## 3 Result and Discussion
### Modeling of Behavior in Mechanical Ventilation Operation
#### 3.2.1 K-Means Clustering  
As observed from the previous analysis, there were differences in the behavior of operating mechanical ventilation systems among different households, where it requires multiple models to cover all cases. In this regard, K-means cluster analysis would be helpful. Moreover, the Pearson correlation coefficients between the status of the mechanical ventilation system and external factors were used as the input feature of the cluster analysis. The inertia and silhouette coefficients were calculated for \(K\) from 2 to 7, as shown in Figure 9. When \(K=5\), the inertia is smaller and the silhouette coefficient is greater than that of \(K=6\) or 7. Therefore, these households are divided into five clusters. The clustering centers of the five clusters are provided in Table 4. Five motivation patterns were discovered. (1) Outdoor air PM\({}_{2.5}\) concentration-driven (Cluster 1): In this cluster, the Pearson's correlation coefficient between the outdoor PM\({}_{2.5}\) concentration and the state of the mechanical ventilation system is significantly higher than the other factors (with \(p\)-value being 0.00). This indicated that households of this cluster might have been sensitive to the outdoor air quality when they chose to switch on the ventilation system. (2) Outdoor temperature-driven (Cluster 2): In this cluster, only the Pearson's correlation coefficient between outdoor temperature and the state of system is significant as \(-0.32\) (absolute value greater than 0.2). Figure 10 shows the relationship between mechanical ventilation system operation rate and outdoor temperature. The 50% operation rate point and the value of the outdoor temperature at this point are marked. Thus, households of this cluster may be susceptible to outdoor temperature and tend to close the window and switch on mechanical ventilation system when outdoor temperatures drops to 6.8 \({}^{\circ}\)C. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Cluster** & **CO\_In** & **PM\_2.5\_In** & **T\_In** & **PM\_2.5\_Out** & **RH\_Out** & **H** & **M** & **Spring** & **Summer** & **Autumn** & **Winter** \\ \hline
1 & 0.1 & \(-\)0.03 & \(-\)0.13 & 0.4 & \(-\)0.06 & 0.07 & \(-\)0.01 & \(-\)0.09 & 0.18 & \(-\)0.18 & \(-\)0.06 & 0.08 \\
2 & 0.02 & \(-\)0.13 & \(-\)0.2 & 0.14 & \(-\)0.32 & \(-\)0.07 & \(-\)0.04 & \(-\)0.05 & \(-\)0.09 & \(-\)0.23 & \(-\)0.07 & 0.34 \\
3 & 0.12 & \(-\)0.1 & 0.31 & 0.03 & 0.35 & 0.13 & 0.03 & \(-\)0.51 & 0.24 & 0.36 & \(-\)0.33 & \(-\)0.27 \\
4 & 0.05 & \(-\)0.12 & \(-\)0.28 & 0.26 & \(-\)0.36 & \(-\)0.12 & \(-\)0.03 & \(-\)0.37 & 0.23 & \(-\)0.4 & \(-\)0.19 & 0.34 \\
5 & 0.08 & \(-\)0.06 & \(-\)0.02 & 0.04 & 0.07 & \(-\)0.01 & 0.04 & 0.16 & \(-\)0.01 & \(-\)0.01 & 0.1 & \(-\)0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Cluster centers of the behavior in operating the mechanical ventilation system. Figure 9: Inertia and silhouette score of models when \(K\) changes from 2 to 7. Temperature and time-driven (Cluster 3): In this cluster, the Pearson's correlation coefficients of indoor and outdoor temperature (with the status of the system) are both greater than 0.3, while that related to the month is \(-\)0.51. This indicated that these households were more inclined to switch on the system in spring and summer seasons. When the temperature increased, the air conditioner would be switched on and the windows would be closed in summer, while they were more willing to keep the system operating for ventilation. 4. Mixed factors-driven (Cluster 4): In this cluster, the correlation coefficient of indoor and outdoor temperature, outdoor PM\({}_{2.5}\) concentration and month (with the status of the system) are all significant. This suggests that the system operation behavior of this cluster could be affected by a combination of these factors. 5. Random behavior (Cluster 5): In this cluster, the correlation coefficients of all these factors (with the status of the system) are not significant.