# Extension of DBSCAN in Online Clustering: An Approach Based on Three-Layer Granular Models
## 5 Experiment and Discussion
### Spatial Benchmark Data
Secondly, by comparing with the two other DBSCAN extensions (i.e., C-DBSCAN and G-DBSCAN) on online clustering, it is found that the major superiority of the proposed method is less computation cost; this would be more obvious in big data analysis. Moreover, the accuracy of the proposed method can also outperform other DBSCAN methods when selecting suitable parameters. The reasons behind this phenomenon can be explained as: (1) C-DBSCAN leverages huge information of historical data in the online clustering process, causing a high computation cost; (2) G-DBSCAN can reduce the time consumption with the help of grid cells, but sub-grids have poor representation ability, especially for a dataset with a lot of anomaly data (e.g., blue points in Figure 10), leading to an unsatisfactory accuracy. The proposed granule-based DBSCAN method makes use of the granules' structure description ability and good representation ability, and both the time consumption and accuracy of online spatial data clustering are improved. Therefore, it is concluded that these results not only verify the feasibility of the proposed method on online clustering, but also illustrate \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Cluster 1** & **Cluster 2** & **Cluster 3** \\ \hline IG\({}_{\text{y}}\) & [0, 0.022] & [0, 0.003] & [0, 0.006] \\ \hline IG\({}_{\text{n}}\) & [0.0018, 0.3038] & [0.0387, 0.4747] & [0.0039, 0.2559] \\ \hline  & **Cluster 4** & **Cluster 5** & **Cluster 6** \\ \hline IG\({}_{\text{y}}\) & [0, 0.021] & [0, 0.005] & [0, 0.01] \\ \hline IG\({}_{\text{n}}\) & [0.0300,0.2203] & [0.0037,0.2137] & [0.0509,0.4409] \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of granular intervals in the medium space. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(z_{1}\) & \(z_{2}\) & \(z_{3}\) & \(z_{4}\) & \(z_{5}\) \\ \hline C1 & (0.0953, 0.5005) & (0.3181, 0.5696) & (0.2808, 0.1761) & (0.3042, 0.3694) & (0.1163, 0.2112) \\ \hline C2 & (0.5333, 0.7704) & (0.7013, 0.7656) & (0.712, 0.841) & (0.6139, 0.8009) & (0.553, 0.8449) \\ \hline C3 & (0.5329, 0.3078) & (0.6032, 0.1249) & (0.5328, 0.4072) & (0.4611, 0.1334) & (0.5553, 0.2053) \\ \hline C4 & (0.2533, 0.7857) & (0.217, 0.4002) & (0.4159, 0.4317) & (0.2205, 0.6264) & (0.3876, 0.7231) \\ \hline C5 & (0.6318, 0.294) & (0.6254, 0.6233) & (0.6097, 0.5299) & (0.5676, 0.6134) & (0.6329, 0.4129) \\ \hline C6 & (0.8482, 0.2836) & (0.8402, 0.5621) & (0.8256, 0.4199) & (0.8166, 0.1532) & (0.8591, 0.7181) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimal prototypes in each cluster. the improvement of the proposed DBSCAN extension on online spatial data clustering. Thirdly, comparing results with the other two \(k\)-means-based online clustering methods, the proposed method has great superiority on accuracy, not on computation time. This is because the Chameleon data has stronger constraints on the structure clustering, so conventional clustering methods, such as \(k\)-means, cannot perform well, even though they have superiority on computation time. All in all, by combining the results in both the toy dataset and the benchmark Chameleon dataset, we can conclude that it is feasible to apply the proposed DBSCAN-based granules to extend DBSCAN in online clustering. Moreover, the proposed method in this paper could achieve better accuracy on online spatial data clustering than conventional methods, and it can also have superior computation time to other DBSCAN extension algorithms on online clustering.