## 5 Ablation Study and Discussion
### Parameter Selection  
To evaluate the impact of hyperparameters on the model's overall performance, we explored the sliding window size, sliding window overlap rate, and the number of hierarchical layers. We adjusted them sequentially and finally chose the optimal parameters. First, we analyzed the effect of sliding window size on the model's recognition performance. The four datasets were previously downsampled uniformly to a sampling rate of about 33 Hz per second. Since the repetition period of different actions varies, we experimented by changing the window size in seconds.  
In Figure 6, our proposed model is more stable to changes in window size compared to other models. It also indicates that some complex actions require longer sliding window sizes for segmentation to achieve good recognition results. When the initial window size is small, the performance is average because the HMC structure has difficulty capturing information on multi-scales. As the window size increases, the model's performance improves, demonstrating the effectiveness of the hierarchical architecture and multi-scale convolution for feature extraction at different scales. The DCS-LSTM can also better capture temporal context information. Considering the performance, we chose a sliding window size of 1 s for the PAMAP2 and USC-HAD datasets, while the Opportunity and SKODA datasets chose a sliding window size of 1.5 s for action recognition.  
Then, based on the optimal sliding window size, we also discussed the impact of sliding window overlap rate on model performance. Due to the varying durations and complexities of different actions, the sliding window overlap rate is also critical in affecting action recognition. In Figure 7a, the model's performance on most datasets increases as the window overlap rate starts to increase, and the model reaches its best result when the overlap rate reaches 0.5. As the overlap rate continues to increase, the model's performance starts to decrease. This suggests that an appropriate overlap ratio can help the model better capture local patterns and relationships in time series data, maximizing the information in the data while ensuring computational efficiency. Therefore, we chose 50% as the window overlap rate for model training. Finally, based on the optimal configuration, we explored the number of layers in the hierarchical architecture of our proposed model.  
In Figure 7b, as the number of layers increases from zero to two, the model's performance improves on each dataset. This indicates that our proposed HMA Conv-LSTM network can effectively capture multi-scale features and some fine-grained subtle action processes. However, when the number of layers reaches three, the performance starts to deteriorate. The window size may be the cause of this situation. When the number of layers is three, the minimum division of the partition length is small, and the multi-scale convolution operation can no longer capture finer features. The model's best results are obtained when the number of layers is two. Therefore, we choose two as the number of hierarchical layers for model construction.  
Figure 6: Performance of different window sizes, which shows the performance comparison of our proposed model with the self-attention model.