# Research on Hybrid Recommendation Model for Personalized Recommendation Scenarios
## 3 NRH Recommendation Model
### User Profile Construction
#### 3.2.2 User Dynamic Preference Portraits  
The dynamic user preference portrait part is mainly portrayed from the perspective of neighborhood features of interactive items. The Ripple set (water wave set) \(S^{k}_{u}\) is constructed based on the click history vu of a specific User \(u\). Vu is used as the starting point of preference propagation, propagated outward layer by layer on the item-attribute knowledge graph to form Ripple set \(S^{k}_{u}(k=1,2,\cdots,H)\) for each layer of Hop, where  
Figure 2: User profile modeling based on historical preferences. Ripple set \(S_{u}^{k}\) is the user click history set. The Ripple set is the set of triples after preference propagation by \(\mathbf{v}_{u}\). Based on the original RippleNet item vector \(\mathbf{v_{1}}\), the item-image \(v^{\prime}\) based on Node2 vec-side knowledge representation is introduced in the item-image representation part. The two are aggregated to obtain the item-vector representation \(\mathbf{v}\) of the dynamic preference propagation part. The User u and item \(\mathbf{v}\) information are fused to form the dynamic user preference image \(\mathbf{o}\). The specific process is as follows:  
The historical clicked items of User u are recorded as \(\mathbf{v_{u}}\) in the item-attribute knowledge graph, and the preference-related entity set of historical items vu is thus generated, i.e., the preference-related entity set is created for User u in RippleNet by a circular recursive method, as shown in (10). \[\xi_{u}^{k}=\left\{t\mid(h,r,t)\in G,h\in\xi_{u}^{k-1}\right\},\;k=1,2,\cdots,H, \tag{10}\]  
where \(\xi_{u}^{0}=V_{u}=\{v\mid y_{uv}=1\}\) indicates the set of user history click items. These entities can be considered preference-related entities of User \(u\) in the knowledge graph based on historical clicks on \(\mathbf{v_{u}}\). After defining preference-related entities, all the K-hop Ripple sets of User \(u\) are defined as follows:  
\[\mathcal{S}_{u}^{k}=\left\{(h,r,t)\mid(h,r,t)\in\mathcal{G}\;and\;h\in \mathcal{E}_{u}^{k-1}\right\},k=1,2,\ldots,H, \tag{11}\]  
In each Hop, an aggregated Embedding is used for item portrait representation. The original Ripple model computes the correlation probability \(p_{1i}\) for each triplet (\(\mathbf{h_{i}}\), \(\mathbf{r_{i}}\), \(\mathbf{t_{i}}\)) for item \(\mathbf{v_{1}}\) with head \(\mathbf{h_{i}}\) and relationship matrix \(\mathbf{R_{i}}\) in the original Ripple model, respectively. \[p_{1i}=softmax\Big{(}v_{1}^{T}R_{i}H_{i}\Big{)}=\frac{exp\big{(}v_{1}^{T}R_{i} h_{i}\big{)}}{\sum(h,r,t)\in S_{u}^{1}exp\big{(}v_{1}^{T}Rh\big{)}}, \tag{12}\]  
Additionally, in the item vector \(\mathbf{v_{2}}\) modeled using Node2 vec-side with the head hi and relationship \(\mathbf{r_{i}}\), the correlation probability \(p_{2i}\) for each triplet (\(\mathbf{h_{i}}\), \(\mathbf{r_{i}}\), \(\mathbf{t_{i}}\)) is calculated. \[p_{2i}=softmax\Big{(}cos\Big{(}v_{2}^{T},(h_{i}+r_{i})\Big{)}\Big{)}=\frac{ exp\big{(}cos\big{(}v_{2}^{T},(h_{i}+r_{i})\big{)}\big{)}}{\sum(h,r,t)\in S_{u} ^{1}exp\big{(}cos\big{(}v_{2}^{T},(h_{i}+r_{i})\big{)}\big{)}}, \tag{13}\]  
After obtaining the correlation probabilities, all the tail entities \(t_{i}\) in \(\mathcal{S}_{u}^{1}\) are multiplied by the corresponding correlation probabilities \(p_{1i}\) and \(p_{2i}\), respectively, returning vectors \(o_{1u}^{1}\)\(o_{2u}^{1}\), and where \(o_{ju}^{1}\) (\(j=1,2\)) can be regarded as the first response of User u to the historical click record of item \(\mathbf{v}\), which is used to form the first propagated dynamic preference portrait of User u.  
\[o_{1u}^{1}=\sum_{(h_{i},r_{i},t_{i})\in S_{u}^{1}}p_{1i}t_{i}, \tag{14}\]  
\[o_{2u}^{1}=\sum_{(h_{i},r_{i},t_{i})\in S_{u}^{1}}p_{2i}t_{i}, \tag{15}\]  
\[o_{u}^{1}=f\Big{(}o_{1u}^{1},o_{2u}^{1}\Big{)}, \tag{16}\]  
Here the fusion function \(f(x)\) is chosen as the linear regression function \(y=wx+b\).