# A Novel K-Means Clustering Algorithm with a Noise Algorithm for Capturing Urban Hotspots
## 6 Conclusions  
In this paper, a novel noise-based K-means clustering algorithm has been proposed to effectively solve the problems of difficulty in determining the clustering numbers and the sensitivity of initializing the clustering center for a K-means clustering algorithm. The noise-based K-means clustering algorithm has been applied to capture urban hotspots in large cities from across the world. When the clustering operation was completed, the clustering results were evaluated by the DB index, PBM index, SC, and SSE, and the experimental results of each evaluation standard were statistically analyzed by Wilcoxon rank sum testing to obtain the significant differences for the urban hotspot distribution for each clustering algorithm. The proposed noise-based K-means clustering algorithm obtained better optimal results for urban hotspots over the FCM, K-means, and K-means plus methods. The method presented here can better serve a large number of people in large cities. In addition, the proposed noise-based K-means clustering algorithm can also be applied in the fields of the document classification, customer classification, ride data analysis, criminal network analysis, the detailed analysis of call records, and so on. There are also some shortcomings for the method presented here. On the one hand, the amount of GPS data is too small to effectively reflect the distributions and the relationships of urban hotspots. On the other hand, it is difficult to effectively avoid specific buildings in the city, even if the optimal results of urban hotspots are used in urban road planning. As such, these problems will be further solved in future work. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{3}{*}{**Taxi GPS Dataset**} & \multirow{3}{*}{**Clustering Result Evaluation Method**} & \multicolumn{3}{c}{**Noise-Based K-Means Versus K-Means Plus**} \\ \cline{3-6}  & & & \multirow{2}{*}{\(\mathbf{k}\)} & \multirow{2}{*}{\(\mathbf{p}\)} & \multirow{2}{*}{\(\mathbf{h}\)} & \multicolumn{2}{c}{_Stats_} \\ \cline{3-6}  & & & & & \multicolumn{1}{c}{_Zval_} & \multicolumn{1}{c}{_Ranksum_} \\ \hline \multirow{4}{*}{Aracaju (Brazil)} & **SC** & & 3.38194 \(\times\)\(10^{-4}\) & 1 & 3.5841 & 543 \\  & SSE & & 2.04071 \(\times\)\(10^{-5}\) & 1 & \(-\)4.2604 & 252 \\  & DBI & & 1.80570 \(\times\)\(10^{-1}\) & 0 & 1.3390 & 460 \\  & PBM & & 3.79330 \(\times\)\(10^{-1}\) & 0 & 0.8791 & 443 \\  & SC & & 1.60981 \(\times\)\(10^{-4}\) & 1 & 3.7735 & 550 \\  & SSE & & 2.59598 \(\times\)\(10^{-5}\) & 1 & \(-\)4.2063 & 254 \\  & DBI & & 1.80570 \(\times\)\(10^{-1}\) & 0 & 1.3390 & 460 \\  & PBM & & 2.56300 \(\times\)\(10^{-2}\) & 1 & \(-\)2.2316 & 327 \\  & SC & & 9.09100 \(\times\)\(10^{-2}\) & 0 & 1.6906 & 473 \\  & SSE & & 9.61900 \(\times\)\(10^{-2}\) & 0 & -1.6636 & 348 \\  & DBI & & 5.31000 \(\times\)\(10^{-2}\) & 0 & 1.9341 & 482 \\  & PBM & & 3.36910 \(\times\)\(10^{-1}\) & 0 & \(-\)0.9603 & 374 \\  & SC & & 1.34000 \(\times\)\(10^{-3}\) & 1 & 3.2054 & 529 \\  & SSE & & 9.20913 \(\times\)\(10^{-4}\) & 1 & \(-\)3.3136 & 287 \\  & DBI & & 3.36910 \(\times\)\(10^{-1}\) & 0 & 0.9603 & 446 \\  & PBM & & 9.03110 \(\times\)\(10^{-1}\) & 0 & 0.1217 & 415 \\  & **SC** & & 7.64300 \(\times\)\(10^{-2}\) & 0 & 1.7718 & 476 \\  & SSE & & 5.62903 \(\times\)\(10^{-4}\) & 1 & \(-\)3.4489 & 282 \\  & DBI & & 4.73480 \(\times\)\(10^{-1}\) & 0 & 0.7168 & 437 \\  & PBM & & 3.79330 \(\times\)\(10^{-1}\) & 0 & \(-\)0.8791 & 377 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Statistical analysis results of Wilcoxon testing for noise-based K-means vs. K-means plus. **Author Contributions:** Conceptualization, X.Z. and X.R. ; data curation, M.L. ; formal analysis, W.D. ; funding acquisition, X.Z. and W.D. ; investigation, W.D. and X.R. ; methodology, X.Z. and X.R. ; project administration, M.L. and X.Z. ; resources, X.R. ; software, X.R. and X.Z. ; validation, W.D. and W.T. ; visualization, X.R. ; writing--original draft, X.R. and X.Z. ; writing--review and editing, W.D., W.T. and X.Z.