## 6 Numerical Experiment
### Results and Discussion: Tuning GMD Components \(n\) for Model Performance  
Based on Section 6.1.1, the trends in the classification performance of each ML model for GMD components \(n\) are verified. Figure 9 shows the test accuracy values obtained using components \(n\in\{2\}\cup\{10,20,\ldots,200\}\) and months \(\forall m\in M\). The results are shown for the SVC with an RBF kernel, RF, and DNN, which are represented by red, blue, and green lines, respectively. In particular, the averages and standard deviations (1 SD) of each model by dataset \(\mathcal{D}_{m}\) for the 20 seeds are indicated. The vertical and horizontal axes represent the accuracy and GMD components \(n\), respectively. The title presents the model that achieved the highest average accuracy, along with the GMD component number \(n\), which yielded the highest average accuracy. In addition, we conducted the Shapiro-Wilk test on the distribution of 20 accuracy values when the average was maximal, confirming the normality of the distribution. According to the test results, \(p\geq 0.0  
Figure 9 shows that for all months, the accuracy tends to increase as \(n\) increases, particularly in the SVC and RF. This is because if the GMD components \(n\) are tiny, the expressiveness of the RPs in the target area might be rough, and the difference in the simi  
Figure 10: Average and standard deviation (ISD) of 20 accuracies on training data by month in \(\theta_{\text{th}}=1.00\) and ML models. This metric is used to evaluate the generalization performance of the ML models, and the lower the difference in the accuracy of the test data is, the higher the generalization performance. Compared with the test data, SVC and DNN exhibit a gradual increase in accuracy with respect to the number of components \(n\), whereas RF shows an increase in accuracy from smaller values of \(n\) compared with the other two models. Figure 9: Average and standard deviation (ISD) of 20 accuracies on test data by month for the \(\theta_{\text{th}}=1.00\) and ML models. Each graph title indicates the maximum average and its standard deviation by components \(n\) in the form of average (ISD) and the \(p\)-value for the Shapiro–Wilk test for the accuracy distribution of 20 seeds obtained by components \(n\). There is a tendency that the higher the number of GMD components is, the higher the accuracy across all months. Additionally, for all months, distribution normality for 20 accuracies is confirmed with \(p>0.050\), and accuracies are higher than those of random classification (accuracy \(\approx\) 0.170) in the range of 3 SD on components \(n>2\), with any accuracy average by SVC and RF. larity of each ID feature might be less likely to occur. In particular, models with minimal components, such as \(n=2\), significantly reduce the classification performance. Conversely, components \(n\) that are too large may cause the expressiveness to peak and are less likely to contribute to the classification performance. The classification performance varies by the period of data acquisition; focusing on the maximal average by each month, the highest performance is achieved in January by SVC, with an accuracy of =0.336 (0.013), and the lowest performance is achieved in June by RF, with an accuracy of =0.238 (0.040) and a chance level of approximately 0.170. Nonetheless, in any month, the normality of the accuracy distribution is confirmed to be \(p>0.050\), and the classification performance, excluding the results from DNN, is higher than that of random classification (accuracy \(\approx\) 0.170) in the range of 3 SD, i.e., a confidence interval of 99.7%. As a result, features consisting of only sparse trajectories would include sufficient information to classify the user age groups. Here, we focus on the learning trends of each model. The SVC achieves the highest performance in January and February, whereas the RF achieves superior accuracy from March to June. Notably, during the period from March to June, the RF consistently outperforms the other two models across all the components \(n\).