# Light Graph Convolutional Recommendation Algorithm Based on Hybrid Spreading
## 3 Model Design  
### General Framework  
In a spreading-based recommendation algorithm, it is typically assumed that equal resources exist for all the user's interaction items, and the resources obtained by the user are considered as a weighted linear aggregation of the average resources of the items they have selected. After the spreading process, the more resources an item receives, the higher its likelihood of being selected. However, this assumption is idealized. In reality, this characterization treats the user choice as interest in items, whereas the spreading process should be interpreted as the flow of the user interest, reflecting users' differentiated preferences for different items.  
Our proposed LGCNHS is divided into two parts. The first part is the embedding-optimized LightGCN, which introduces user features and item features to optimize the embedding layer based on LightGCN. Subsequently, through the propagation layer and prediction layer, it deeply explores personalized user features and semantic features of items, learning the latent embedding representations of users and items. It then transforms them into an allocation weight matrix, which is used to adjust the resource allocation process in subsequent steps. This approach addresses the issues of over-reliance on user behavior and insufficient integration of latent item information. The second part integrates an allocation weight matrix into the hybrid spreading. During the second round of the hybrid spreading process, the allocation weight matrix is introduced to adjust resource allocation based on the weights. This ensures that the higher the user's interest level in items, the more resources are allocated. This method compensates for the limitations of traditional hybrid spreading recommendation algorithms in exploring user-item interaction data and fully considers the complex latent relationships between users and items. Finally, recommendations are generated for target users based on the resource values of each item. The general framework structure of the model is illustrated in Figure 1.  
Furthermore, to better understand the general framework of the LGCNHS, we have drawn a flowchart of the LGCNHS. The overall process of the model is illustrated in Figure 2. The overall process is as follows:  
1. First, user features and item features are input into the optimized embedding layer. The user embedding vector and item embedding vector are learned through the propagation layer and predictive layer, resulting in the allocation weight matrix.
2. Additionally, the user-item bipartite graph is constructed using the user-item interaction data, and the first round of the hybrid spreading process is performed to obtain the user resource vector.
3. Finally, the allocation weight matrix is combined with the user resource vector for the second round of the hybrid spreading process to generate recommendations.  
Figure 1: Diagram of the frame structure. \(\mathbf{x_{u}}\) denotes the user features vector, \(\mathbf{x_{o}}\) denotes the item features vector, \(\mathbf{\mathrm{e}}_{u}^{(k)}\) and \(\mathbf{\mathrm{e}}_{o}^{(k)}\) denote the embedding vector of user \(u\) and item \(o\) output from the \(k\)th propagation layer, \(\mathbf{g_{uo}}\) denotes the allocation weight, \(\mathbf{c_{u}}\) and \(\mathbf{c_{u}^{\prime}}\) denote the user resource vector obtained after the first round of probabilistic spreading and heat spreading, \(\mathbf{t_{o}}\) and \(\mathbf{t_{o}^{\prime}}\) denote the item resource vector obtained after the second round of probabilistic spreading and heat spreading, \(\mathbf{f}\) denotes the initial resource vector of target user, \(\mathbf{f}\) denotes the resource vector of target user after hybrid spreading, \(\lambda\) denotes the hyperparameter.  
In the following sections, each model component will be described in detail.