# The Influence of Motion Data Low-Pass Filtering Methods in Machine-Learning Models
## 3 Results  
During regular walking, main effects of the order and cutoff (\(p\) < 0.01 for all) were mainly found on the gait characteristics in the sagittal plane (step length, foot angle, and shank angle) (Table 1). A significant interaction effect between order and cutoff was also found for these gait characteristics (\(p\) < 0.01 for all). For example, the calculated step length in regular walking increased along with decreasing order and increasing cutoff value (Figure 1). In gait-slip trials, there was a main effect of the order on toe clearance and gait speed (\(p\) < 0.05 for both), and a main effect of the cutoff only on gait speed (\(p\) < 0.05). In gait-trip trials, there was a main effect of the order only on thigh angle (\(p\) < 0.01), and a main effect of the cutoff on both thigh angle and step length (\(p\) < 0.05 for both). Post-hoc analysis results were highly consistent with these findings (see Supplementary Material), indicating that the selection of filter parameter could significantly affect the gait characteristics across different gait types. The ICC between the standard filter (fourth-order Butterworth with 6 Hz cutoff) and other filters showed that most (\(>\)90%) of the filters selected showed a high similarity (ICC \(>\) 0.9 in Figure 2) with the standard method for all of the gait characteristics. Among all the filters, the sixth-order filter with a cutoff of 8 Hz and the fourth-order filter with a cutoff of 6 Hz showed the highest similarity (ICC \(>\) 0.99), with the standard one for all of the \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Regular Gait**} & \multicolumn{3}{c}{**Gait-Slip**} & \multicolumn{3}{c}{**Gait-Trip**} \\ \cline{2-9}  & **Order** & **Cutoff** & **O\(\times\)C** & **Order** & **Cutoff** & **O\(\times\)C** & **Order** & **Cutoff** & **O\(\times\)C** \\ \hline
**Step length** & **64.1** ** & **55.4** ** & **8.6** ** & 0.8 & 0.6 & 0.1 & 2.6 & **2.1** * & 0.6 \\ \hline
**Step width** & 0.5 & 0.7 & 0.2 & 0.3 & 0.1 & 0.0 & 0.3 & 0.1 & 0.0 \\ \hline
**Toe clearance** & 0.0 & 0.5 & 0.0 & **3.6** & **6.2** ** & 0.7 & 0.0 & 0.2 & 0.0 \\ \hline
**Gait speed** & 0.9 & 0.6 & 0.0 & **3.1** & 1.4 & 0.0 & 0.7 & 0.3 & 0.0 \\ \hline
**Foot angle** & **19.7** ** & **25.5** ** & **6.4** ** & 2.4 & 1.3 & 0.5 & 0.8 & 0.3 & 0.0 \\ \hline
**Shank angle** & **37.4** ** & **44.8** ** & **10** & 1.8 & 0.8 & 0.3 & 1.8 & 0.8 & 0.2 \\ \hline
**Thigh angle** & 1.0 & 1.1 & 0.1 & **6.3** ** & **6.1** ** & 1.0 & **15.3** ** & **7.2** ** & 0.3 \\ \hline \hline \end{tabular}  
* indicates \(p\) < 0.05; ** indicates \(p\) < 0.01; bolded value indicates a significant effect.  
\end{table} 
Table 1: 3 \(\times\) 9 ANOVA results (F value) for the order and cutoff effects on each gait characteristic in different types of gait trials. gait characteristics, while the filters with a higher order but a lower cutoff (i.e., sixth-order with cutoff of 4 Hz), as well as those with a lower order but a higher cutoff (i.e., 2 nd order with 18 Hz), led to the lowest ICC. All the classification models demonstrated a strong performance, with an average AUC greater than 0.8 (Figure 3). Our results showed that incorporating more features tends to improve the AUC, while the AUC across different classifiers with the same number of inputs remained similar. Two-way ANOVA results showed the significant main effects of filter orders (\(p<0.05\) for all, Table 2) and cutoffs (\(p<0.01\) for all) on both AUC and overall accuracy for all of the models, regardless of which classifier was employed. Post-hoc analysis also found that there were significant differences in the AUC and overall accuracy across models using different filter parameters (see Supplementary Material). Among all the filters we examined, the standard filter and another two filters (the sixth-order filter with a cutoff of 8 Hz and the fourth-order filter with a cutoff of 6 Hz) could result in the best performance for the classification models using LR and SVC.