DDGHM: Dual Dynamic Graph with Hybrid Metric Training for Cross-Domain Sequential Recommendation

Basic prediction. Motivated by previous studies (Ma et al., 2019; Guo et al., 2021; Sun et al., 2021), we calculate the matching between sequence-level embeddings $\textbf{SE}_{al,S_{A}}$, $\textbf{SE}_{bl,S_{B}}$ and item embedding matrices $\textbf{H}_{al}$, $\textbf{H}_{bl}$ in corresponding domains, to compute the recommendation probabilities:

where $\textbf{b}_{A}$ and $\textbf{b}_{B}$ are bias items. Then the negative log-likelihood loss function is employed as follows:

where $\mathbb{S}$ denotes the training sequences in both domains.

Collaborative metric. The collaborative metric aims to achieve representation alignment, which means that similar instances are expected to have similar representations. Here, we model the observed behavior sequences as a set of positive user-item pairs $\mathcal{T}$ and learn a user-item joint metric to encode these relationships (Hsieh et al., 2017). The learned metric tries to pull the pairs in $\mathcal{T}$ closer and push the other pairs further apart. Specifically, we learn the model parameters by optimizing the large margin nearest neighbor objective (Park et al., 2018):

where $j$ is an item in the historical sequences of user $i$, $k$ is an item that never appears in these sequences. $D(i,j)$ is defined as the Euclidean distance between the sequence embedding of user $i$ and the embedding of item $j$. Specifically, $\mathbf{W}^{rank}_{ij}$ denotes the Weighted Approximate-Rank Pairwise (WARP) loss (Weston et al., 2010), calculated as $log(rank_{D}(i,j)+1)$ where $rank_{D}(i,j)$ indicates the rank of item $j$ in user $i$’s recommendations. Following (Hsieh et al., 2017), we empirically set the safety margin $m$ to 1.5 in our experiments.

Contrastive metric. The contrastive metric aims to realize representation uniformity, which means that the distribution of representations is preferred to preserve as much information as possible. To do this, the contrastive loss minimizes the difference between the augmented and the original views of the same user historical sequence, and meanwhile maximizes the difference between the augmented sequences derived from different users.

Putting together. Finally, we combine the basic prediction loss of both domains with collaborative and contrastive metrics via a multi-task training scheme:

where $\lambda_{col}$ and $\lambda_{con}$ are hyper-parameters to balance different types of losses.

Datasets. We conduct experiments on the Amazon dataset (McAuley et al., 2015), which consists of user interactions (e.g. userid, itemid, ratings, timestamps) from multiple domains. Compared with other recommendation datasets, the Amazon dataset contains overlapped user interactions in different domain and is equipped with adequate sequential information, and thus is commonly used for CDSR research (Ma et al., 2019; Guo et al., 2021; Li et al., 2021). Specifically, we pick two pairs of complementary domains ”Movie & Book” and ”Food & Kitchen” for experiments. Following the data preprocessing method of (Ma et al., 2019; Ma et al., 2022), we first pick the users who have interactions in both domains and then filter the users and items with less than 10 interactions. After that, we order and split the sequences from each user into several small sequences, with each sequence containing interactions within a period, i.e, three months for ”Movie&Book” dataset and two years for ”Food&Kitchen” dataset. We also filter the sequences that contain less than five items in each domain. The detailed statistics of these datasets are shown in Table 1.

Evaluation method. Following (Ma et al., 2019; Sun et al., 2021; Guo et al., 2021), we use the latest interacted item in each sequence as the ground truth. We randomly select 75% of the sequences as the training set, 15% as the validation set, and the remaining 10% as the test set. We choose three evaluation metrics, i.e., Hit Rate (HR), Normalized Discounted Cumulative Gain (NDCG) and Mean Reciprocal Rank (MRR), where we set the cut-off of the ranked list as 5, 10, and 20. For all the experiments, we repeat them five times and report the average results.

Parameter settings. For a fair comparison, we choose Adam (Kingma and Ba, 2014) as the optimizer, and tune the parameters of DDGHM and the baseline models to their best values. Specifically, we study the effect of the hidden dimension $D$ by varying it in $\{16,32,64,128,256,512\}$, and the effects of hyper-parameters $\lambda_{col}$ and $\lambda_{con}$ by varying them in $\{0.1,0.3,0.5,0.7,1,3,5,10\}$. And we set the batch size $N=100$.

Traditional recommendations. POP is the simplest baseline that ranks items according to their popularity judged by the number of interactions. BPR-MF (Rendle et al., 2012) optimizes the matrix factorization with implicit feedback using a pairwise ranking loss. Item-KNN (Sarwar et al., 2001) recommends the items that are similar to the previously interacted items in the sequence, where similarity is defined as the cosine similarity between the vectors of sequences.

Sequential recommendations. GRU4REC (Hidasi et al., 2015) uses GRU to encode sequential information and employs ranking-based loss function. BERT4Rec (Sun et al., 2019) adopts a bi-directional transformer to extract the sequential patterns. SRGNN (Wu et al., 2019) obtains item embeddings through a gated GNN layer and then uses a self-attention mechanism to compute the session level embeddings. CL4SRec (Xie et al., 2020) uses item cropping, masking, and reordering as augmentations for contrastive learning on interaction sequences.

Cross-Domain Recommendations. NCF-MLP++ is a deep learning based method which uses multilayer perceptron (MLP) (He et al., 2017) to learn the inner product in the traditional collaborative filtering process. We adopt the implementation in (Ma et al., 2019). Conet (Hu et al., 2018) enables dual knowledge transfer across domains by introducing a cross connection unit from one base network to the other and vice versa. DDTCDR (Li and Tuzhilin, 2020) introduces a deep dual transfer network that transfers knowledge with orthogonal transformation across domains. DARec (Yuan et al., 2019) transfers knowledge between domains with shared users, learning shared user representations across different domains via domain adaptation technique.

Cross-domain sequential recommendations. $\pi$-Net (Ma et al., 2019) proposes a novel parallel information-sharing network with a shared account filter and a cross-domain transfer mechanism to simultaneously generate sequential recommendations for two domains. PSJNet (Sun et al., 2021) is a variant of $\pi$-Net, which learns cross-domain representations by extracting role-specific information and combining useful user behaviors. DA-GCN (Guo et al., 2021) devises a domain-aware graph convolution network with attention mechanisms to learn user-specific node representations under the cross-domain sequential setting. DAT-MDI (Chen et al., 2021) uses a potential mapping method based on a slot attention mechanism to extract the user’s sequential preferences in both domains. DASL (Li et al., 2021) is a dual attentive sequential learning model, consisting of dual embedding and dual attention modules to match the extracted embeddings with candidate items.

General comparison. We report the comparison results on two datasets Movie & Book and Food & Kitchen in Table 2. For space save, we report the results when the cut-off of the ranked list is 10 in Appendix C. From the results, we can find that: (1) DDGHM outperforms SR baselines, indicating that our model can effectively capture and transfer the cross-domain information to promote the recommendation performance of a single domain. (2) Comparing DDGHM with CDR baselines, the improvement in both domains on two datasets is also evident. It proves the effectiveness of DDGHM  in dynamically modeling the intra-domain and the inter-domain sequential transitions with a graphical framework. (3) Compared with CDSR baselines, DDGHM achieves better performance in terms of all metrics, which demonstrates that DDGHM is able to extract user preferences more accurately by leveraging complementary information from both domains.

Study of the dual dynamic graph modeling (RQ2). To study how each component of the dual dynamic graph modeling module contributes to the final performance, we compare DDGHM with its several variants, including DDGHM-L, DDGHM-G, and DDGHM-GA. (a) DDGHM-L applies only the local graphs in dual dynamic graph modeling to extract item and sequence embeddings. (b) DDGHM-G applies only the global graph. (c) DDGHM-GA retains the dual dynamic graph structure, but replaces FAG with a simple GRU as cross-domain transfer unit (CTU) (Ma et al., 2019). The comparison results are also shown in Table 2. From it, we can observe that: (1) Both DDGHM-L and DDGHM-G perform worse than DDGHM, showing that integrating intra-domain transitions with inter-domain transitions can boost the performance. (2) DDGHM-L outperforms DDGHM-G on two datasets, indicating that intra-domain collaborative influences still take the dominant place when extracting user preferences. And this is because that simply encoding inter-domain transitions in a shared latent space ignores the domain feature distribution bias. (3) DDGHM shows superiority over DDGHM-GA, which proves that the FAG completes transferring more effectively than other CTUs in existing research and is especially applicable in the dual dynamic graphical model.

Study of the hybrid metric training (RQ3). In order to verify the effectiveness of each component of the hybrid metric training module, we further conduct more ablation studies, where (a) DDGHM-col only employs collaborative metric, (b) DDGHM-con only applies contrastive metric, and (c) DDGHM-cc trains the recommendation model without either metric. The results are shown in Table 4, from which we can conclude that: (1) Both DDGHM-con and DDGHM-col perform worse than DDGHM . The reasons are two-folds. On the one hand, employing collaborative metric loss augments the similarity of similar instance embeddings thus achieving representation alignment. On the other hand, adopting contrastive metric loss preserves the discrepancy of different feature distributions thus retaining representation uniformity. Both of them play an important role in enhancing the representations. (2) DDGHM significantly outperforms DDGHM-cc, which indicates that the combination of two metrics effectively optimizes the training module and further promotes model performance.

Influence of sequence length (RQ4). We report the comparison results of HR@20 under different sequence average length settings in Table 3. Here, for space save, we only report the results of several baselines which perform best in each category, i.e., SR, CDR, and CDSR. And $L$ means the average length of sequences. From it, we can observe that in both domains, the shorter the average length of sequences is, the grater improvement our model brings. Therefore, DDGHM is able to effectively alleviate the data sparsity problem and performs well even when sequences are short.

Parameter analysis (RQ5). We now study the effects of hyper-parameters on model performance, including $\lambda_{col}$, $\lambda_{con}$, and $D$. We first study the effects of $\lambda_{col}$ and $\lambda_{con}$ on the model, varying them in $\{0.1,0.3,0.5,0.7,1,3,5,10\}$, and then report the results in Fig. 4 and Fig. 5. The bell-shaped curves show that the accuracy will first gradually increase with $\lambda_{col}$ or $\lambda_{con}$ and then slightly decrease. We can conclude that when $\lambda_{col}$ and $\lambda_{con}$ approach 0, the collaborative loss and contrastive loss cannot produce positive effects. But when $\lambda_{col}$ and $\lambda_{con}$ become too large, the metric loss will suppress the negative log-likelihood loss, which also reduces the recommendation accuracy. Empirically, we choose $\lambda_{col}=1.0$ and $\lambda_{con}=0.7$ on the dataset Movie & Book while $\lambda_{col}=1.0$ and $\lambda_{con}=0.5$ on the dataset Food & Kitchen. Finally we perform experiments by varying dimension $D$ in range $\{16,32,64,128,256,512\}$. 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 256. It indicates that a larger embedding dimension can provide more accurate embeddings for items thus enriching the representations of user preferences. Since a too large embedding dimension will cause huge computational and time cost, we choose $D=256$ here for both datasets.