# Modeling and Analysis of New Hybrid Clustering Technique for Vehicular Ad Hoc Network
## 3 Clustering Model
### Covering Rough Set Model
#### 3.1.2 Group Implementation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Scenario** & **Algorithm** & **Maximum** & **Average** & **Minimum** \\ \hline \multirow{3}{*}{LD1} & RK-Means & 0.3901 & 0.2061 & 0.0977 \\  & K-Means++ & 0.4466 & 0.3913 & 0.3777 \\  & OK-Means & 0.4554 & 0.3208 & 0.1787 \\ \hline \multirow{3}{*}{LD2} & RK-Means & 0.0806 & 0.0663 & 0.0543 \\  & K-Means++ & 0.1804 & 0.0344 & 0.0138 \\  & OK-Means & 0.3852 & 0.2752 & 0.1504 \\ \hline \multirow{3}{*}{LD3} & RK-Means & 0.5057 & 0.4197 & 0.2838 \\  & K-Means++ & 0.4018 & 0.3018 & 0.2852 \\  & OK-Means & 0.5238 & 0.4328 & 0.2733 \\ \hline \multirow{3}{*}{LD4} & RK-Means & 0.7129 & 0.5925 & 0.4697 \\  & K-Means++ & 0.4734 & 0.3248 & 0.2725 \\  & OK-Means & 0.4533 & 0.2082 & 0.1471 \\ \hline \multirow{3}{*}{HD1} & RK-Means & 0.4274 & 0.3391 & 0.2165 \\  & K-Means++ & 0.5644 & 0.5002 & 0.4825 \\  & OK-Means & 0.4878 & 0.3106 & 0.2098 \\ \hline \multirow{3}{*}{HD2} & RK-Means & 0.6412 & 0.4352 & 0.3348 \\  & K-Means++ & 0.6825 & 0.5901 & 0.4729 \\  & OK-Means & **0.5689** & 0.5138 & 0.2246 \\ \hline \multirow{3}{*}{HD3} & RK-Means & 0.4524 & 0.3402 & 0.2204 \\  & K-Means++ & 0.5254 & 0.5021 & 0.3358 \\  & OK-Means & **0.3098** & **0.2191** & 0.1604 \\ \hline \multirow{3}{*}{HD4} & RK-Means & 0.5393 & 0.4183 & 0.2912 \\  & K-Means++ & 0.4852 & 0.3801 & 0.3012 \\ \cline{1-1}  & OK-Means & **0.4694** & **0.3592** & **0.2781** \\ \hline \hline \end{tabular}
\end{table} 
Table 9: DB numerical results. Figure 15: DI comparison results. As shown in Figure 12, the RMSE values of the RK-Means clustering algorithm were lower in all scenarios compared with those of the other clustering algorithms, which indicated that the vehicles were distributed in the convergence area, so the cluster similarity was high. In the low-density scenario, the average RMSE values were 5.818225, 10.99553, and 8.458949 for RK-Means, K-Means++, and OK-Means, respectively. In the high-density scenario, the average RMSE value was 11.26924 for RK-Means, 11.55046 for K-Means++, and 16.88988 for OK-Means. The overall evaluation results were 8.54373 for RK-Means, 11.273 for K-Means++, and 12.67441 for OK-Means. The improvements demonstrated by the proposed model compared with the other algorithms were substantial in all scenarios, with concrete numerical differences. The proposed RK-Means algorithm demonstrated more improvements than RK-Means++ and OK-Means, indicating that the cluster node distribution converged and the intra-cluster distance was small. The total internal errors were reduced by 32.5% and 24.2% compared with OK-Means and K-Means++, respectively. Table 8 presents the numerical results for the SC index and shows that RK-Means and K-Means++ performed better in all scenarios, especially in the high-density scenarios, compared to OK-Means. A high SC value indicates high cluster-to-cluster dissimilarity (i.e., clusters distributed with large inter-cluster distances). The SC results for the two scenarios showed that the values obtained for RK-Means were higher than those obtained for K-Means++ and OK-Means. The maximum average SC values in the LD scenario (LD1, LD2, LD3, and LD4) were 0.9672, 0.9572, and 0.9498 for RK-Means, RK-Means++, and OK-Means, respectively. The maximum average SC values in the HD scenario (HD1, HD2, HD3, and HD4) were 0.9623 for RK-Means, 0.9631 for RK-Means++, and 0.9599 for OK-Means. The bold and underlined SC values in Table 8 represent good results and indicate that the proposed algorithm has higher cluster-to-cluster dissimilarity than the other models. The SC value of the proposed model in the LD scenario was higher than those of K-Means++ and OK-Means++. The results of the proposed algorithm are similar to those obtained for the K-Means++ and OK-Means++. and OK-Means.