# 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} \hline \hline
**Scenario** & **Algorithm** & **Maximum** & **Minimum** \\ \hline \multirow{4}{*}{LD1} & RK-Means & **0.367654729** & **0.355499648** \\  & K-Means++ & 3.79731923 & 3.276113551 \\  & OK-Means & 4.150443082 & 3.059492927 \\ \hline \multirow{4}{*}{LD2} & RK-Means & **1.333829075** & **0.429344109** \\  & K-Means++ & 3.934093954 & 3.566997337 \\  & OK-Means & 3.306255255 & 3.126828608 \\ \hline \multirow{4}{*}{LD3} & RK-Means & **0.414085438** & **0.34182981** \\  & K-Means++ & 3.393721654 & 3.017981096 \\  & OK-Means & 4.140321739 & 2.71766411 \\ \hline \multirow{4}{*}{LD4} & RK-Means & **0.307420352** & **0.243036348** \\  & K-Means++ & 3.089658018 & 3.080243497 \\  & OK-Means & 4.46502773 & 3.59913184 \\ \hline \multirow{4}{*}{HD1} & RK-Means & **0.314635087** & **0.284018779** \\  & K-Means++ & 3.329564536 & 2.984212427 \\  & OK-Means & 3.872622844 & 3.549938092 \\ \hline \multirow{4}{*}{HD2} & RK-Means & **0.3274165729** & **0.156418243** \\  & K-Means++ & 3.18453398 & 2.148264416 \\  & OK-Means & 4.632240821 & 3.13175631 \\ \hline \multirow{4}{*}{HD3} & RK-Means & **0.457573309** & **0.392045916** \\  & K-Means++ & 3.415059785 & 2.724496284 \\  & OK-Means & 4.024010542 & 3.64913853 \\ \hline \multirow{4}{*}{HD4} & RK-Means & **0.397510108** & **0.31507142** \\  & K-Means++ & 3.344376756 & 3.210557584 \\ \cline{1-1}  & OK-Means & 3.11267672 & 2.720969446 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The standard deviation of speed numerical results. Figure 17: RK-Means standard deviation of speed in high-density scenarios. cluster in a highway topology under low-density and high-density scenarios. When the clustering process was completed, the clustering results were evaluated by calculating the RMSE, SC index, DB, and DI. The evaluation results of each index standard were statistically analyzed, and the intra-cluster similarity and inter-cluster dissimilarity were computed for each clustering algorithm. The proposed RK-Means clustering algorithm obtained better optimal results for a highway VANET topology than the K-Means++ and OK-Means methods. RK-Means improved the similarity by 32.5% compared with OK-Means and 24.2% compared with K-Means++. The proposed clustering model demonstrated improvements in clustering performance based on the DI of 16.8% and 31.5% compared with K-Means++ and OK-Means, respectively. For the cluster speed stability, the effectiveness of using a covering rough set was clear, as the cluster had a small value of speed standard deviation, which meant that there was minimal difference in the intra-cluster vehicle speed, the cluster lifetime was high, and the cluster changing rate was low. The proposed method can be used to improve VANET cluster-based routing techniques and network performance. In addition, the RK-Means clustering algorithm can be used in the fields of document classification, data mining, data analysis, network analysis, and so on. The evaluation results pertained to a highway VANET topology only. The application of RK-Means has so far been limited to highway scenarios, so the main aim of future work is to apply the algorithm to a city map topology by modifying the rough set input parameters to cover all directions and angles and to improve its stability by proposing a cluster head selection model to enhance the routing performance. H.N.A.--writing (original draft preparation), algorithm, methodology, and results; G.C.H.--investigation, project administration, and supervision; N.A.M.R.--investigation, project administration, and supervision; N.M.L.T.--review, editing, investigation, project administration, and supervision; C.F.K.--review, editing, and funding acquisition. All authors have read and agreed to the published version of the manuscript. The APC was funded by Ningbo Municipal Key Discipline, China. Data are contained within the article. The authors declare no conflict of interest. ## References

* [PERSON] and [PERSON] (2022)A Novelty of Hypergraph Clustering Model (H GCM) for Urban Scenario in VANET.