# Extension of DBSCAN in Online Clustering: An Approach Based on Three-Layer Granular Models
## 6 Conclusions  
To realize fast and effective online spatial data clustering, this paper developed a DBSCAN extension algorithm with a combination of granular models focusing on online clustering. The proposed algorithm was developed with three layers via granular computing. The first layer is to construct structural granules via DBSCAN and GrC in the input space. The numerical results on synthetic spatial data verify the superiority of DBSCAN on clustering data with arbitrary shapes compared to conventional methods. Moreover, DBSCAN-based granules are found to well inherit the structure description ability, which is useful in spatial data clustering. Then, the second layer made use of the reconstruction error for rule formation in the medium space. Granular intervals are constructed via justifiable granulating, and utilized to form fuzzy rules for determining the data's belonging. The numerical results show that these rules have a good ability on distinguishing different clusters' data, and this ability will be outstanding when the data are more structural. Finally, making use of structural DBSCAN-based granules and fuzzy rules in medium space, online clustering on spatial data was implemented by rule-based modeling. Experiments on synthetic and typical spatial datasets verified the feasibility of the proposed method in online spatial data clustering. Through the comparison with well-known \(k\)-means-based methods, the superiority of the proposed method on improving the performance of spatial data clustering is verified. Moreover, via the comparison with different DBSCAN extensions on online clustering, the proposed granule-based method is demonstrated to have less computation overhead and a relatively good performance, especially in online clustering orienting to big spatial data.  
By making use of this proposed method, researchers can develop some practical engineering applications about online recognition and spatial data in the future; for example, geographical information systems, logistics monitoring services, and so on. However, some limitations can also be found. For example, since the major superiorities of the proposed method are based on DBSCAN and GrC, it may be possible to develop online spatial data clustering algorithms based on more advanced density-based methods. Moreover, the discussion on how to trade off the number of granules with the computation overhead is not implemented in this paper, which would be also a meaningful topic in practical applications, which usually require comprehensive performances.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Granule-Based**} & & & & \\ \cline{2-9}  & \(c\) = 5 & \(c\) = 10 & \(c\) = 15 & \(c\) = 20 & & & \\ \hline Acc. & 0.7550 & 0.8760 & 0.8990 & 0.9134 & 0.8979 & 0.8754 & 0.5218 & 0.5854 \\ \hline Time & 0.0671 & 0.1185 & 0.1861 & 0.1907 & 0.4347 & 0.3924 & 0.1419 & 0.1576 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Performance of online clustering on the Chameleon data.  
Author ContributionsWriting--original draft preparation, experiment, X.Z.; writing--review and editing, X.S.; writing and editing, supervision, funding acquisition, T.O. All authors have read and agreed to the published version of the manuscript.  
This research was supported by JSPS KAKENHI Grant Number JP22K17961.  
Not applicable.  
The authors declare no conflict of interest.