# Hypergraph Position Attention Convolution Networks for 3D Point Cloud Segmentation
## 3 Method
### Hypergraph Position Attention Convolution Networks
#### 3.3.1 Hyperedge Position Attention Convolution Module  
The purple part of Figure 2 shows our proposed hyperedge position attentional convolution module, which aims to focus on the local features of the point cloud efficiently. We utilize hyperedge-hyperedge propagation to construct a position adaptive attention mechanism that focuses on the most relevant parts of local features. This allows the convolution kernel to dynamically adapt to the complex spatial variations and geometric structure of the point clouds. The attention mechanism dynamically adapts the weights of input features, and we calculate the attention weights between hyperedge and hyperedge as follows:  
\[\tilde{\alpha}_{ij}=\theta(Conv1D[\sigma_{e_{i}}\parallel q_{e_{j}}]) \tag{9}\]  
where \(||\) denotes the connectivity relation and \(Conv1D\) denotes the 1 \(\times\) 1 convolution operation. \(\theta\) denotes the DWConv operation, which is used to reduce the number of parameters in the convolution operation. The first term \(\sigma_{e_{i}}\) in \(\theta\) denotes the hyperedge feature information constructed based on the spatial location relationship of the point cloud, which helps to aggregate the spatial information of the unordered vertices. The second term \(q_{e_{i}}\) denotes the computation of the spatial location relationship between neighboring points on each edge, which aims to enhance the local feature information. Considering the spatial relationships between neighboring hyperedges, our method can capture the local structural information to improve the performance of the model more accurately. Through computing the attention weights, we are able to efficiently assess the degree of association between hyperedges, which leads to more accurate feature aggregation and point cloud segmentation.  
Next, we normalize the attention weights of all neighbors of hyperedge \(i\) and obtain the final measure of the hyperedge attention factor for the whole hypergraph as follows:  
\[\alpha=soft\max(\tilde{\alpha}_{ij})=\frac{exp(\tilde{\alpha}_{ij})}{\sum_{k \in E_{i}}exp(\tilde{\alpha}_{ik})} \tag{10}\]  
Figure 2: Point cloud segmentation framework based on hypergraph position attention convolution networks. (**a**) denotes the ResNet-like module, (**b**) denotes the hypergraph position attention convolution module, and (**c**) denotes the skip connection module.  
With this approach, we generate a new attention factor \(\alpha\) for the hyperedge-hyperedge relationship, \(\alpha\)\(\in\)[0,1]. Thus, the final output equation obtained by our proposed method is as follows:  
\[\alpha^{\prime}=\text{ReLu}(BN(\alpha)) \tag{11}\]  
where \(BN\) denotes Batch Normalization and \(ReLu\) denotes the activation function. We apply operations such as the \(ReLU\) function to it to obtain the final coefficients.  
**Comparison with existing methods:** Current hypergraph attention convolution operators [21; 26] usually use the vertex-hyperedge-vertex feature transformation model, which introduces an attention mechanism to handle vertex convolution and hyperedge convolution, as well as automatically learning the different weights of vertices and hyperedges during the feature transformation and propagation process. However, the method increases the number of model parameters and leads to training difficulties. In contrast, we design the hypergraph position attention convolution with the hyperedge-hyperedge feature propagation model. It eliminates the need for the vertex-hyperedge transformation process and simplifies the architecture of the model, which reduces the number of network parameters and decreases the complexity of the model. Thus, the designed convolution operator improves some of the limitations of the current hypergraph attention networks and provides a more effective solution for point cloud segmentation and other related tasks. Furthermore, experimental comparisons are made later in the network analysis to demonstrate the effectiveness of the method.