# Adaptive Channel-Enhanced Graph Convolution for Skeleton-Based Human Action Recognition
## 3 Method
### Adaptive Channel-Enhanced Graph Convolution  
The skeleton sequence consists of frames, each of which contains a collection of 2D or 3D joint coordinates that comprise the skeleton. The GCN is designed to represent the topological organization of human actions. In this model, the graph consists of nodes representing joints and edges representing bones. In this study, we propose a new network architecture that stacks the ACE-GCN to extract the spatio-temporal features of skeleton sequences and uses a classifier to predict the class score to obtain the correct action classification. Figure 1 illustrates the fundamental structure of the ACE-GCN, which consists of distinct sub-modules for handling the spatial and temporal data of human action skeletal sequences. These sub-modules are referred to as the ACE-GC module and the TCN module, respectively. In this section, we provide a detailed description of the network structure of the ACE-GC module and explain the model's structure and implementation process through equations. The attention mechanism can refine the graph topology in each channel to obtain the discriminative graph topology that is critical for the recognition of overall human actions. The ACE-GC network structure is shown in Figure 2. ACE-GC consists of three parts: feature transformation, channel graph topology modeling, and feature aggregation. Figure 1: Basic block of the proposed ACE-GCN. Figure 2: Display the structure of the ACE-GC module. **Feature transformation:** ACE-GC utilizes the human action skeleton graph as the input feature tensor \(X\), where \(X\) is a tensor with dimensions \(X\in R^{N\times C\times T\times V}\). In this context, \(C\) denotes the quantity of feature channels, T signifies the number of time frames of the action, and \(V\) indicates the count of joint points in the skeleton graph. To minimize the number of parameters, this study used a \(1\times 1\) convolution to carry out feature transformation on the input data, resulting in weighted features across multiple channels. The formula is shown in Equation (7):  
\[\widetilde{X}=\theta(X)=XW,\widetilde{X}\in\mathbb{R}^{N\times\frac{C}{r}\times T \times V} \tag{7}\]  
where \(r\) is the channel reduction rate, and \(r=8\) and \(r=16\) are used in the experiments in this study. \(W\) is the weight matrix,\(W\in\mathbb{R}^{N\times C\times\widetilde{C}}\). **Channel graph topology modeling:** The heuristic adjacency matrix is shared by all channels and trained through backpropagation. This study uses channel affinity attention to learn the channel affinity matrix, which can assign higher weights to different channels to avoid clustering similar redundant information. It can also refine the graph topology features in the channel by weighting all channels to obtain a non-shared channel graph topology \(A^{\prime}\), as shown in Figure 3.  
For channel topology modeling, we initially employ a global average pooling layer to aggregate the time dimension. This pooling method preserves both long-term and short-term temporal information without sacrificing any spatial information regarding the graph structure. Then, the input feature \(X\) is transformed into a high-level feature \(\widetilde{X}\). This high-level feature \(\widetilde{X}\) is used as the query matrix \(\widetilde{X}_{1}\) and the key matrix \(\widetilde{X}_{2}\), respectively. By applying the transpose of the product of the query matrix \(\widetilde{X}_{1}^{T}\) and the key matrix \(\widetilde{X}_{2}\), the channel similarity matrix \(S\) is obtained, as shown in Equation (8):  
\[S(\theta(X_{1}),\theta(X_{2}))=dot(\theta(X_{1}),\theta(X_{2}))=dot(\widetilde {X}_{1}^{T},\widetilde{X}_{2}) \tag{8}\]  
The channel similarity matrix \(S\) calculates the correlation between joint pairs in each channel. By calculating the inner product, the remote dependence in the spatial data can be obtained. On the contrary, by calculating the similarity between joint pairs, the irrelevance between joint pairs in the channel, i.e., the channel affinity, can be obtained.