Enhancing Sequential Recommendation with Graph Contrastive Learning

In the literature, Recurrent Neural Networks (RNN) are usually applied to build sequential recommendation systems. For example, GRU4Rec Hidasi et al. (2016) treats users’ behavior sequences as time series data and uses a multi-layer GRU structure to capture the sequential patterns. Moreover, some works, e.g., NARM Li et al. (2017) and DREAM Yu et al. (2016), combine attention mechanisms with GRU structures to learn users’ dynamic representations. Simultaneously, Convolutional Neural Networks (CNN) have also been explored for sequential recommendation. Caser Tang and Wang (2018) is a representative method that uses both horizontal and vertical convolutional filters to extract users’ sequential behavior patterns. Recently, SASRec Kang and McAuley (2018) and BERT4Rec Sun et al. (2019) only utilize self-attention mechanisms to model users’ sequential behaviors. Beyond that, HGN Ma et al. (2019) models users’ dynamic preferences using hierarchical gated networks. Along another line, Graph Neural Networks (GNN) have been explored to model complex item transition patterns. For instance, SR-GNN Wu et al. (2019) converts sequences to graph structure data and employs the gated graph neural network to perform information propagation on the graph. GC-SAN Xu et al. (2019) dynamically builds a graph for each sequence and models the local dependencies and long-range dependencies between items by combining GNN and self-attention mechanism. In addition, GCE-GNN Wang et al. (2020) builds the global graph and local graph to model global item transition patterns and local item transition patterns, respectively.

Self-supervised learning is an emerging unsupervised learning paradigm, which has been successfully applied in computer vision Jing and Tian (2020) and natural language processing Devlin et al. (2019). There are several recent works applying self-supervised learning techniques in recommendation tasks. For example, Zhou et al. (2020) maximizes the mutual information among attributes, items, and sequences by different self-supervised optimization objectives. Xie et al. (2021) maximizes the agreement between two augmented views of the same interaction sequence through a contrastive learning objective. Wu et al. (2021) proposes a joint learning framework based on both the contrastive learning objective and recommendation objective. Moreover, in Wei et al. (2021), contrastive learning is used to solve the cold-start recommendation problem. In Zhang et al. (2022), a diffusion-based graph contrastive learning method is developed to improve the recommendation performance based on users’ implicit feedback. Additionally, self-supervised learning has also been applied to exploit the item multimodal side information for recommendation Liu et al. (2021); Lei et al. (2021b).

As each individual user may only be interested in some specific properties of items, the global context information should be user-specific. Following Ma et al. (2019), we design the following user-specific gating mechanism to capture the global context information tailored to the user’s personalized preferences,

where $\mathbf{W}_{g1}\in{\mathbb{R}}^{d\times 1}$ and $\mathbf{W}_{g2}\in{\mathbb{R}}^{L\times d}$, $\sigma(\cdot)$ is the sigmoid function, $\otimes$ is the element-wise product. Here, the user embedding $\mathbf{p}_{u}$ describes the user’s general preferences. Similarly, for augmented view $\mathcal{G}_{S}^{{}^{\prime\prime}}$, we can obtain $\mathbf{Q}_{S}^{{}^{\prime\prime}}$.

Besides the graph augmented representations of a sequence, we also employ traditional sequential model to encode users’ interaction sequences. Specifically, we choose SASRec Kang and McAuley (2018) as the backbone model, which stacks the Transformer encoder Vaswani et al. (2017) to model the user interaction sequences. Given the node representation $\mathbf{H}^{\ell-1}$ at the $(\ell-1)$-th layer, the output of Transformer encoder at the $\ell$-th layer is as follows,

where $FFN(\cdot)$ denotes the feed-forward network, $h$ represents the number of heads, $\mathbf{W}_{i}^{Q},\mathbf{W}_{i}^{K},\mathbf{W}_{i}^{V}\in\mathbb{R}^{d\times{\nicefrac{{d}}{{h}}}}$, and $\mathbf{W}^{h}\in{\mathbb{R}}^{d\times d}$ are the projection matrices. Specifically, we use the shared embedding $\mathbf{E}_{S}^{(0)}$ with learnable position encoding as the initial state $\mathbf{H}^{0}$. Here, the Residual Network, Dropout, and Layer Normalization strategies are omitted in the formula for convenience. Then, the attention mechanism is defined as,

where $\mathbf{Q}$, $\mathbf{K}$, and $\mathbf{V}$ denote the queries, keys, and values respectively, and $\sqrt{d}$ is the scaling factor.

We concatenate the representations $\mathbf{Q}_{S}^{{}^{\prime}}$ and $\mathbf{Q}_{S}^{{}^{\prime\prime}}$ obtained from the augmented graph views and the embeddings at the last layer of the Transformer encoder $\mathbf{H}^{\ell}$ as follows,

where $\mathbf{M}\in\mathbb{R}^{1\times d}$, $\mathbf{W}_{T}\in\mathbb{R}^{3d\times d}$ is the weight matrix, and $AttNet(\cdot)$ denotes the attention network. Then, given the user interaction sequence $S$ with length $n$, the interaction probabilities between the user and items at the $(n+1)$-th step can be defined as follows,

where $\hat{\mathbf{y}}^{(S)}\in\mathbb{R}^{1\times|V|}$, and the $j$-th element of $\hat{\mathbf{y}}^{(S)}$ denotes the interaction probability of the $j$-th item.

Sequential recommendation aims to predict the next item that the user $u$ would like to interact with, based on her interaction sequence $S_{u}$ (Here, we include the subscript $u$ for clear discussion). Following Tang and Wang (2018), we split the sequence $S_{u}=\{v_{u}^{1},v_{u}^{2},\cdots,v_{u}^{|S_{u}|}\}$ into a set of subsequences and target labels as follows: $\{(S_{u}^{1:1},v_{u}^{2}),(S_{u}^{1:2},v_{u}^{3}),\cdots,(S_{u}^{1:|S_{u}|-1},v_{u}^{|S_{u}|})\}$, where $|S_{u}|$ denotes the length of $S_{u}$, $S_{u}^{1:k-1}=\{v_{u}^{1},v_{u}^{2},\cdots,v_{u}^{k-1}\}$, and $v_{u}^{k}$ is the target label of $S_{u}^{1:k-1}$. Then, we formulate the following main learning objective based on cross-entropy,

where $\hat{\mathbf{y}}^{(S_{u}^{1:k})}(v_{u}^{k+1})$ denotes the predicted interaction probability of $v_{u}^{k+1}$ based on the subsequence $S_{u}^{1:k}$ using Eq. (10). In this work, we jointly optimize the main sequential prediction task and other two auxiliary learning objectives. The final objective function of GCL4SR is as follows,

where $\lambda_{1}$ and $\lambda_{2}$ are hyper-parameters. The optimization problem in Eq. (12) is solved by a gradient descent algorithm.

The performance comparison results are summarized in Table 2. Overall, GCL4SR outperforms all baseline methods on all datasets, in terms of almost all evaluation metrics.

Compared with RNN and CNN based models (e.g., GRU4Rec and Caser), the models based on self-attention mechanism (e.g., SASRec, GC-SAN, and GCL4SR) usually achieve better performance. This is because that self-attention mechanism is more effective in capturing long-range item dependencies. GC-SAN achieves better performance than SASRec on Home dataset, by introducing a graph built based on an individual sequence to improve the sequence representation. GCE-GNN outperforms SR-GNN by additionally exploiting global-level item transition patterns.

Moreover, CL4SRec, S³-Rec, and GCL4SR usually outperform their backbone structure SASRec. This demonstrates that the self-supervised learning objectives can help improve sequential recommendation performance. In addition, GCL4SR achieves better results than CL4SRec and S³-Rec. This is because that CL4SRec and S³-Rec augment the sequence representation by the auxiliary learning objectives that only exploit the local context in each individual sequence. However, GCL4SR augments the sequence representation using subgraphs of the transition graph built based on sequences of all users, which can provide both local and global context for learning sequence representations.

To study the importance of each component of GCL4SR, we consider the following GCL4SR variants for evaluation: 1) GCL4SR_{w/o G}: we remove the graph contrastive learning loss by setting $\lambda_{1}$ to 0 in Eq. (12); 2) GCL4SR_{w/o GM}: we remove both the graph contrastive learning loss and the MMD loss by setting $\lambda_{1}$ and $\lambda_{2}$ to 0 in Eq. (12); 3) GCL4SR_{w/o W}: we remove the edge weights of the augmented graph views when performing GCN operations at the first layer of the shared GNNs used in graph contrastive learning.

Table 3 summarizes the performance of GCL4SR variants and SASRec on Poetry and Phones datasets. We can note that GCL4SR_{w/o GM} outperforms the backbone model SASRec in terms of HR@20, on both datasets. This indicates the context in the global transition graph can help improve sequential recommendation performance. By including the MMD loss, GCL4SR_{w/o G} achieves better performance than GCL4SR_{w/o GM}. By further combining the graph contrastive learning loss, GCL4SR outperforms GCL4SR_{w/o G}, in terms of N@20, on both datasets. These observations demonstrate that both the MMD loss and graph contrastive learning loss can help learn better item and sequence representations for sequential recommendation. Moreover, GCL4SR outperforms GCL4SR_{w/o W} in terms of all metrics. This observation indicates that the transition frequency between items across all sequences can help distinguish the importance of neighboring items for better sequential recommendation performance.

We also perform experiments to study the impacts of three hyper-parameters: the sampling depth $M$ and sampling size $N$ used in graph-based augmentation, and the embedding dimension $d$. Figure 3 shows the performance of GCL4SR with respect to different settings of $M$, $N$, and $d$ on Poetry and Phones datasets. As shown in Figure 3(a), larger sampling size tends to produce better recommendation performance. For the sampling depth, we can notice the best settings for $M$ are 4 and 3 on Poetry and Phones datasets, respectively. In addition, the best performance is achieved by setting $d$ to 64 and 96 on Poetry and Phones datasets, respectively.

To further investigate the effectiveness of the graph augmented sequence representation learning module, we employ other structures to build the basic sequence encoder. Specifically, we consider the following settings of GCL4SR for experiments: 1) GCL4SR-GRU: we use the GRU4Rec as the backbone structure to build the basic sequence encoder; 2) GCL4SR-HGN: we use HGN as the backbone structure to build the basic sequence encoder; 3) GCL4SR-SAS: The default model that uses SASRec as the backbone structure to build the sequence encoder.

Table 4 shows the performance of GCL4SR with different sequence encoders, as well as the performance of backbone models. Observe that GCL4SR-HGN, GCL4SR-GRU, and GCL4SR-SAS outperform the corresponding backbone encoder models. This indicates that the graph augmented sequence representation learning module is a general module that can help improve the performance of existing sequential recommendation methods. Moreover, GRU4Rec and SASRec achieve better performance than GCL4SR-HGN. This indicates the basic sequence encoder dominates the performance of GCL4SR, and the graph augmented sequence representation learning module is a complementary part that can help further improve the recommendation performance.