## 3 Experiment Results and Analysis
### Experimental Results and Comparison Analysis  
#### 3.3.1. _Taxis GPS Data Set_  
Figures 4-8 show the convergence diagrams for the searching optimal initial clustering centers stage of the GAK, PSOK, PSOCK, PSOWK, PSO-GAK, and the proposed algorithms utilizing Section 3.2 parameters in five distinct GPS data sets. Figures 9-13 is the convergence diagram for k-means clustering stage of 7 algorithms (the above six algorithms plus K-means++ algorithm). Tables 5-7 are the comparison tables for the average Silhouette coefficient (SC), the average degree of separation (SP), and the average SSE value of 20 \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**DS** & **VRP** & **NLDP** & **NC** & **NP** & \(\omega\) & \(c_{1}\) & \(c_{2}\) & **FRW** & **FRC** & **ACCR** & **AVCR** \\ \hline Aracaju & 0.8,-0.8 & 16,513 & 120 & 41 & 0.9 & 1.5 & 1.5 & 0.2,1.2 & 1.0,2.0 & 0.5,1.0 & 0.5,1.0 \\ Beijing & 0.8,-0.8 & 17,387 & 130 & 41 & 0.6 & 1.2 & 1.2 & 0.2,1.2 & 1.0,2.0 & 0.5,1.0 & 0.5,1.0 \\ Chongqing & 0.4,-0.4 & 19,149 & 130 & 41 & 0.6 & 1.1 & 1.1 & 0.2,1.2 & 1.0,2.0 & 0.5,1.0 & 0.5,1.0 \\ Rome & 0.1,-0.1 & 20,254 & 140 & 51 & 0.6 & 1.5 & 1.5 & 0.2,1.2 & 1.0,2.0 & 0.5,1.0 & 0.5,1.0 \\ San Francisco & 0.3,-0.3 & 21,826 & 140 & 51 & 0.8 & 1.6 & 1.6 & 0.2,1.2 & 1.0,2.0 & 0.5,1.0 & 0.5,1.0 \\ \hline \hline \end{tabular}  
* DS: data set; NLDP: number of location data points; NC: number of clusters.  
\end{table} 
Table 4: PSO and fuzzy system parameter setting. training sessions respectively (plus Random Swap Clustering algorithm). In order to accurately analyze the above evaluation indexes, each algorithm was iterated 180 times in a single run to guarantee convergence. Figures 14-19 show The obtained clustering centers of Aracaju, Beijing, Chongqing, Rome, and San Francisco after the operation of six algorithms. Clustering centers outcome are shown on the Baidu Map background. Tables 5-7 demonstrate that the proposed algorithm has superior clustering performance in terms of Silhouette coefficient, degree of separation and SSE, as well as the ability to capture better clustering results and locate more effective urban hotspots. However, in Table 7's San Francisco data set, the K-Means++ algorithm delivers just slightly worse than the proposed algorithm. It reveals that the K-Means++ algorithm can be used as a preliminary coarse-grained clustering algorithm in such applications. The tables also demonstrate that the overall clustering performance of the RS algorithm is good, and the clustering effect is better than the K-Means++ algorithm in most cases. In Table 5, the average Silhouette coefficient of the proposed algorithm is higher than other algorithms. The greater the Silhouette coefficient, the more compact within a cluster and more dispersed between the clusters, indicating that the clustering effect is superior to the competitors. In Table 6, the proposed algorithm has a higher SP value than other algorithms. The higher the SP value, the greater the separation between clustering  
Figure 5: The SSE convergence curve for the searching optimal initial clustering centers stage of taxi GPS dataset from Beijing (China). Figure 6: The SSE convergence curve for the searching optimal initial clustering centers stage of taxi GPS dataset from Chongqing (China). Figure 7: The SSE convergence curve for the searching optimal initial clustering centers stage of taxi GPS dataset from Roma (Italy). Figures 4-8 show that the proposed algorithm undergoes minimal change during the iterative convergence process. Within the five groups of taxi GPS data sets, the pro