# Time Series Clustering Model based on DTW for Classifying Car Parks
## 3 Results and Discussion of Car Parks Clustering  
After consulting and understanding the managers' demand of car parks, we divide the car parks into 3 clusters (groups) for the purpose of being easy to manage. The proposed DTW +DBPAM model is employed to classify data1 and results are given in Figure 4.  
Figure 4 shows that the occupancy rates of car parks during 2019.11.13 (Sunday) and 2019.11.19 (Saturday) are obviously different. Most of these 27 car parks have different occupancy rates between workday and weekend. The occupancy rates of car parks on Saturday-Sunday in cluster 1 is slightly higher than that on Monday to Friday while the occupancy rates of car parks on Saturday-Sunday in cluster 3 are absolutely lower than those on Monday to Friday, and the occupancy rates of car parks on Sunday-Monday in cluster 2 are obviously lower than those on Tuesday to Saturday. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**DataSet**} & \multicolumn{6}{c}{**Purity**} \\ \cline{2-9}  & \multicolumn{2}{c}{**ED+PAM**} & \multicolumn{2}{c}{**ED+DBPAM**} & \multicolumn{2}{c}{**DTW +PAM**} & \multicolumn{2}{c}{**DTW +DBPAM**} \\ \cline{2-9}  & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** & **Train** & **Test** \\ \hline EthanolLevel & 0.3188 & 0.38555 & 0.3562 & 0.408 & 0.35495 & 0.3532 & **0.3935** & **0.4726** \\ SyntheticControl & 0.67875 & 0.723333 & 0.7213 & 0.7867 & 0.71375 & 0.745 & **0.76875** & **0.791667** \\ Strawbeerry & 0.76132 & 0.75938 & 0.8066 & 0.7767 & 0.671749 & 0.6802 & **0.820611** & **0.8223** \\ CBF & 0.597043 & 0.627957 & 0.6022 & 0.64 & **0.709409** & **0.683871** & 0.553763 & 0.575269 \\ Beef & 0.53334 & 0.68334 & 0.5236 & 0.7225 & **0.54584** & 0.7 & 0.4792 & **0.75** \\ Coffee & 0.87112 & 0.89092 & 0.9115 & **0.9461** & 0.8667 & 0.94546 & **0.9556** & 0.9091 \\ SmoothSubspace & 0.63832 & 0.63998 & 0.6017 & 0.6549 & **0.70334** & **0.77998** & 0.6125 & 0.6833 \\ MoteStrain & 0.83558 & 0.8173 & 0.8722 & 0.8934 & 0.83538 & 0.82124 & **0.9855** & **0.9843** \\ SonyAlBORobotsurface1 & 0.8012 & 0.78388 & 0.83148 & 0.86844 & 0.73118 & 0.76844 & **0.992** & **1** \\  & 0 & 0 & 0 & 1 & 3 & 2 & 6 & 6 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of 4 methods on 9 datasets. Figure 4: Results of clustering on data1. Figure 4 contains three graphs which were listed by clusters: (**a**) cluster 1, (**b**) cluster 2, (**c**) cluster 3. Similarly, we also group these 27 car parks by the proposed DTW +DBPAM on data2 and results are given in Figure 5.  
Figure 5 also shows that the occupancy rates of car parks on 2019.11.20 (Sunday) to 2019.11.26 (Saturday) are obviously different. Although the results of data2 is same to results of data1, the occupancy rates of car parks between Monday to Friday and Saturday-Sunday in each class are clearly different. The occupancy rates of car parks on Saturday-Sunday in cluster 1 is slightly higher than that on Monday to Friday while the occupancy rates of car parks on Saturday-Sunday in cluster 2 is obviously higher than that on Monday to Friday and the occupancy rates of car parks on Saturday-Sunday in cluster 3 is obviously lower than that on Monday to Friday. According to the analysis mentioned above, the change of occupancy rates of car parks in cluster 2 is sensitive to the holiday, which means that occupancy rates of car parks decreases during holidays. Therefore, we know that the location of the car parks in cluster 2 is near the office area. However, the change of occupancy rates of car parks in cluster 1 and cluster 3 is insensitive to the holiday, which means that occupancy rates do not change during holidays. However, the change of the occupancy rates on Monday to Friday is obviously different from that on Saturday-Sunday in cluster 1 and cluster 3. The occupancy rates of car parks on Saturday-Sunday in cluster 1 are slightly higher than those on Monday to Friday. The reason is that people like to go shopping or entertainment on weekends.