## 3 Experiment Results and Analysis
### Experimental Results and Comparison Analysis
#### 3.3.1. _Taxis GPS Data Set_
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** & **Aracaju** & **Beijing** & **Chongqing** & **Rome** & **San Francisco** \\ \hline K-means++ & 0.0415 & 0.2430 & 0.1361 & 0.0756 & 0.0383 \\ RS & 0.0410 & 0.2442 & 0.1304 & 0.0760 & 0.0390 \\ GAK & 0.0424 & 0.2488 & 0.1355 & 0.0644 & 0.0371 \\ PSOK & 0.0439 & 0.2809 & 0.1570 & 0.0850 & 0.0434 \\ PSOCK & 0.0432 & 0.2748 & 0.1488 & 0.0840 & 0.0392 \\ PSOWK & 0.0438 & 0.2813 & 0.1636 & 0.0851 & 0.0443 \\ PSO-GAK & 0.0445 & 0.2843 & 0.1618 & 0.0864 & 0.0427 \\ FPSO-GAK & 0.0447 & 0.2858 & 0.1650 & 0.0865 & 0.0451 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Average degree of separation of 8 algorithms trained 20 times in 5 GPS data sets. Figure 8: The SSE convergence curve for the searching optimal initial clustering centers stage of taxi GPS dataset from San Francisco (USA). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Algorithms** & **Aracaju** & **Beijing** & **Chongqing** & **Rome** & **San Francisco** \\ \hline K-means++ & 18.9475 & 213.4044 & 101.0077 & 51.3587 & 34.6147 \\ RS & 19.9865 & 212.5084 & 105.8674 & 51.0076 & 34.5113 \\ GAK & 19.0157 & 212.8031 & 100.7465 & 52.6603 & 35.1143 \\ PSOK & 19.8867 & 224.2299 & 109.4038 & 54.0949 & 36.4149 \\ PSOCK & 19.8712 & 223.6972 & 109.3995 & 54.1288 & 36.6931 \\ PSOWK & 19.5313 & 223.5987 & 110.5026 & 55.8484 & 35.7416 \\ PSO-GAK & 19.6945 & 224.5453 & 109.3748 & 55.1924 & 36.1069 \\ FPSO-GAK & 18.4654 & 212.3069 & 100.3002 & 50.5796 & 34.3267 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Average SSE of 8 algorithms trained 20 times in 5 GPS data sets. posed really is in the optimal state, the optimization effect is noticeable, and its curve variations are negligible. It indicates that the proposed algorithm can obtain relatively better clustering centers by using the initialization operation of the k -means++ algorithm when initializing the populations. Assuming that the proposed algorithm is equivalent to the K-means++ algorithm, the two algorithms' convergence curves will coincide in the convergence scenario, which is not observed in the experiments. In the iterative optimization process of the proposed algorithm, the fitness value changes slightly, and the location distribution of particles and the clustering center are constantly modified to achieve a more optimal clustering centers distribution throughout the whole GPS data set. The final clustering effect can better accommodate actual requirements. The convergence curves of the proposed algorithm and PSO-GAK algorithm remain close to each other, indicating that the parameters of the proposed algorithm should be further adjusted to improve its convergence effect, which will be studied in future work. Figures 9-13 show that the proposed algorithm can obtain better particles than the GAK, PSOK, PSOCK, PSOWK, PSO-GAK and K-means++ as the input initial clustering centers of the K-means algorithm. With optimization by the proposed algorithm, improved clustering centers can be captured, significantly reducing the K-means algorithm's sensitivity to initial clustering centers. When SSE is employed as the objective function of the k-means clustering algorithm, the clustering centers obtained by the proposed algorithm are used to perform the K-means clustering algorithm, which has faster convergence characteristics and a lower SSE value overall. Figure 11: The SSE convergence curve of taxi GPS dataset from Chongqing (China). Figure 12: The SSE convergence curve of taxi GPS dataset from Roma (Italy). Figure 10: The SSE convergence curve of taxi GPS dataset from Beijing (China). In Figure 9, the proposed algorithm begins to converge in the second generation and converges entirely in the fourth generation, and the SSE obtained is significantly smaller than other algorithms. In Figure 10, before the seventh generation, the convergence speed of the proposed algorithm is faster than other algorithms, and the SSE value is also relatively small.