# Knowledge-Aware Enhanced Network Combining Neighborhood Information for Recommendations
## 3 Our Approach
### Recommendation Module
#### 3.3.1. URL  
The URL includes a collaborative propagation part and a knowledge graph-aware propagation part. We will discuss both parts in detail below. _Collaborative propagation:_ We know that the user's prior information (i.e., historical interaction items) largely represents the information about the user's personalized preferences. Therefore, to enrich the description of the user, KCNR does not use a simple embedding representation of the user alone, but combines it with the user's prior information and the knowledge information in the KG, to describe the user. Specifically, KCNR first finds multiple entities in the KG, corresponding to multiple interaction items of user \(u\), based on the correspondence between items and entities in the KG, which constitutes the initial entity propagation set of user \(u\), and lets it propagate in the KG, to obtain user personalized preferences. The initial entity propagation set of user \(u\) is defined as follows:  
\[\varphi_{u}^{0}=\{e|(v,e)\in D\;and\;v\in|y_{uv}=1\}. \tag{3}\]  
With the above processing, we can add the interaction information that best represents the potential semantics of the user to the initial set of entity propagation of the user \(u\), which is used to enhance the user embedding representation. _Knowledge graph-aware propagation:_ In the KG, entities connected by a variety of relationships often have strong knowledge associations. Thus, by propagating entities along the associated paths in the KG, we can obtain the extended entity set of the user's initial entity propagation set, as well as the set of triplets of different depths, which can also further enhance the user's embedding representation, due to the strong correlation between them. The extended set of entities of user \(u\) in the KG, can be recursively represented as:  
\[\varphi_{u}^{l}=\Big{\{}t|(h,r,t)\in\mathbf{G}\;and\;h\in\varphi_{u}^{l-1} \Big{\}},\;\;\;l=1,2,\cdots,L, \tag{4}\]  
where \(l\) represents different depths. Then, we define the user's \(l\)-\(th\) triplet set as:  
\[\varphi_{u}^{l}=\Big{\{}(h,r,t)\Big{|}(h,r,t)\in\mathbf{G}\;and\;h\in\varphi_ {u}^{l-1}\Big{\}},\;\;\;l=1,2,\cdots,L. \tag{5}\]  
Figure 2: Illustration of the proposed KCNR model, which consists of a recommendation module, knowledge graph embedding module, and information complementary module. Through collaborative propagation and knowledge graph-aware propagation, users' preferences are continuously diffused in the KG, and we are then able to capture users' knowledge-based higher-order interaction information, effectively enhancing the ability of the model to augment user representations with latent vectors. However, each tail entity in the KG tends to have different head entities and their corresponding relationships. For example, _Farewell Atlanticis_ and _Interstellar_ are relatively similar in the genre of films, but the actors and directors are less similar. Therefore, we adopt a knowledge-aware attention network [24] to generate different scores for tail entities of triplets (i.e., different weights for different head entities and relations), which are used to indicate that, when different head entities are obtained, different meanings when entities and relationships are used. The knowledge-aware network is shown in Figure 3. Assuming that \((h,r,t)\) is the \(i\)-\(th\) triplet in the set of user extended entities in the set of triplets at the \(l\)-\(th\) layer, the attention embedding of the tail entity is as follows:  
\[att_{i}=\delta\Big{(}e_{i}^{h},r_{i}\Big{)}e_{i}^{t}, \tag{6}\]  
where \(e_{i}^{h}\) is an embedding representation of the head entity, \(r_{i}\) is an embedding representation of relation, and \(e_{i}^{t}\) is an embedding representation of the tail entity. We use \(\delta\Big{(}e_{i}^{h},r_{i}\Big{)}\) to control the attention scores (weights) generated by \(e_{i}^{h}\) and \(r_{i}\).