# The Influence of Motion Data Low-Pass Filtering Methods in Machine-Learning Models
## 4 Discussion  
We aimed to investigate the effect of filter parameters on kinematic gait features and the machine-learning models built upon the filtered gait features. The results showed \begin{table}
\begin{tabular}{l l l l l l l l} \hline \hline \multirow{2}{*}{**Classifier**} & \multicolumn{2}{l}{**AUC**} & \multicolumn{5}{l}{**Accuracy**} \\ \cline{2-9}  & **Order** & **Cutoff** & **O\(\times\)C** & **Order** & **Cutoff** & **O\(\times\)C** \\ \hline
**LR** & **4.2 * & **3.0 ** & 1.4 & **12.7 ** & **9.1 ** & **3.1 ** \\ \hline
**SVC** & **15.2 ** & **21.9 ** & **7.6 ** & **27.5 ** & **11.9 ** & **4.2 ** \\ \hline
**RFC** & **3.6 * & **3.0 ** & 1.5 & **11.7 ** & **11.8 ** & **5.3 ** \\ \hline \hline \end{tabular}  
* indicates \(p<0.05\); ** indicates \(p<0.01\); bolded value indicates a significant effect.  
\end{table} 
Table 2: \(3\times 9\) ANOVA results (F value) for the order and cutoff effects on AUC and overall accuracy for different classifiers. Figure 3: The average AUC of gait type classification models with different number of features using Logistic Regression (LR), Support Vector Classification (SVC), and Random Forest Classification (RFC). \begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Model** & **Rank** & **1** & **2** & **3** & **25** & **26** & **27** \\ \hline \multirow{4}{*}{LR} & Order & 4 & 2 & 6 & 2 & 2 & 6 \\ \cline{2-7}  & Cutoff & 6 & 4 & 8 & 18 & 20 & 4 \\ \cline{2-7}  & AUC & 0.945 & 0.944 & 0.944 & 0.931 & 0.93 & 0.893 \\ \cline{2-7}  & Low CI & 0.905 & 0.902 & 0.903 & 0.886 & 0.884 & 0.844 \\ \cline{2-7}  & High CI & 0.985 & 0.987 & 0.984 & 0.975 & 0.976 & 0.942 \\ \hline \multirow{4}{*}{SVC} & Order & 2 & 6 & 4 & 6 & 4 & 6 \\ \cline{2-7}  & Cutoff & 4 & 8 & 6 & 6 & 4 & 4 \\ \cline{2-7}  & AUC & 0.95 & 0.95 & 0.948 & 0.935 & 0.93 & 0.882 \\ \cline{2-7}  & Low CI & 0.916 & 0.913 & 0.909 & 0.890 & 0.885 & 0.842 \\ \cline{2-7}  & High CI & 0.984 & 0.986 & 0.987 & 0.980 & 0.974 & 0.923 \\ \hline \multirow{4}{*}{RFC} & Order & 6 & 6 & 4 & 2 & 2 & 6 \\ \cline{2-7}  & Cutoff & 12 & 10 & 8 & 20 & 18 & 4 \\ \cline{1-1} \cline{2-7}  & AUC & 0.943 & 0.941 & 0.939 & 0.915 & 0.914 & 0.863 \\ \cline{1-1} \cline{2-7}  & Low CI & 0.905 & 0.891 & 0.897 & 0.860 & 0.857 & 0.797 \\ \cline{1-1} \cline{2-7}  & High CI & 0.981 & 0.990 & 0.980 & 0.969 & 0.971 & 0.929 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The filters yielding the best (top 3) and worst (bottom 3) AUC for each type of classification models using different filters (\(n=27\)). Confidence intervals (CI) for each filter are also provided. that the values of gait characteristics in the sagittal plane (step length, foot angle, and shank angle) were significantly affected by the selection of filter parameters, especially during regular walking. The selection of filter parameters could also significantly affect the performance of classification models using different classifiers (LR, SVC, and RFC). Our results suggest that the standard Butterworth filter (fourth-order, cutoff: 6 Hz) is suitable for development of classification models with low-medium complexity, while for models with high complexity (i.e., ensemble models), a filter with a higher order and higher cutoff might yield better performance. Theoretically, filtered outputs depend on the order and cutoff frequency of a filter, as the cutoff frequency determines the pass-band and the order determines the roll-off rate [7, 28]. Our results indicated that altering the filter order and cutoff mainly affected gait characteristics in the sagittal plane during regular walking, especially for step length. One possible reason is that participants walked in the A-P direction, which generated higher amplitude and rapid movements in the sagittal plane (especially the foot motion). For instance, foot movements at touchdown occur quickly, introducing higher-frequency components into the signal. Step length is typically calculated at touchdown when the foot abruptly reduces its speed to zero upon contact with the ground.