2}^{A}, \dots, v_{m}^{A}]$ and $[v_{1}^{B}, v_{2}^{B}, \dots, v_{n}^{B}]$ , we design a parallel cross-attention mechanism (PCM), which can model the dependencies between cross session features and project the cross features to the common feature subspace. The cross attention weights from domain B to A can be computed with a method similar to soft attention: $\begin{array}{c} e_{i, j}^{A < - B} = Leak Re LU ((v_{i}^{A} ⊙ W_{i j} v_{j}^{B}) + (v_{i}^{A} + W_{i, j} v_{j}^{B})) \\ (13) & α_{i, j}^{A < - B} = \frac{exp (e_{i, j}^{A < - B})}{\sum_{j = 1}^{n} exp (e_{i, j}^{A < - B})} \\ {\hat{v}}_{i}^{A} = \sum_{j = 1}^{n} α_{i, j}^{A < - B} e_{i, j}^{A < - B} \end{array}$ where parameters $W_{i j} \in R^{d \times d}$ and $W_{i, j} \in R^{d \times d}$ transform item j in B session into A session space. $e_{i, j}^{A < - B}$ shows the significance of $v_{j}^{B}$ node representation in domain B to $v_{i}^{A}$ node representation in domain A, and we choose LeakReLU as the activation function. $α_{i, j}^{A < - B}$ is weight, and it is asymmetric as their session and feature space are different. This means that their contributions to each other are unequal. At last, we obtain the output node representation by calculating the linear combination. Finally, following the equation (10) and we can build enhanced node representation in domain A is $[{\hat{v}}_{1}^{A}, {\hat{v}}_{2}^{A}, \dots, {\hat{v}}_{m}^{A}]$ .

Similarly, we can introduce node representations in domain A to domain B, and the enhanced node representation in domain B is $[{\hat{v}}_{1}^{B}, {\hat{v}}_{2}^{B}, \dots, {\hat{v}}_{n}^{B}]$ , which can be calculated by: $\begin{matrix} (14) & \begin{array}{c} e_{j, i}^{B < - A} = Leak Re LU ((v_{j}^{B} ⊙ W_{j i} v_{i}^{A}) + (v_{j}^{B} + W_{j, i} v_{i}^{A})) \\ α_{j, i}^{B < - A} = \frac{exp (e_{j, i}^{B < - A})}{\sum_{i = 1}^{m} exp (e_{j, i}^{B < - A})} \\ {\hat{v}}_{j}^{B} = \sum_{i = 1}^{m} α_{j, i}^{B < - A} e_{j, i}^{B < - A} \end{array} \end{matrix}$ Furthermore, according to equation (3), (8), we can get the local and global representation under enhanced features $l_{PCM}^{A}$ , $g_{PCM}^{A}$ , $l_{PCM}^{B}$ , $g_{PCM}^{B}$ . Then session representations under enhanced features are formulated as $s_{PCM}^{A} = l_{PCM}^{A} : g_{PCM}^{A}$ and $s_{PCM}^{B} = l_{PCM}^{B} : g_{PCM}^{B}$ .

3.5. Bilinear fusion mechanism

To this end, the model generates three representations of current session from session itself, common features, and enhanced features, respectively. To balance the information importance from different ways, we build the final session representation in domain A as: $\begin{matrix} (15) & s^{A} = f^{A} ⊙ s_{u}^{A} + (1 - f^{A}) ⊙ (s_{C L}^{A} \oplus s_{PCM}^{A}) \end{matrix}$ where $s^{A}$ is the combination of three representations $s_{s}^{A}$ , $s_{C L}^{A}$ , and $s_{PCM}^{A}$ . $f^{A}$ is used to balance representations and is determined by: $\begin{matrix} (16) & f^{A} = σ (W_{u}^{A} \cdot s_{u}^{A} + W_{C L 1}^{A} \cdot s_{C L}^{A} \cdot W_{C L 2}^{A} + W_{PCM 1}^{A} \cdot s_{PCM}^{A} \cdot W_{PCM 2}^{A} + b^{A}) \end{matrix}$ where $W_{s}^{A}$ , $W_{C L 1}^{A}$ , $W_{C L 2}^{A}$ , $W_{PCM 1}^{A}$ , $W_{PCM 2}^{A} \in R^{2 d \times 2 d}$ are the parameters, $b^{A}$ is the bias term. $σ (\cdot)$ is the sigmoid function, after it each value falls into (0,1). Thus, the distill score $f^{A}$ controls the amount of information to transfer and store. A higher value of $f^{A}$ means that final session representation is more likely generated by session itself and we should pay more attention to current session information. A lower value of $f^{A}$ means that cross-domain session stores more information for building session features and we should care it.

Similarly, we build the final session representation in domain B as: $\begin{matrix} (17) & s^{B} = f^{B} ⊙ s_{s}^{B} + (1 - f^{B}) ⊙ (s_{C L}^{B} \oplus s_{PCM}^{B}) \end{matrix}$ where $s^{B}$ is the combination of three representations $s_{s}^{B}$ , $s_{C L}^{B}$ , and $s_{PCM}^{B}$ . $f^{B}$ is used to balance representations and is determined by: $\begin{matrix} (18) & f^{B} = σ (W_{u}^{B} \cdot s_{u}^{B} + W_{C L 1}^{B} \cdot s_{C L}^{B} \cdot W_{C L 2}^{B} + W_{PCM 1}^{B} \cdot s_{PCM}^{B} \cdot W_{PCM 2}^{B} + b^{B}) \end{matrix}$ where $W_{s}^{B}$ , $W_{C L 1}^{B}$ , $W_{C L 2}^{B}$ , $W_{PCM 1}^{B}$ , $W_{PCM 2}^{B} \in R^{2 d \times 2 d}$ are the parameters, $b^{B}$ is the bias term. $σ (\cdot)$ is the sigmoid function, after it each value falls into (0,1). Thus, the distill score $f^{B}$ controls the amount of information to transfer and store. A higher value of $f^{B}$ means that final session representation is more likely generated by session itself and we should pay more attention to current session information. A lower value of $f^{B}$ means that cross-domain session stores more information for building session features and we should care it.

3.6. Objective function

We use a bi-linear decoding scheme with parameter $W_{s}^{A} \in R^{d \times 2 d}$ to calculate recommendation score ${\hat{y}}_{i}^{A}$ for candidate item $v_{i}^{A}$ : $\begin{matrix} (19) & {\hat{y}}_{i}^{A} = softmax (v_{i}^{A} W_{s}^{A} s^{A}) \end{matrix}$

Then, we employ the cross-entropy error between ground truth distribution $y_{i}^{A}$ and ${\hat{y}}_{i}^{A}$ is defined as loss in domain A as follows: $\begin{matrix} (20) & {Loss}^{A} = \sum_{i = 1}^{| v |} y_{i}^{A} log ({\hat{y}}_{i}^{A}) + (1 - y_{i}^{A}) log (1 - {\hat{y}}_{i}^{A}) \end{matrix}$

Similarly, the loss for domain B is defined as: $\begin{matrix} (21) & {Loss}^{B} = \sum_{j = 1}^{| v |} y_{j}^{B} log ({\hat{y}}_{j}^{B}) + (1 - y_{j}^{B}) log (1 - {\hat{y}}_{j}^{B}) \end{matrix}$ where ${\hat{y}}_{j}^{B} = softmax (v_{j}^{B} W_{s}^{B} s^{B})$ and it means the recommendation score of candidate item $v_{j}^{B}$ .

In the case of joint learning, the final loss of the dual cross-domain session-based recommendation is a linear combination of both losses in different domains: $\begin{matrix} (22) & Loss = {Loss}^{A} + {Loss}^{B} + α * L_{C L} + β * L_{diff} \end{matrix}$ where α and β are hyperparameters to control the scale of the constrative learning and domain preference difference constraint. It should be note that, we jointly optimize the four throughout the training. All parameters as well as the item embeddings are learned in an end-to-end back-propagation training way. Finally, the whole procedure of DCMI is summarized in Algorithm 1.

Algorithm 1

The whole procedure of DCMI

4. Experiments and analysis

4.1. Datasets and experiment settings

Since Amazon dataset1

¹
https://nijianmo.github.io/amazon/index.html

contains the session sequence of a same user in different domains, we conduct experiments on the Amazon dataset to validate the effectiveness of the proposed method. Amazon dataset is a public dataset involving 29 category data. We take book-movie and food-kitchen as cross-domain information to satisfy cross-domain characteristics, and select users who have interactions in both domains. Specifically, book <- movie denotes that the information from the movie domain is incorporated into the book domain, and vice versa. The detailed statistics of these datasets are reported in Table 2. To satisfy the session characteristics, we select the users who interact in both domains, filter the users with less than 10 interactions and items whose frequency is less than 5, and ignore each user’s identity information. Furthermore, for a session in each domain, we use sequence splitting preprocessing to obtain sessions and corresponding labels. For example, for an interaction session

s = [v_{1}, v_{i}, \dots, v_{m}]

, we build a series of sub-interaction sequences and labels as

([v_{1}], v_{2}), ([v_{1}, v_{2}], v_{3}), \dots, ([v_{1}, v_{2}, \dots, v_{m - 1}], v_{m})

. For evaluation metrics, we use Recall@20 and MRR@20 (Mean Reciprocal Rank) to measure the prediction accuracy and the order of recommendation ranking.

\begin{array}{c} (23) & Recall @ K = \frac{n_{h i t}}{N} \\ (24) & MRR @ K = \frac{1}{N} \sum_{t \in G} \frac{1}{Rank (t)} \end{array}

where K is the top number of ranking lists, and we use 20 in our work.

n_{hit}

is the number of items which is desired in top K ranking lists. N is the number of top-K recommendation attempts.

Rank (t)

is the rank of the chosen item within the n-th top-K recommendation list. Recall is an emulation of unranked retrieval results, and MRR is evaluation of ranked lists.

Table 2

Dataset statistics of Amazon

Datasets	#items	Overlapped-users	Training	Validation	Testing
Movie	45692	10325	98736	19747	13164
Book	85783	10325	98736	19747	13164
Food	38980	6892	32069	6413	4275
Kitchen	46170	6892	32069	6413	4275

4.2. Baselines

We compare DCMI with some mainstream SR methods. The baselines include:

POP [6] recommends the top-n items according to their occurrence in the training data.

FPMC [22] combines a MC and matrix factorization for next-basket recommendations. We neglect the user representation to adapt SR.

Item-KNN [3] recommends the top similar items with the last item, of which the similarity is computed by co-occurrence.

GRU4Rec [7] uses a RNN with session-parallel mini-batch training process and ranking-based loss functions for SR.

NARM [10] uses a RNN-based method and attention mechanism to capture user’s local interest and main purpose.

SR-GNN [20] uses global preference and local interest based on node representations for recommendation.

SR-IEM [19] makes recommendation from user’s long-term preference with self-attention mechanism and recent behavior in an ongoing session with the last item embedding.

CDHRM [29] incorporate cross-domain session information by exploring correlations among users’ cross-domain behaviors with RNNs.

DAT-MDI [2] introduces different sessions from multiple domains and uses GNN to learn the item representation in each session.

DDGHM [35] integrates information from other domains to improve recommendation performance with dual dynamic graph modeling and hybrid metric learning.

MIFN [17] designs a mixed information flow network for cross-domain sequential recommendation to consider both the flow of behavioral information and the flow of knowledge by incorporating a behavior transfer unit and a knowledge transfer unit.

4.3. Parameter setup

Following the baseline methods, the hidden size of the latent vectors in this work is selected followed by their work [2,3,6,7,10,19,20,22]. For example, In reference [20], the dimensionality of latent vectors is 100, learning rate is 0.01, a decay factor is 0.1 after every 3 epochs, and batch_size is 100. In reference [19], the dimensionality of latent vectors is 200, learning rate is 0.001, a decay factor is 0.1 after every 3 epochs, and batch_size is 128. For our model, we take the Adam optimizer to optimize the model and the initial learning rate is 0.001, and it decays by 0.05 after each 4 epoch. All the parameters in our model are initialized with a Gaussian distribution with a mean of 0 and a standard deviation of 0.1. Besides, we use Book and Food dataset as domain A and Movie and Kitchen as domain B to verify the accuracy of our model.

4.4. Performance comparison

The performances of baseline methods and our proposed method DCMI in terms of Recall@20 and MRR@20 on public real-world datasets are shown in Table 3. The values are average results per model over five trials, where the best result of each column is highlighted. From the table, we can observe that:

Table 3
Experimental results on the Amazon dataset. Performance comparisons in %. Bold face indicates the best result in terms of the corresponding metric ( $p ⩽ 0.05$ )

Method Book-Movie Food-Kitchen

Book Movie Food Kitchen

Recall@20 MRR@20 Recall@20 MRR@20 Recall@20 MRR@20 Recall@20 MRR@20

POP 0.72 0.16 0.53 0.13 2.11 0.51 1.89 0.21

FPMC 3.98 1.71 1.26 0.84 3.35 1.87 2.53 0.95

Item-KNN 9.52 1.93 6.52 1.36 10.17 2.43 11.75 1.57

GRU4Rec 15.12 13.82 14.11 12.01 11.23 8.10 9.45 8.33

NARM 15.30 15.11 14.65 13.45 12.26 9.35 9.70 8.67

SR-GNN 15.61 15.45 13.79 11.63 12.67 9.94 10.20 9.38

SR-IEM 16.01 15.77 15.02 14.20 12.46 10.4 10.83 9.59

CDHRM 15.94 15.82 15.15 14.61 12.88 10.38 10.71 9.68

DAT-MDI 16.22 15.98 15.53 14.85 13.32 10.21 10.83 10.02

DDGHM 16.36 15.99 15.62 14.98 13.66 10.54 10.91 10.1

MIFN 16.85 16.02 15.64 14.56 13.79 10.88 11.04 10.13

DCMI 17.08 16.14 16.05 15.33 14.19 11.04 11.19 10.73

Method	Book-Movie	Food-Kitchen
POP	0.72	0.16	0.53	0.13	2.11	0.51	1.89	0.21
FPMC	3.98	1.71	1.26	0.84	3.35	1.87	2.53	0.95
Item-KNN	9.52	1.93	6.52	1.36	10.17	2.43	11.75	1.57
GRU4Rec	15.12	13.82	14.11	12.01	11.23	8.10	9.45	8.33
NARM	15.30	15.11	14.65	13.45	12.26	9.35	9.70	8.67
SR-GNN	15.61	15.45	13.79	11.63	12.67	9.94	10.20	9.38
SR-IEM	16.01	15.77	15.02	14.20	12.46	10.4	10.83	9.59
CDHRM	15.94	15.82	15.15	14.61	12.88	10.38	10.71	9.68
DAT-MDI	16.22	15.98	15.53	14.85	13.32	10.21	10.83	10.02
DDGHM	16.36	15.99	15.62	14.98	13.66	10.54	10.91	10.1
MIFN	16.85	16.02	15.64	14.56	13.79	10.88	11.04	10.13
DCMI	17.08	16.14	16.05	15.33	14.19	11.04	11.19	10.73

Among the existing methods, the traditional methods perform the worst. Specifically, for the traditional methods, the evaluation metrics of FPMC based on MC are higher than POP which is based on co-occurrence items. This indicates that consecutive items have a dependency relationship. Besides, the performance of Item-KNN is better than FPMC, suggesting that the last-clicked item plays a key role in recommendation. However, it ignores the order relationship between items, and the learned item representation is insufficient.

Compared to the traditional methods, since the neural network methods can model the complex contextual information, they excessively outperform the traditional methods in session-based recommendation. The GRU4Rec and NARM methods, which rely on RNN, demonstrate the effectiveness of RNN in sequence modeling. However, there is not only the sequence modeling in session-based recommendation, but also the changes of user preferences within the sessions are also need to be considered.

For the methods which only model the ongoing session information, the SR-GNN method that based on GNN achieves improvements over the RNN-based method (GRU4Rec). This may be because graph-structured data is able to capture more complex item transition patterns, and it verifies that GNN is friendly to model the session information. The performance of SR-GNN and SR-IEM show that graph modeling is more suitable for session-based recommendation than the traditional methods, sequence modeling by RNN framework.

Furthermore, the session-based recommendation with cross-domain information (CDHRM, DAT-MDI, DDGHM, MIFN) outperforms single-domain information, indicating that introducing session information from cross-domain is effective for modeling current session representation and improving the representation quality. Specifically, DDGHM outperforms CDHRM and DAT-MDI regarding all metrics in both domains. It demonstrates that contrastive learning helps capture uniformity representation, which means that the distribution of preferences from the cross-domain is preferred to preserve as much information as possible. Furthermore, MIFN performs better than DDGHM. On the one hand, it demonstrates that employing knowledge information and interaction level information is better than only interaction information, and MIFN can capture cross-domain knowledge and transfer it into cross-domain to learn better information. On the other hand, it also proves that capturing rich information is necessary for cross-domain session-based recommendation.

Our approach of DCMI outperforms all the GNN-based methods on all the datasets. Specifically, DCMI outperforms the DAT-MDI by 5.3% on the Book dataset, 3.35% on the Movie dataset, 6.53% on the Food dataset, and 3.32% on the Kitchen dataste. Compared to the MIFN method, DCMI outperforms MIFN by 1.3% on the Book dataset, 2.6% on the Movie dataset, 2.9% on the Food dataset, and 1.3% on the Kitchen dataste regarding Recall@20. Considering the differences between DAT-MDI, MIFN, and DCMI, DCMI explores the common features of cross-domain sessions and deeply studies the mutually guided relationships between two interests in the cross-domain session. In contrast, other methods do not make further explore the dependency relationship, indicating that efficiently exploring cross-domain session information of the same user assures high recommendation performance. Additionally, the results of DCMI and all the other baseline methods in “Book-Movie” are better than those in “Food-Kitchen”. We think that it is because the data is sparse in “Food-Kitchen” compared to “Book-Movie”. With more interaction data, the models can capture more preference information for dual cross-domain session-based recommendation.

4.5. Influence of dual cross-domain session-based recommendation framework

Table 4
Performance comparisons of DCMI with different framework

Method Book-Movie Food-Kitchen

Book<-Movie Book->Movie Food<-Kitchen Food->Kitchen

Recall@20 MRR@20 Recall@20 MRR@20 Recall@20 MRR@20 Recall@20 MRR@20

CMI 16.28 15.99 / / 13.32 10.24 / /

CMI / / 15.38 14.83 / / 10.87 10.16

DCMI 17.08 16.14 16.05 14.93 14.19 11.04 11.19 10.73

Method	Book-Movie	Food-Kitchen
CMI	16.28	15.99	/	/	13.32	10.24	/	/
CMI	/	/	15.38	14.83	/	/	10.87	10.16
DCMI	17.08	16.14	16.05	14.93	14.19	11.04	11.19	10.73

Fig. 4.

Running time comparsions.

To explore the effect of dual cross-domain for session-based recommendation framework, we implement independent experiments of session-based recommendation with book, movie, food, and kitchen datasets, respectively. For example, Book<-Movie refers that movie data plays a source domain and book data plays a target domain. The effectiveness of the framework is verified from Recall@20, MRR@20, and time consuming for each iteration. The performance results are shown in Table 4 and Fig. 4. we can observe that:

The improvement of DCMI on each dataset is more significant than DAT-MDI which also considers cross-domain information. Considering the difference of them, we think that introducing cross-domain session is helpful to explore more rich information and helps the model to obtain more accurate prediction results. Additionally, it may reduce the influences of the noise and irrelevant data in each session for a certain domain.

Compared with the corresponding framework in Table 4 and Fig. 4, the dual cross-domain session-based recommendation framework achieves significant improvements in Recall, MRR, and time consuming. We think the main reason for this is that our dual cross-domain session-based recommendation helps the model to quickly learn about the relationships of items and preferences. In terms of scalability, we should note that the overall computation complexity of our model is $O (n^{2} d + n d + n d^{2})$ . As n is typically larger than d, the complexity is dominated by the $n^{2} d$ term.

4.6. Influence of cross-preference interaction module

To illustrate the effect of cross-preference interaction module (CPI) in our model, we compare CPI with three variants CPI-CL, CPI-AM, and CPI-PCM.

CPI-CL denotes that there is only contrastive learning in CPI for learning cross-domain feature interactions.

CPI-AM denotes that there is only adversarial mechanism in CPI for learning cross-domain feature interactions, and without contrastive learning.

CPI-PCM refers that there is only parallel cross-attention mechanism in CPI for learning cross-domain feature interactions, and without contrastive learning and adversarial mechanism.

Table 5 shows the results of CPI-CL, CPI-AM, and CPI-PCM for dual cross-doamin session-based recommendation. From the table, we can observe that:

In Table 5, it is obviously shown that all three variant models perform better than the baseline methods which make recommendation in one domain, the results validates the rationality of incorporating multiple cross information into session-based recommendation via contrastive learning, adversarial mechanism, and parallel cross-attention mechanism. The result also indicate again that modeling the cross-domain session data is friendly to recommendation.

Compared with DAT-MDI which explore item representation information from other domain sessions, the results of DCMI and its variants are higher. It demonstrates that integrating cross session data directly is easily to bring noise and interaction information is more suited to build in the high level. At the same time, common features, specific features and enhanced features are both important for dual cross-doamin session-based recommendation.

The enhanced features is more effective than the common features and specific features th enhance session representation. Although some preference in session show common and specific semantics, the final decisions are finally decided by enhanced preference. Hence, it is reasonable that the discrimination of preference features is more obvious than mixed characteristic.

Additionally, CPI-CL, CPI-AM and CPI-PCM performs worse than DCMI on book-movie dataset and food-kitchen dataset, this demonstrates that feature interaction between cross domain is complex, and comprehensive interactions are helpful for improving the session representation. Additionally, the result of DCMI confirms the usefulness of cross-preference interaction module for better recommendation.

Table 5
Performance comparisons of DCMI with different interaction module

Method Book-Movie Food-Kitchen

Book Movie Food Kitchen

Recall@20 MRR@20 Recall@20 MRR@20 Recall@20 MRR@20 Recall@20 MRR@20

CPI-CL 16.72 15.99 15.53 14.73 13.41 10.51 10.89 10.21

CPI-AM 16.69 15.97 15.55 14.75 13.40 10.62 10.90 10.21

CPI-PCM 16.82 16.07 15.56 14.96 13.48 10.88 10.99 10.26

DCMI 17.08 16.14 16.05 14.93 14.19 11.04 11.19 10.73

Method	Book-Movie	Food-Kitchen
CPI-CL	16.72	15.99	15.53	14.73	13.41	10.51	10.89	10.21
CPI-AM	16.69	15.97	15.55	14.75	13.40	10.62	10.90	10.21
CPI-PCM	16.82	16.07	15.56	14.96	13.48	10.88	10.99	10.26
DCMI	17.08	16.14	16.05	14.93	14.19	11.04	11.19	10.73

4.7. Influence of bilinear fusion mechanism

To investigate the influence of fusion mechanism in modeling the session representation, we compare DCMI with various aggregation operations including max pooling, average pooling, and concatenation.

Max pooling takes the maximum value of each dimension for $s_{s}^{A}$ , $s_{C L}^{A}$ , and $s_{PCM}^{A}$ as the session A representation. Taking the maximum value of each dimension for $s_{s}^{B}$ , $s_{C L}^{B}$ , and $s_{PCM}^{B}$ as the session B representation.

Average pooling uses average values of each dimension of each dimension for $s_{s}^{A}$ , $s_{C L}^{A}$ , and $s_{PCM}^{A}$ as the session A representation. Using average values of each dimension of each dimension for $s_{s}^{B}$ , $s_{C L}^{B}$ , and $s_{PCM}^{B}$ as the session B representation.

Concatenation takes the combination of $s_{s}^{A}$ , $s_{C L}^{A}$ , and $s_{PCM}^{A}$ denote the session A representation. Taking the combination of $s_{s}^{B}$ , $s_{C L}^{B}$ , and $s_{PCM}^{B}$ denote the session B representation.

Table 6 shows the performances of DCMI with different fusion mechanism. Compared to max pooling, average pooling, and concatenation, DCMI with bilinear gating mechanism which shows in Section 4.4 achieves the best performance in terms of the evaluation. It demonstrates that the ways of integration in our work is more helpful in capturing inherent features from different semantic session representations. For the most part, concatenation operation outperforms max pooling and average pooling operations on each datasets, it verifies that session representations are built from session itself, common features of cross transition, and enhanced features of cross transition are very meaningful for modeling final session representation.

Table 6
Performance comparisons of DCMI with different fusion mechanism

Method Book-Movie Food-Kitchen

Book Movie Food Kitchen

Recall@20 MRR@20 Recall@20 MRR@20 Recall@20 MRR@20 Recall@20 MRR@20

max pooling 16.82 16.09 16.01 14.80 13.75 10.91 11.06 10.49

average pooling 16.85 16.09 15.98 14.79 13.77 10.95 11.10 10.42

concatenation 16.99 16.11 16.02 14.86 14.09 11.00 11.11 10.70

DCMI 17.08 16.14 16.05 14.93 14.19 11.04 11.19 10.73

Method	Book-Movie	Food-Kitchen
max pooling	16.82	16.09	16.01	14.80	13.75	10.91	11.06	10.49
average pooling	16.85	16.09	15.98	14.79	13.77	10.95	11.10	10.42
concatenation	16.99	16.11	16.02	14.86	14.09	11.00	11.11	10.70
DCMI	17.08	16.14	16.05	14.93	14.19	11.04	11.19	10.73

4.8. Influence of hyper-parameter setting

In order to verify the improvement of ormodel, we have implemented many experiments on the hyper-parameter α and β in Eq. (22) to check the change of the recommendation performance.

Figure 5 shows the impact of α and β on Book -> Movie dataset. The curves show that the accuracy will first gradually increase with α and β and then slightly decrease. We can derived that when α and β are 0, the common and specific features cannot produce positive effects. But when α and β become larger, the recommendation accuracy is reduced. Empirically, we choose $α = 0.1$ and $β = 0.1$ on the Book -> Movie dataset while $α = 0.3$ and $β = 0.2$ on the Food -> Kitchen dataset. Finally we perform experiments by varying dimension d in range {32,64,100,128,200,256,512}. The results on two datasets are shown in Fig. 6. From them, we can see that the performance gradually improves when d increases and finally keeps a fairly stable level after d reaches 128 and 256. It indicates that a larger latent vectors can provide more accurate embeddings for items thus helping to learn accurate preferences. Since larger latent vector would bring huge computional and time cost, we choose d = 128 for the “Book-Movie” dataset and d = 256 for the “Food-Kitchen” dataset.

Fig. 5.

Recommendation performance with different α and β.

Fig. 6.

Recommendation performance with different dimensions.

5. Conclusion

In this paper, we propose an end-to-end dual cross-domain with multi-channel interaction model (DCMI) for the session-based recommendation. Specifically, we apply a GNN-based neural network to build session representation from session-self information. Then, we introduce a cross-preference interaction module to learn the multi-channel interactions of cross-domain sessions of the same user and build session representations from common features, specific features and enhanced features, respectively. Finally, we design a bilinear fusion mechanism to adaptively balance the importance of session representations from itself and cross-domain. We evaluate our model on public datasets, demonstrating that our model significantly improves compared to the state-of-the-art models.

As to the future work, DCMI can be enhanced from at least two directions. First, currently we extract complex cross-domain information with interactions, and the baseline method has shown that results can be improved by introducing knowledge information. Hence, we will further study the integration ways of knowledge graphs and structures of DCMI. Second, dual cross-domain session-based recommendation is limited to overlapped user information between two domains. Therefore, we will study how to make recommendations with less overlapped users.

Footnotes

Acknowledgements

This work was supported by Shannxi Science and Technology Planning Project under No.2023-JC-QN-0705, Key Research and Development Projects of Shannxi Provience under No.2023-YBGY-227, Xi’an Science and Technology Planning Project under No.2022JH-RYFW-0138, Science and Technology Planning Project of Beilin Distinct under No.GX2216.

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Dual cross-domain session-based recommendation with multi-channel integration

Abstract

Keywords

1. Introduction

2.1. Session-based recommendation

2.2. Cross-domain recommendation

2.3. Dual learning

3. The proposed algorithm

3.1. Task definition

3.4. Cross-preference interaction module

3.6. Objective function

4.1. Datasets and experiment settings

1 https://nijianmo.github.io/amazon/index.html

4.3. Parameter setup

4.4. Performance comparison

Footnotes

Acknowledgements

References

¹
https://nijianmo.github.io/amazon/index.html