## 3 Results
### Investigating of Relationship between Environment Barriers and Gait Classification Results  
By analyzing the gait classification results conducted in the previous section, it can be considered that the performance of gait classification is confirmed. However, one more thing is needed to use the proposed pedestrian environment monitoring and environmental barrier identification method. This study investigates the relationship between the presence of environmental barriers and the ratio of abnormal gaits in a specific location.  
Figure 7: Accuracy and cost of testing using the first and second dataset: (**a**) accuracy (red line for the first data set and green line for the second dataset); and (**b**) binary cross-entropy cost between ground truth and predicted labels for test (red line for the first data set and green line for the second dataset).  
To confirm the feasibility of the suggested method, the three relationships between the presence of environment barriers and the ratio of abnormal gaits (ground truth, first dataset, and second dataset, respectively) are measured. The ratio of abnormal gaits in a specific location (cell) is a continuous variable, whereas the presence of environment barriers can be represented as a binary variable (existence as one and absence as zero). To investigate the relationship between the presence of environmental barriers and the ratio of abnormal gaits statistically, the point biserial correlation coefficient is used in this study. This coefficient is usually used when one is dichotomous and the other is continuous [60,61]. The point biserial coefficient is calculated using Equation (10) as follows:  
\[r_{pb}=\frac{(M_{1}-M_{0})\sqrt{(n_{1}n_{0}/n^{2})}}{\sqrt{\frac{1}{n}\sum \limits_{i=1}^{n}\left(X_{i}-\overline{X}\right)^{2}}} \tag{10}\]  
where \(r_{pb}\) is the point biserial correlation coefficient, \(M_{1}\) is the mean value of the continuous variable \(X\) (ratio of abnormal gaits) for all data points in group 1 (existence of environment barrier), \(M_{0}\) is the mean value of the continuous variable \(X\) (ratio of abnormal gaits) for all data points in group 2 (absence of environment barrier), \(n_{1}\) is the number of data points in group 1, \(n_{0}\) is the number of data points in group 2, and \(n\) is the total sample size.  
The point biserial coefficient calculation results are presented in Table 2. The three correlation results present correlation coefficients over 0.7 and statistical significance (\(\alpha<0.005\), \(p=0.001\)). A correlation coefficient greater than 0.7 indicates a high degree of correlation. The results showed that the ratio of abnormal gaits and the existence (presence and absence) of environmental barriers are highly correlated. These correlation coefficients of the three types of data sources and the existence of environmental barriers are very similar. This means that the suggested method can both (1) classify normal and abnormal gaits and (2) be feasible to newly added data for robust DRNN-based walking environment monitoring.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Correlation Coefficient**} & \multicolumn{3}{c}{**Ratio of Abnormal Gaits**} \\ \cline{2-4}  & **Ground Truth** & **First Dataset** & **Second Dataset** \\ \hline Environment Barrier & 0.760 & 0.742 & 0.735 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Correlation between environment barriers and three types of ratio of abnormal gaits.  
Figure 8: The test results and performance metrics: (a) gait classification results and performance metrics of the test results of the first dataset; and (b) gait classification results and performance metrics of the test results of the second dataset.