## 3 Method
### Meta-Path Aggregation Layer  
Based on meta-paths, the structural and semantic information among users, items, and their attributes is captured. Different types of nodes that are strongly correlated to the target node are sampled by utilizing random walks. At each step, the walker either visits the neighbor nodes of the target node with equal probability or returns to the initial node. And the number of samples for each type of node is fixed to ensure that all node types are sampled. Correlation paths are obtained by sampling the strongly correlated neighbor nodes of each node. All node features along the meta-path are converted into a single vector by using a linear mean encoder. The vector representation of a meta-path is to concatenate the vector representation of each node on the meta-path. And then, a graph convolutional neural network is used to aggregate the feature matrix to achieve the aggregated vector representation of each node. The meta-path aggregation process is shown in Figure 2.  
By aggregating meta-path semantic information that includes node attributes, the model achieves node representation optimization for improved recommendation performance. The aggregation process consists of two main steps and is implemented as Equation (5):  
\[h_{p(v,u)}=f_{\theta}(p(v,u))=f_{\theta}(h^{{}^{\prime}}_{v},h^{{}^{\prime}}_ {u},\{h^{{}^{\prime}}_{t},\
abla_{t}\in\{m^{(v,u)}\}\}) \tag{5}\]  
where \(p(v,u)\) is a given meta-path from the target node \(v\) to its meta-path neighbor \(u\). And the intermediate nodes of \(p(v,u)\) are referred to as \(m^{(v,u)}=p(v,u)\backslash(v,u)\), which includes all nodes along the meta-path except \(v,u\). The features of all nodes on \(p(v,u)\) are transformed into an embedding vector by leveraging a linear mean encoder. The relevant information is captured from the intermediate nodes. Overall, this approach allows us to aggregate and represent the features of the nodes along \(p(v,u)\), enabling the incorporation of abundant valuable structural and semantic information in the following tasks. The term \(h^{{}^{\prime}}_{v}\) represents the vector representation of \(v\) through feature interaction transformation, and then, the model uses an attention mechanism to assign a weight to and sum the meta-path instances of \(P\) related to the target node \(v\). Different meta-paths can promote the representation of target nodes to varying degrees. We calculate the standardized importance weights of each meta-path as \(a^{P}_{vu}\) and then perform a weighted sum over all meta-paths that have \(v\) as the target node, i.e., Equation (6). \[ \begin{array}{l}e^{P}_{vu}=LeakyReLU(w^{T}_{p}\cdot[h^{{}^{\prime}}_{v}||h _{p(v,u)}])\\ a^{P}_{vu}=\frac{\exp{(e^{P}_{vu})}}{\sum_{v\in N^{P}_{v}}\exp{(e^{P}_{vu})}}\\ h^{P}_{v}=\sigma(\sum_{u\in N^{P}_{v}}a^{P}_{vu}\cdot h_{p(v,u)})\end{array}  \tag{6}\]  
where \(w^{T}_{p}\) is the parameterized attention vector of the meta-path \(P\). \(N^{P}_{v}\) is a set of meta-path neighbors based on \(v\). Then, based on the attention coefficient, the vector representation of node \(v\) is updated by aggregating its meta-path neighbors. Thereby, an aggregation layer is performed between meta-paths that merges the semantic information on all meta-paths  
Figure 2: Meta-path encoding and aggregation strategy. containing \(v\). Once more, different meta-path information is aggregated by assigning distinct weights to diverse meta-paths through attention mechanisms. \[ \begin{split}\beta_{P_{j}}&=\frac{\exp{(e_{P_{j}})}}{ \sum_{p_{\in}\in\mathcal{P}}\exp{(e_{P})}}\\ h_{v}&=\sigma(W_{o}\sum_{P\in\mathcal{P}}\beta_{P} \cdot H_{v}^{P})\end{split}  \tag{7}\]  
The set of latent meta-paths passing through \(v\) is \(\mathbb{P}=\{P_{1},P_{2},...,P_{j},...,P_{J}\}\), and \(J\) is the number of meta-paths. Among them, \(e_{P_{j}}\) is the concatenation vector representation of all nodes on \(P_{j}\). \(\beta_{P_{j}}\) denotes the weight coefficient of the meta-path \(P_{i}\) that consists of \(v\).