# Adaptive Channel-Enhanced Graph Convolution for Skeleton-Based Human Action Recognition
## 3 Method
### Adaptive Channel-Enhanced Graph Convolution
In our method, the affinity matrix \(M\) is obtained by selecting the maximum similarity along the rows of the similarity matrix \(S\) and then expanding them to the same size as \(S\). In the expanded affinity matrix \(M\), joint pairs with higher similarity have a lower affinity. In addition, since the affinity matrix \(M\) is an adaptive weight matrix used for channel topology refinement, the _Softmax_ function is used to normalize the matrix, as shown in Equation (9):  
\[M=\text{softmax}(\underset{1\to V}{\text{expand}}(\underset{1\to V}{MAX}(S))-S_{V \times V}),M\in\mathbb{R}^{N\times\frac{C}{r}\times V} \tag{9}\]  
The resulting attention matrix is used to calculate weighted features through matrix operations so that each channel has an adaptive merging weight to integrate the nodes. Then, the channel correlation modeling function \(C(\cdot)\) uses the weighted features to calculate the distance between features along the channel dimension. The nonlinear transformation  
Figure 3: Detailed flowchart of channel graph topology modeling. of these distances is used to determine the specific topological relationship between joint pairs on the channel. The specific topological relationship is merged to obtain a higher-level semantic graph. The correlation \(Z\) of the specific topological relationship between the joint pairs on the channel is calculated, as shown in Equation (10):  
\[Z=C(M\widetilde{\mathrm{X}}_{1},\widetilde{\mathrm{X}}_{2})=\tanh(M\widetilde{ \mathrm{X}}_{1}-\widetilde{\mathrm{X}}_{2}),\ \ \ Z\in\mathbb{R}^{N\times\frac{C}{r}\times V} \tag{10}\]  
\(Z\) reflects the specific cross-channel topological relationships between joints. Lastly, by applying the channel-specific topological connection \(Z\) to refine the shared graph topology \(A\), the adaptive channel-specific graph topology \(A^{\prime}\) can be obtained, as shown in Equation (11):  
\[A^{\prime}=Z\cdot\varepsilon+A,A^{\prime}\in\mathbb{R}^{N\times\frac{C}{r} \times T\times V} \tag{11}\]  
\(\varepsilon\) is a trainable parameter that adjusts the strength of the channel topology refinement. **Channel aggregation:** For the refined adaptive channel graph topology \(A^{\prime}\) and the advanced feature \(\widetilde{X}\), ACE-GC aggregates features along the channel, as shown in Figure 1:0  
The channel-wise feature aggregation operation utilizes [PERSON] summation notation to aggregate the features of all nodes, thereby obtaining the feature representation for each node. The aggregated features, denoted as \(Z^{\prime}\), are shown in Equation (12):  
Figure 1:1  
\(\mathit{einsum}(\cdot)\) refers to the [PERSON] summation convention. ACE-GC creates a distinct channel graph topology for each channel to represent the node relationship of a certain sort of action feature. The Edgeconv operation can aggregate branches to build a multi-branch aggregation module that aggregates local neighborhood information and captures different levels of physical and semantic attributes. The aggregation connects all channel graph topologies in parallel, thus obtaining a global-local feature information aggregation. Therefore, this aggregation operation can improve the model's understanding of the input data. \(\varnothing\theta\) is a learned nonlinear mapping function, typically implemented as an MLP. The output of the ACE-GCN is shown in Equation (13):  
Figure 1:2