## 3 Proposed Method
### Hierarchical Multi-Scale Convolution
#### 3.3.2 Hierarchical Architecture  
HAR relies on sequential data captured by sensors placed at various body locations, which contain spatial and temporal information about physical actions. Due to the varying durations and complexities of different actions, some actions may require longer sliding window sizes for segmentation to achieve good recognition results. However, sliding window sizes that are too large may cause the general network model to overlook some fine-grained subtle action processes, thereby affecting action recognition. In contrast, our proposed hierarchical architecture can split the action window and extract features from the sensor sequence data at a finer granularity to effectively recognize the finer action processes. The specific structure of the whole HMC module is shown in Figure 2c. To construct the HMC network architecture, we divide the sensor feature sequence weighted by the SFS module in the time dimension, as shown in Figure 3. The HMC can capture some subtle changes of actions in human motion. By capturing the sub-actions in the sensor feature sequences, the model can obtain more detailed information, thus realizing a finer-grained HAR. In this work, we have tested experimentally and finally selected the hierarchical architecture with 2 layers of division, and the experiments show good results, as detailed in Section 5. For the sensor feature sequence \(x=[c^{1},c^{2},\ldots c^{i},\ldots,c^{t}]\) weighted by the SFS module, each feature vector \(c_{i}\) consists of \([c^{i}_{1},c^{i}_{2},\ldots c^{i}_{j},\ldots,c^{t}_{k}]\), where \(t\) denotes the number of timesteps, and \(K\) denotes the number of features of a single timestep sensor. When the hierarchical number of partitions \(level=0\), the sequence is not hierarchical and the feature sequence is unchanged and defaults to 1 partition, \(x^{0}_{1}=x\); when the number of partitions \(level=1\), the sequence is divided into 2 partitions, i.e.,  
\[x^{1}_{1}=\left[c^{1},c^{2},\ldots,c^{t}\right],\;x^{1}_{2}=\left[c^{\frac{t}{ 2}+1},\ldots,c^{t-1},c^{t}\right] \tag{6}\]  
When the number of strata \(level=2\), the sequence is divided into 4 partitions, i.e.,  
\[x^{2}_{1}=\left[c^{1},c^{2},\ldots,c^{t}\right],x^{2}_{2}=\left[c^{\frac{t}{ 2}+1},\ldots,c^{\frac{t}{2}}\right],x^{2}_{3}=\left[c^{\frac{t}{2}+1},\ldots, c^{\frac{t}{2}}\right],x^{2}_{4}=\left[c^{\frac{t}{2}+1},\ldots,c^{t}\right] \tag{7}\]  
When the number of strata \(level=n\), the sequence is divided into \(2^{n}\) partitions, i.e.,  
\[x^{n}_{i}=\left[c^{\frac{t_{n}(i-1)}{2^{n}}+1},c^{\frac{t_{n}(i-1)}{2^{n}}+2}, \ldots,c^{\frac{t_{n}i}{2^{n}}}\right],i\in\{1,\ldots,2^{n}-1,2^{n}\} \tag{8}\]  
In fact, we divide the features into two each time, so the \(i\)-th sub-partition of the \(l\)-th layer comes from the \(\lfloor\frac{i+1}{2}\rfloor\) parent partition of the \(l\)-1-th layer; the formulaic expression is  
\[x^{l-1}_{j}=\left[x^{l}_{i*2-1},x^{l}_{i*2}\right] \tag{9}\]  
After the hierarchical division, all sub-partitions are presented as a pyramidal tree structure. We perform multi-scale convolutional operations on each partition of the division. We use multi-scale convolutional neural networks to extract and splice features in the sensor dimension and time dimension to strengthen the network's ability to recognize features at different scales by multi-scale mining of the data to improve the characterization ability of the final acquired features. Figure 3: Delineation of the Hierarchical Architecture. Then, we first splice the multi-scale features extracted from each partitioned layer in the time dimension, and then perform feature superposition; the final features are fused to a multi-channel feature \(y^{\prime}\) of the same dimension as that obtained from the original feature \(x\) through the multi-scale convolutional network, which serves as the output of the whole HMC network.