# Sequence-Information Recognition Method Based on Integrated mDTW
## 4 Experiments
### Ablation Study  
The target of Experiment 2 was to investigate the effect of model hyperparameters on different complexity of characters. We manually selected 100 handwriting sample couples, including 33 simple, 34 normal, and 33 complex. We investigated 7 groups of hyperparameters, where we only change \(\alpha\), \(\beta\) is configured as a constant vector \(\{1,10,100\}\). Table 4 compares the data we obtained from experiments. It could be concluded that the value of \(\alpha_{2}\) plays a significant role in our algorithm. On the contrary, the other two \(\alpha\) variables are not key factors. Meanwhile, appropriate gaining of \(\alpha_{1}\) and \(\alpha_{3}\) could increase matching accuracy. Considering that the normal complexity is a major part of all characters, we set \(\alpha\) as \(\{0.1,0.8,0.1\}\) for clustering. The challenge of data significance arises from the inherent properties of diverse variables. One particularly well-established feature in the realm of handwriting analysis research is the pen's moving displacement, denoted as \(\Delta x\). This variable has gained widespread recognition for its efficacy in capturing important variations in writing directions. Researchers have extensively employed it to unveil nuanced aspects of handwriting intricacies. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Methods** & **UCI-HAR** & **WISDM** & **PAMAP2** & **UniMib** & **OPPOR** \\ \hline DCNN 2015 [31] & 95.1\% & - & - & - & - \\ tFFT+Convnet 2016 [32] & 95.7\% & - & - & - & - \\ b-LSTM-S 2016 [33] & - & - & - & - & 92.7\% \\ DeepConvLSTM 2016 [34] & - & - & - & - & 93.0\% \\ CondConv 2018 [35] & - & 98.7\% & 94.0\% & 77.31\% & 81.1\% \\ CIRF 2018 [36] & - & - & - & - & 89.1\% \\ LSTM+CT+CSA 2018 [37] & - & - & 89.96\% & - & - \\ AttnSense 2019 [38] & - & - & 89.3\% & - & - \\ The Layer-wise CNN 2020 [39] & 96.9\% & 98.8\% & 92.9\% & 78.0\% & 81.0\% \\ Lego CNN 2021 [40] & 91.4\% & 97.5\% & 93.5\% & 74.4\% & 88.1\% \\ Real+Virtual 2023 [41] & - & - & 69.9\% & - & - \\ TinyTNAS 2024 [42] & 96.7\% & 96.5\% & 93.7\% & 77.9\% & 93.2\% \\ mDTW+Transformer & 88.7\% & 98.5\% & 94.2\% & 78.5\% & 93.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of HAR methods. However, it is essential to delve into the relationship between pen-moving displacement and pen location. The latter can be conceptualized as the integral of displacement, offering a holistic perspective on the trajectory of the writing instrument. Yet, a notable drawback surfaces: the directional variation information tends to be subdued within the integral representation. Consequently, while pen location provides an overall picture of the writing path, it may lack the granularity required to discern subtle changes in direction. In stark contrast, the utilization of pen-moving displacement emerges as a superior choice in many instances. By focusing on the instantaneous changes in position, this approach excels at capturing the finer nuances of writing directions. The importance of these variations becomes particularly evident when seeking a comprehensive understanding of the intricate dynamics involved in handwriting. We conducted ablation experiments to validate the effectiveness of our method, experimenting on both the HCCR dataset and the Human Action Recognition dataset. In these experiments, we selected three sequence modeling models: GRU, LSTM, and Transformer. We first conducted experiments using these three models individually, and then we integrated them into the mDTW framework. By comparing and observing the impact of the mDTW framework on the accuracy of the experimental results, it can be seen from Table 5 that the experimental results with mDTW achieved an accuracy improvement of about 1% on most datasets. This demonstrates the effectiveness of our proposed method. In summary, the preference for pen-moving displacement over pen location stems from its ability to accentuate crucial directional changes, therefore outperforming the integral representation.