## 4 Discussion  
The K-Means algorithm can achieve very good results on convex, compressible datasets. Urban roads are usually distributed in a neighborhood manner, and the trajectory points of vehicles satisfy convexity and compressibility in a large local area. Using the K-Means algorithm to identify urban hotspots can yield effective results. K-Means algorithm is very sensitive to the initial center points. Excellent initial clustering centers significantly impact the performance of the k-Means clustering algorithm. K-Means is particularly effective in fine-tuning local cluster boundaries, but is incapable of solving global cluster locations. The organic combination of global perception and local fine-tuning is the key to obtaining good initial centers. Literature [50] proposed the method of random swap clustering, which is simple and efficient. Under the condition of a suitable KNN super parameter configuration, this method's random swap efficiency is extremely high, it is an exquisite lightweight clustering method. Inspired by the ideas of randomness and exchange, the FPSO-GAK algorithm combines a variety of heuristic algorithms with the premise of sacrificing a little efficiency to avoid the homogeneity of the random search process and can better obtain global perception ability. At the same time, local search parameters can be fine-tuned automatically to prevent over-dependence on super parameter.  
In practical applications, in order to further improve the clustering efficiency, the inertia weight and learning factor can better meet the iterative requirements by adjusting fuzzy rules. At the same time, the combination mode of PSO and GA can also be changed. PSO can improve the phenomenon that GA is prone to early maturity through global optimization in the early stage. while PSO is prone to fall into local optimization in the late stage, the deficiency can be made up through the global optimization in the late stage of GA.  
Compared with many existing research algorithms in this field, the proposed algorithm has a better and relatively efficient non-homogeneous search capability, which can effectively find excellent initial clustering centers and at the same time can reduce the sensitivity of K-Means algorithm to noise to a certain extent. However, the proposed algorithm is relatively complex in structure and has a relatively high time complexity compared to many lightweight algorithms. The proposed algorithm is a class of algorithms based on a heuristic mechanism, which can only guarantee to get a better solution and cannot guarantee to obtain the optimal solution for sure.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline
**City**Algs** & \multicolumn{2}{c}{**GAK**} & \multicolumn{2}{c}{**PSOK**} & \multicolumn{2}{c}{**PSOCK**} & \multicolumn{2}{c}{**PSOWK**} & \multicolumn{2}{c}{**PSO-GAK**} & \multicolumn{2}{c}{**K-Means++**} \\ \cline{2-13}  & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** & **Mean** & **Std** \\ \hline \hline Aracaju & 0.817 & 0.019 & 0.839 & 0.015 & 0.834 & 0.021 & 0.832 & 0.021 & 0.830 & 0.013 & 0.873 & 0.017 \\ Beijing & 0.737 & 0.018 & 0.750 & 0.022 & 0.746 & 0.018 & 0.747 & 0.018 & 0.753 & 0.020 & 0.753 & 0.019 \\ Chongqing & 0.750 & 0.015 & 0.789 & 0.029 & 0.774 & 0.019 & 0.781 & 0.020 & 0.770 & 0.018 & 0.790 & 0.016 \\ Roma & 0.747 & 0.023 & 0.808 & 0.019 & 0.795 & 0.020 & 0.782 & 0.021 & 0.772 & 0.019 & 0.802 & 0.018 \\ San Francisco & 0.700 & 0.021 & 0.722 & 0.024 & 0.721 & 0.027 & 0.727 & 0.024 & 0.717 & 0.026 & 0.745 & 0.021 \\ \hline \end{tabular} mean: mean value; std: standard deviation; lags: algorithms. The above values are the statistical values after 20 rounds of independent running.  
\end{table}
Table 10: CSI index for novel FPSO-GAK vs. other algorithms.