SR-GCL: Session-Based Recommendation with Global Context Enhanced Augmentation in Contrastive Learning

We construct a local session graph $\mathcal{G}\!=\!\left(\mathcal{V},\mathcal{E}\right)$ from each session $s$ to pass the graph-based model. $\mathcal{V}\!=\!\left\{\left\{v_{1},v_{2},...,v_{\left|\mathcal{V}\right|-1}\right\},v_{s}\right\}$ includes all unique items in the session and a star node $v_{s}$. The $i$-th node embedding after passing the $l$-th layer of GNN is represented by a hidden state $h_{i}^{l}\in\mathbb{R}^{d}$. We initialize the hidden states as $h_{i}^{0}\!=\!v_{i}$ and initialization for the hidden state of a star node $v_{s}$ is $h_{s}^{0}$, which is the average value of all $h_{i}^{0}$ as

$$h_{s}^{0}=\frac{1}{N}\sum_{i=1}^{N}h_{i}^{0}$$

(10)

where $N\!=\!\left|\mathcal{V}\right|-1$ is the number of all unique items. A star node is connected to all nodes with bidirectional edges. Information from non-adjacent nodes can be propagated by taking the star node as an intermediate node (Pan et al. 2020a). $\mathcal{E}$ is an edge set consisting of two types of edges. The first one is for connections of all nodes, which are converted into two normalized adjacency matrices (i.e., incoming matrix $A^{I}$ and outgoing matrix $A^{O}$) to pass the GNN. The second one is for connections of a star node.

First, nodes in a graph $\mathcal{G}$ are updated by propagating information of the neighbor nodes. $m_{i}^{l}$ denotes message (i.e., information from the neighbors) for a hidden state $h_{i}$ at the $l$-th layer, which can be formulated as

	$\displaystyle m_{i}^{l}=\left[A_{i}^{I}(\left[h_{1}^{l-1},h_{2}^{l-1},...,h_{N}^{l-1}\right]^{\top}W^{I}+b^{I})\;;\quad\right.$		(11)
	$\displaystyle\left.A_{i}^{O}(\left[h_{1}^{l-1},h_{2}^{l-1},...,h_{N}^{l-1}\right]^{\top}W^{O}+b^{O})\right]$

where N is the number of nodes, and $\left[;\right]$ denotes a concatenation. $A_{i}^{I},A_{i}^{O}\in\mathbb{R}^{1\times N}$ are the corresponding incoming and outgoing weights for the node $h_{i}$ (i.e., the $i$-th row of $A^{I}$ and $A^{O}$). $W^{I},W^{O}\in\mathbb{R}^{d\times d}$ and $b^{I},b^{O}\in\mathbb{R}^{d}$ are learnable parameters for the incoming and outgoing edges, respectively. So we feed the message $m_{i}^{l}$ and the previous state $h_{i}^{l-1}$ into the Gated Graph Neural Networks (GGNNs) (Li et al. 2015) for each node as

		$\displaystyle z_{i}^{l}=\sigma(W_{z}m_{i}^{l}+U_{z}h_{i}^{l-1}),$		(12)
		$\displaystyle r_{i}^{l}=\sigma(W_{r}m_{i}^{l}+U_{r}h_{i}^{l-1}),$
		$\displaystyle\tilde{h}_{i}^{l}=tanh(W_{h}m_{i}^{l}+U_{h}(r_{i}^{l}\odot h_{i}^{l-1})),$
		$\displaystyle\hat{h}_{i}^{l}=(1-z_{i}^{l})\odot h_{i}^{l-1}+z_{i}^{l}\odot\tilde{h}_{i}^{l}$

where $\sigma$ is a sigmoid and $\odot$ is an element-wise multiplication. $z_{i}^{l}$ and $r_{i}^{l}$ are an update gate and reset gate. $W_{z},W_{r},W_{h}\in\mathbb{R}^{d\times 2d}$ and $U_{z},U_{r},U_{h}\in\mathbb{R}^{d\times d}$ are trainable matrices. After the propagation of adjacent nodes, we also consider the overall information from the previous star node $h_{s}^{l-1}$. For each node, we decide how much information from the star node should be propagated with a gate network and attention mechanism as

		$\displaystyle\alpha_{i}^{l}=\frac{(W_{q1}\hat{h}_{i}^{l})^{\top}W_{k1}h_{s}^{l-1}}{\sqrt{d}},$		(13)
		$\displaystyle h_{i}^{l}=(1-\alpha_{i}^{l})\hat{h}_{i}^{l}+\alpha_{i}^{l}h_{s}^{l-1}$

where $W_{q1},W_{k1}\in\mathbb{R}^{d\times d}$ are trainable matrices, and $\sqrt{d}$ is a scaling factor. After all hidden states are updated, the state of a star node is also updated. We apply an attention mechanism to compute different degrees of similarity for all node states $h^{l}=\left[h_{1}^{l},h_{2}^{l},...,h_{N}^{l}\right]$ by regarding the star node as a query. So the current state of the star node $h_{s}^{l}$ is computed as

		$\displaystyle\beta^{l}=softmax\left(\frac{(W_{k2}h^{l})^{\top}W_{q2}h_{s}^{l-1}}{\sqrt{d}}\right),$		(14)
		$\displaystyle\qquad\qquad\qquad h_{s}^{l}=\beta^{l}h^{l}$

where $W_{q2},W_{k2}\in\mathbb{R}^{d\times d}$ are learnable parameters, and $\beta^{l}\in\mathbb{R}^{N}$ are weights for all nodes. Multiple updating can be stacked to accurately represent the transition relationship between items. However, the more propagating information between nodes is repeated, the easier the model could lead to an over-fitting problem with the GNN (Qiu et al. 2019; Pan et al. 2020a). To address this problem, (Pan et al. 2020a) applied a highway gate for all nodes after the multiple updating. The highway gate computes the final hidden states $h^{f}$, which is the weighted sum of $h^{0}$ and $h^{L}$. $h^{0}$ and $h^{L}$ denote the hidden states before and after the $L$-layer GNN. The highway gate can be formulated as

		$\displaystyle h^{f}=g\odot h^{0}+(1-g)\odot h^{L},$		(15)
		$\displaystyle\mbox{where }g=\sigma(W_{g}\left[h^{0};h^{L}\right])$

where $\sigma$ is a sigmoid function, $\left[;\right]$ denotes a concatenation, and $W_{g}\in\mathbb{R}^{d\times 2d}$ is a trainable matrix.

We obtain sequential item embeddings $u\in\mathbb{R}^{\left|s\right|\times d}$ from the corresponding nodes $h^{f}\in\mathbb{R}^{N\times d}$ which passed the GNN, where $\left|s\right|$ is the length of a session, and $N$ is the number of all unique items of a session. We add trainable position embeddings $p\in\mathbb{R}^{\left|s\right|\times d}$ to consider sequential information in an attention mechanism as

$$u^{p}=u+p=\left[u_{1}^{p},u_{2}^{p},...,u_{\left|s\right|}^{p}\right]$$

(16)

To represent the global preference of a session, a soft attention mechanism is applied with the current interest and a star node. This combines the items according to their degrees of preference as

		$\displaystyle\gamma_{i}=W_{0}^{\top}\sigma(W_{1}u_{i}^{p}+W_{2}h_{s}^{L}+W_{3}u_{\left|s\right|}^{p}+b_{0}),$		(17)
		$\displaystyle\qquad\qquad\qquad\tilde{r}=\sum_{i=1}^{\left|s\right|}\gamma_{i}u_{i}^{p}$

where $W_{0}\in\mathbb{R}^{d}$ and $W_{1},W_{2},W_{3}\in\mathbb{R}^{d\times d}$ are learnable parameters, $b_{0}\in\mathbb{R}^{d}$ is a bias, and $\sigma$ is a sigmoid function. That is, the global preference of the session $\tilde{r}$ is determined in consideration of the star node after the $L$-th layer $h_{s}^{L}$ and the last item $u_{\left|s\right|}^{p}$. We finally obtain the representation of the session $s$ to consider not only the global preference but also the current preference as

$$r=\left[\tilde{r};u_{\left|s\right|}^{p}\right]$$

(18)

where $\left[;\right]$ denotes a concatenation. $r\in\mathbb{R}^{2d}$ is used for a recommendation task and contrastive learning.

This is a technique commonly used in CV, which is to obtain a subset by randomly cropping a part of an image (Takahashi, Matsubara, and Uehara 2019). Applying this method to sequence data is equivalent to obtaining a continuous sub-sequence of a sequence. This augmentation method $a_{cr}$ for a sequence $s$ is formulated as

$$s^{a_{cr}}=a_{cr}(s)=\left[x_{i},x_{i+1},...,x_{i+N_{cr}-1}\right]$$

(19)

where $i$ means a starting index randomly selected, and $N_{cr}=\lfloor\gamma_{cr}\times\left|s\right|\rfloor$ is the length of the sub-sequence. It is effective to obtain a local view of the historical session.

This technique applies zero-masking to some parts of a sample. It has been widely adopted to avoid over-fittings in other fields, which is called word-dropout in NLP (Bowman et al. 2015) and node-dropout in GNN (Wu et al. 2021; You et al. 2020). To apply this technique for a session $s$, we randomly make a set $\mathcal{I}_{ma}=\left\{i_{1},i_{2},...,i_{N_{ma}}\right\}$ indicating masked indices, where $N_{ma}=\lceil\gamma_{ma}\times\left|s\right|\rceil$ is the number of masked items. The items pointed by $\mathcal{I}_{ma}$ are replaced with a special item [mask]. This method $a_{ma}$ can be formulated as

	$\displaystyle s^{a_{ma}}=a_{ma}(s)=\left[\tilde{x}_{1},\tilde{x}_{2},...,\tilde{x}_{\left|s\right|}\right],$		(20)
	$\displaystyle\mbox{where }\tilde{x}_{j}=\begin{cases}x_{j}\qquad\qquad\mbox{if }j\notin\mathcal{I}_{ma}\\ \mbox{[mask]}\qquad\;\mbox{if }j\in\mathcal{I}_{ma}\end{cases}$

As items within a session implicitly represent the intention of a user, even if $s^{a_{ma}}$ has only several elements of the session, it could still reserve the main intention.

This aims to shuffle a part of a given sequence. For sessions in the real-world, the order of users’ interactions is not strictly enforced, but flexible due to various unobservable external factors (Tang and Wang 2018; Covington, Adams, and Sargin 2016). To apply this method to a session $s$, we randomly shuffle a continuous sub-sequence $\left[x_{i},x_{i+1},...,x_{i+N_{re}-1}\right]$, where $i$ is a starting index randomly selected, and $N_{re}=\lceil\gamma_{re}\times\left|s\right|\rceil$ is the length of the sub-sequence. This augmentation method $a_{re}$ is formulated as

$$s^{a_{re}}=a_{re}(s)=\left[x_{1},...,\tilde{x}_{i},...,\tilde{x}_{i+N_{re}-1},...,x_{\left|s\right|}\right]$$

(21)

where $\left[\tilde{x}_{i},\tilde{x}_{i+1},...,\tilde{x}_{i+N_{re}-1}\right]$ is a shuffled sub-sequence. With this method, we encourage our model to rely less on the order of a session. This enhances the model to be more robust when it encounters unexpected sessions.

Figure 5 shows the effect of individual augmentation operators by varying the ratio $\gamma$ from 0.1 to 0.9, where $\gamma$ means the degree of transformation of each session. If this value is large, it is difficult to have the same underlying semantics as the original session. Otherwise, if it is too small, the contrastive effect between differently augmented views of the same sample would be reduced. For the experiment, we use two augmented sessions generated by using the same method with a fixed ratio. Note that even if the same augmentation method is used, two generated sessions may be different due to the randomness of applied positions.

Taken overall, we can see that Change and Injection augmentations have better performance than other methods except for the case of Figure 5 (b). Also, our proposed methods are relatively less influenced by $\gamma$. The reason is that even if the degrees of deformation are severe, they do not generate very different views from the original sample due to the consideration of the global context. In contrast, Crop and Mask are sensitive to $\gamma$. They also show the opposite tendency as $\gamma$ increases because they play a similar role in hiding information of a session. Meanwhile, Reorder shows a significant difference between P@20 and MRR@20. It maintains relatively low performance on MRR@20. The reason is that Reorder makes the current interest difficult to be known. To be specific, our model considers the last clicked-item as a proxy of current interest, but this method could shuffle the order of the sub-session including the last item, which dilutes the meaning. Of course, other augmentations can also stochastically affect this, but Reorder can perturb these sequential dependencies more. In summary, a high ratio of reordering could cause a mismatch between the global preference and the current interest.

Figure 6 shows the performance according to the combinations of two augmentation methods. We use two augmented sessions generated by two fixed methods. The results show that exactly one combination cannot be the best for session data. However, our proposed methods (i.e., Change and Injection) can provide more options for session augmentations, which show the improved performance than the combinations of conventional methods (i.e., Crop, Mask, and Reorder) except for the case of Figure 6 (b). It is notable that the combination of weak augmented methods (i.e., Change and Injection) and a strong method (i.e., Reorder) has better performance as mentioned in the advanced experiment.

Our framework allows setting the number of selected methods flexibly due to our multi-positive loss described in the main text. This means that the number of negative samples of contrastive loss can be adjusted independently without changing the batch size. In this experiment, we tested how different the number of randomly selected methods impact the performance.

Figure 7 shows the performance varying the number of selected methods $M$. When the batch size is $N$, the number of augmented representations used for contrastive learning per batch is $N\times M$. CMR means that we use an augmentation set including Crop, Mask, and Reorder. CI stands for Change and Injection. The cases except for Figure 7 (b) show two results. First, the performance using the augmentation sets including CI is generally better than only CMR. Second, the number of selected methods does not need to be fixed to 2. Even though there is no optimal number of augmentations to ensure the best performance for all conditions, it can be optimized according to a specific purpose. The results could confirm that our contrastive learning framework is effective when the selected number is two or more, which means that there must be other views of the same session to take advantage of contrastive learning.