# Cross-Domain Person Re-Identification Based on Feature Fusion Invariance
## 2 Materials and Methods
### Integration Features
#### 2.2.2 Local Feature
We divide these neighboring nodes into three types, as shown in Figure 3, namely, \(N_{SP}\), \(N_{AP}\), and \(N_{SI}\). Among them, \(N_{SP}\) refers to neighboring nodes of corresponding parts of different person images, \(N_{AP}\) refers to neighboring nodes  
Figure 2: Schematic diagram of person parts. Utilizing local features is intended to capture fine details from crucial body parts of a person, thereby enhancing identification accuracy in intricate environments. (**a**) illustrates the person image being uniformly divided into six regions from top to bottom, (**b**) demonstrates a further fine-grained division of the person’s image into six sections, and (**c**) illustrates the dynamic alignment of corresponding regions across different images. of neighboring parts of different person images, and \(N_{SI}\) refers to neighboring nodes of different parts of the same person image. The traditional GAT [28] is used to distinguish the importance of neighboring nodes and gather information. We distinguish the attention weight in the learning process between local relations and local internal relations. In the complete local graph, the attention weight \(\alpha(f_{p}^{i},f_{q}^{j})\) between node \(f_{p}^{i}\) and its neighboring node \(f_{q}^{j}\) is calculated according to the cosine similarity. Specifically, we first transform \(f_{p}^{i}\) and \(f_{q}^{j}\) by using the transformation matrix \(W\) and then calculate the cosine similarity to measure their correlation. Finally, we use the softmax function to obtain the attention weight \(\alpha(f_{p}^{i},f_{q}^{j})\). \[\alpha(f_{p}^{i},f_{q}^{j})=\frac{exp(\phi(Wf_{p}^{i},Wf_{q}^{j}))}{\sum_{f_{q} ^{k}\in N(f_{p}^{i})}exp(\phi(Wf_{p}^{i},Wf_{q}^{k}))}\times K \tag{3}\]  
where \(\phi(\_,\_) is the cosine similarity function, \(N(f_{p}^{i})\) is the neighbor node set of node \(f_{q}^{j}\), and \(k\) is the adjustment coefficient considering different types of neighbor nodes. There are three types of neighboring nodes. When node \(f_{q}^{j}\) belongs to different neighbor node sets, we define a different \(K\). When \(i\
eq j\) and \(p=q\), both \(f_{p}^{i}\) and \(f_{q}^{j}\) come from the corresponding parts of different images, and \(f_{q}^{j}\) belongs to the adjacent node set \(N_{SP}\), that is, \(N(f_{p}^{i})=N_{SP}\). Let us set \(K=1\) in our experiment. When \(i\
eq j\), \(p=q+1\), or \(p=q-1\), \(N(f_{p}^{i})\) and \(f_{q}^{j}\) come from adjacent parts of different images, and \(f_{q}^{j}\) belongs to the adjacent node set \(N_{AP}\), that is, \(N(f_{p}^{i})=N_{AP}\). We set \(k\) to a constant smaller than \(N_{SP}\) because the correlation decreases with increasing spatial distance. When \(i=j\), \(p\
eq q\), \(f_{p}^{i}\), and \(f_{q}^{j}\) come from different parts of the same image, and \(f_{q}^{j}\) belongs to the adjacent node set \(N_{SI}\), that is, \(N(f_{p}^{i})=N_{SI}\). With decreasing spatial distance, the correlation between parts increases. Therefore, context information is injected into the attention weight to consider the structural information, and \(k\) is expressed as  
\[K=\frac{1}{|p-q|\times s} \tag{4}\]  
We learn the local relationship from the neighbor node sets \(N_{SP}\) and \(N_{AP}\), and we learn the local internal relationship from the neighbor node set \(N_{SI}\). To integrate the interlocal  
Figure 3: The neighbor nodes are categorized into three types: \(N_{SP}\), \(N_{AP}\), and \(N_{SI}\). Specifically, nodes originating from corresponding parts of distinct pedestrian images are clustered into \(N_{SP}\), those hailing from adjacent parts of separate pedestrian images are classified as \(N_{AP}\), and nodes stemming from disparate parts within the same pedestrian image are assembled into \(N_{SI}\). relationship and the intralocal relationship, we aggregate these local features with the attention weight to obtain the feature \(z_{p}^{i}\) as follows:  
\[z_{p}^{i}=\sigma(f_{p}^{i}+\sum_{f_{q}^{i}\in N(f_{p}^{i})}\alpha(f_{p}^{i},f_{q }^{i})Vf_{q}^{i}) \tag{5}\]