Beyond Clicks: Modeling Multi-Relational Item Graph for Session-Based Target Behavior Prediction

For a session $s$ in the session set $S$, let $P^{s}=[p^{s}_{1},p^{s}_{2},p^{s}_{3},...,p^{s}_{|P^{s}|}]$ denote the target behavior sequence and $Q^{s}=[q^{s}_{1},q^{s}_{2},q^{s}_{3},...,q^{s}_{|Q^{s}|}]$ represent the auxiliary behavior sequence. Moreover, we construct a Multi-Relational Item Graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$ based on all behavior sequences from all sessions, where $\mathcal{V}$ is the set of nodes in the graph containing all available items and $\mathcal{E}$ is the edge sets involving multiple types of directed edges. Each edge is a triple consisting of the head item, the tail item, and the type of this edge. For instance, if we construct the graph based on behaviors of sharing and clicking, then an edge $(a,b,\textnormal{share})\in\mathcal{E}$ means that a user shared item $a$ and subsequently shared item $b$, and an edge $(a,b,\textnormal{click})\in\mathcal{E}$ means that a user clicked item $b$ after clicking item $a$. Given the above notations, we formulate the problem as follows:

The overall architecture of the proposed MGNN-SPred is depicted in Figure 1. The input to MGNN-SPred contains a Multi-Relational Item Graph (MRIG) and the two types of behavior sequences. SR-MRIG first learns item correlations from MRIG by graph neural networks and encode them into item representations. Afterwards, a user’s two behavior sequences are regarded as two sub-graphs in the MRIG where the items in each sub-graph are connected with a virtual node (“T” or “A” in Figure 1), respectively. Subsequently, SR-MRIG aggregates the nodes of each sub-graph to the corresponding virtual node, thus getting the representation of each behavior sequence. Finally, to fuse the two behavior representations and obtain user preference representations, a gating mechanism is adopted to adaptively decide the importance of different behaviors and perform weighted summation over them. For the purpose of recommendation, SR-MRIG calculates each item’s score by user and item representations via a bi-linear product and use the scores to rank them for recommendation.

There are abundant relationships between items lying in users’ historical behaviors. If a user buys item $a$, and subsequently buys item $b$ in the same session, it indicates that item $a$ and item $b$ probably have some dependency, but does not reflect similarity too much since a user less likely buys two very similar items within a short duration. In comparison, if a user clicks item $a$, and subsequently clicks item $b$, it indicates that item $a$ and item $b$ are probably with large similarity. This is intuitive because a user usually browses a number of similar items, and picks the most suitable one to buy.

We construct the multi-relational item graph by taking all items as nodes and each type of behavior corresponds as one directed edge, denoting different relationships between items. The process of constructing MRIG is shown in Algorithm 1. The both target and auxiliary behavior sequences from all sessions $P^{s}$ and $Q^{s}$ (${\forall}s\in\mathcal{S}$) are provided as input. The algorithm browses all behavior sequences, collects all items in the sequences as the nodes of the graph, and constructs edges between two consequent items in the same sequence with their behavior types as the edge types. After constructing the graph with target and auxiliary behaviors, there are two types of directional edges in the graph.

For each node $v\in\mathcal{V}$, we use $\bar{\mathbf{e}}_{v}\in\mathbb{R}^{|\mathcal{V}|}$ denotes its one-hot representation. Before we feed the one-hot representations of nodes into GNN, we first convert each of them into a low-dimensional dense vector $\mathbf{e}_{v}\in\mathbb{R}^{d}$ by a learnable embedding matrix $\mathbf{E}\in\mathbb{R}^{|\mathcal{V}|\times d}$: $\mathbf{e}_{v}=\mathbf{E}^{\top}\bar{\mathbf{e}}_{v}$.

After collecting the vectors $\mathbf{e}_{v}({\forall}v\in\mathcal{V})$, we feed them with MRIG $\mathcal{G}$ into GNN to generate global representations of nodes $\mathbf{g}_{v}$. The representations are expected to encode multiple item-to-item relations. We take node $v$ as an example for illustration. First of all, we collect neighbors of node $v$. Each node in the graph has four types of neighboring node sets. According to the type and direction, we name the four sets as “target-forward”, “target-backward”, “auxiliary-forward”, and “auxiliary-backward”. Take the type of “target” as an example, we obtain neighbor groups corresponding to forward and backward directions as below:

For the type of “auxiliary”, its neighbor groups, i.e., $\mathcal{N}_{\textnormal{a}+}(v)$ and $\mathcal{N}_{\textnormal{a}-}(v)$, are acquired by the same way.

At each step of representation propagation in GNN, we first aggregate each group of neighbors by mean-pooling to obtain the representation of this group, defined as below:

The representations of the three remaining groups are calculated in a similar fashion. Consequently, for the propose of joint considering different relations between items, we combine these four representations of different neighbor groups by sum-pooling:

Finally, we update the representation of the center node $v$ by:

After performing $K$ iterations, we take the node representation of the last step as the representation of the corresponding item: $\mathbf{g}_{v}=\mathbf{h}^{K}_{v}$. In practice, we implement the GNN in a minibatch setting which is inspired by (Hamilton et al., 2017) to ensure scalability.

We have tried different ways to compute the representation of the virtual node for the target and auxiliary behavior sequences, including using attention mechanism to assign different importance weights to the nodes and performing sub-graph propagating for several times. Empirically, we have found that simple mean-pooling could already achieve comparable performance while retaining low complexity. We denote the summarized representations of target behavior sequence $P$ and auxiliary behavior sequence $Q$ as $\mathbf{p}$ and $\mathbf{q}$, respectively, which are given as:

We argue that the two different types of behavior sequence representations might contribute differently when building an integrated representation. This is because the auxiliary behavior is not exactly the same with the target behavior to be predicted, and different users might have different concentration on different behaviors. For instances, some users might browse the item pages frequently and click various items arbitrarily, and another users might only click the items they want to buy. It is self-evident that the contributions of auxiliary behavior sequence for the next item prediction are different in these situations. We define the following gating mechanism to calculate the relative importance weight $\alpha$:

where $[\mathbf{p};\mathbf{q}]$ denotes the concatenation of the two representations, $\sigma$ is the sigmoid function, and $\mathbf{W}_{g}\in R^{1\times 2d}$ is a trainable parameter of our model. Finally, we obtain the user preference representation $\mathbf{o}$ for the current session by the weighted summation of $\mathbf{p}$ and $\mathbf{q}$:

We further calculate the recommendation score $s_{v}$ of each item $v\in\mathcal{V}$ using the item embedding $\mathbf{e}_{v}$. A bi-linear matching scheme is employed by:

where $\mathbf{W}\in R^{d\times d}$ is a trainable parameter matrix of our model.

To learn the parameters of our model, we apply a softmax function to normalize the scores $\mathbf{s}\in R^{|\mathcal{V}|}$ over all items to get the probability distribution $\hat{\mathbf{y}}$:

Backpropagation for neural networks is adopted to optimize the model by minimizing the cross-entropy loss of the predicted probability distribution $\hat{\mathbf{y}}$ w.r.t. the ground truth. The loss function is defined as follows:

where $(y_{1},\cdots,y_{|\mathcal{V}|})$ denotes the one-hot representation of the ground truth. Note that $\mathcal{L}_{RS}$ is easily extended to a minibatch loss.

We consider the top-100 ranked predictions as recommended items. Following (Wu et al., 2019; Xu et al., 2019), we adopt HR@100 (H@100), MRR@100 (M@100), and NDCG@100 (N@100) to evaluate the recommendation performance of all models after obtaining their recommendation lists. Table 2 shows the performance comparison between our model and the adopted baselines. (1) The first part of the table corresponds to the simple baselines. We observe their results are significantly worse than other methods. (2) The second part involves standard sequential based methods for session-based recommendation. We observe that their results keep at the same level, except for STAMP on WeChat. It shows that: 1) taking session-based recommendation as a sequential modeling task can improve performance; 2) although NARM and STAMP are more advanced approaches which use attention mechanism to combine hidden representations of different time steps, they do not show advantages on the sparse behavior prediction problem we studied (not the same as previous studies focusing on click prediction). (3) The third part is GNN based models. SR-GNN and GC-SAN seem to be better than the sequential methods, and HetGNN further boost the performance. (4) The second-to-last part involves approaches of learning two sequences in other research domains. Their best results are worse than the best performance of the above recommendation methods, which suggests that considering the interaction of items in two sequences might have no benefit for the studied problem. Finally, we can see that our method outperforms all the other methods, demonstrating the superiority of our model for session-based recommendation.

We choose several representative methods in Table 3 to test whether considering the auxiliary behavior sequence indeed boosts the performance of session-based recommendation. The methods with “(w/o a)” mean removing the auxiliary behavior sequence from their full version. Firstly, we observe that our proposed model still consistently achieves better performance in this situation. Moreover, by comparing each method in Table 2 with its “(w/o a)” version, we can find every method beats the one of “(w/o a)” with significant margins. Based on the above illustrations, we demonstrate that considering the auxiliary behavior sequence is indeed meaningful.