## 6 Numerical Experiment
### Results and Discussions: Performance by the Missing Value Rate of the User Trajectory
This implies the IDNN features are prone to overfitting in the instance of this experiments. This trend was confirmed in Section 6.3, and its reasons are the same as those mentioned before; that is, the conversion process of a trajectory to an image cannot eliminate noise. These results also suggest that the GMM-based features are more effective for handling sparse trajectories than IDNN-based features. Overall, the results indicate that GMM-based features provide a more reliable and effective approach for extracting information from sparse trajectories, making them a better fit for scenarios where semantic information is unavailable and data sparsity is a significant challenge. For \(\theta_{\text{th}}=0.95\)-\(0.97\), overfitting is confirmed in GMM-SVC and RF and IDNN-SVC and RF. This may be because the number of samples is small in the feature space, and the model is overfitted to the training data. Here, we analyze the classification results via detailed metrics, such as precision, recall, and F-measure, in addition to accuracy. Note that we focus on only the GMM-RF  
Figure 12: Average of 20 accuracies on training data by \(\theta_{\text{th}}\) for each month. The lower the difference between the accuracies of the training and test data is, the higher the generalization performance. The ML models using the IDNN show a wider range of accuracy differences between the training and test data than those using the GMM. This shows that features based on the GMM are more robust to overfitting than those based on the IDNN. results, which showed the highest accuracy in all months. Table 3 shows each metric for the classification results of the test data by threshold \(\theta_{\text{th}}\) and month. The averages and standard deviations corresponding to datasets of 20 seeds for each metric are indicated in parentheses. Moreover, with respect to the confidence interval of classification accuracy, as in Section 6.2, Table 3 shows the \(p\)-values for the Shapiro-Wilk test for the distribution of accuracies for 20 seeds. Because the \(p\)-values are \(p>0.050\) except for \(\theta_{\text{th}}=0.95\) and 0.98 in May and \(\theta_{\text{th}}=0.95\) in June, we assume that any distribution of accuracies follows a normal distribution. Focusing on the precision, recall, and F-measure in any parameter setting, we can conclude that the levels of classification performance for the classes are similar because these metric values are almost equivalent to the accuracy. This is a natural result because we handle a balanced dataset. For the missing value rate \(\theta_{\text{th}}=1.00\), because the average  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Month** & \(n\) & \(\theta_{\text{th}}(>\theta_{\text{k}})\) & \(A_{\text{M}}\) & \(P_{\text{M}}\) & \(R_{\text{M}}\) & \(F_{\text{M}}\) & **Shapiro–Wilk**\({}^{\dagger}\) \\ \hline \multirow{4}{*}{January} & \multirow{4}{*}{60} & 0.95 & 0.535 (0.087) & 0.562 (0.085) & 0.535 (0.087) & 0.534 (0.086) & n.s. \\  & & 0.96 & **0.5  
accuracy is at its maximum value of 0.331 (0.011) in January and at its minimum value of 0.238 (0.004) in June, it is confirmed that the classification performance is significantly higher than random classification in any month. Furthermore, through adjustments in the threshold \(\theta_{\text{th}}\), the classification performance is increased such that the average accuracy reaches its maximum of 0.545 (0.064) in January and minimum of 0.316 (0.011) in June. The normality of the accuracy distribution for the 20 seeds is confirmed, except for \(\theta_{\text{th}}=0.95\) and 0.98 in May and \(\theta_{\text{th}}=0.95\) in June. These results show that with appropriate parameter settings, the constructed GMM-RF models perform with significantly higher classification accuracy than those produced by random classification. Note that, in GMM-SVC, the classification performance is not as high as that of GMM-RF, but it is confirmed that GMM-SVC has the same tendency and high generalization performance, as shown in Figures 11 and 12.