# A Novel K-Means Clustering Algorithm with a Noise Algorithm for Capturing Urban Hotspots
## 4 Experiment Results and Analysis
### Experimental Results and Comparison Analysis  
The comparison results of the maximum, average and minimum values of noise K-means, FCM, K-means and K-means plus under the evaluation of SC, BM index, DB index and SSE for the taxi GPS data are shown in Tables 3-6. As can be seen from Tables 3-6, the proposed noise K-means clustering algorithm is used to obtain the clustering number of a given GPS dataset, which can improve the clustering effect effectively and much easier to find urban hotspots. It can also obtain the better clustering evaluation results, capture the urban hotspots, which can more effectively reflect the urban operating state through different clustering evaluation methods in the given GPS dataset. As can be seen from Table 3 for SC, the noise-based K-means clustering algorithm has a better performance, which indicates that it can better capture excellent clustering centers (urban hotspots). As can be seen from Table 4 for PBM index, the clustering results of noise K-means and K-means plus performed better in the taxis GPS data. As can be seen from Table 5 for DB index, K-means, noise K-means and K-means plus all performed well in the taxis GPS data, and there is little difference in the overall evaluation value. As can be seen from Table 6 for SSE, the noise K-means performs very well in 5 taxi GPS datasets, that because SSE is the optimization target in the clustering process of each clustering algorithm. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Taxi GPS Dataset** & **The Clustering Number of** & **The Clustering Number of** \\  & **FCM, K-Means, K-Means Plus** & **Noise K-Means** \\ \hline Aracaju (Brazil) & 120 & 125 \\ San Francisco (USA) & 140 & 144 \\ Rome (Italy) & 135 & 137 \\ Chongqing (China) & 130 & 134 \\ Beijing (China) & 125 & 128 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The clustering numbers of the taxi GPS data. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Taxi GPS Dataset** & **Algorithms** & **Maximum** & **Average** & **Minimum** \\ \hline \multirow{4}{*}{Aracaju (Brazil)} & Noise K-means & 0.96083 & 0.95944 & 0.95703 \\  & FCM & 0.94635 & 0.94416 & 0.94285 \\  & K-means & 0.95827 & 0.95577 & 0.95355 \\  & K-means plus & 0.96004 & 0.95784 & 0.95586 \\  & Noise K-means & 0.9369 & 0.93522 & 0.93314 \\  & FCM & 0.92914 & 0.92689 & 0.92494 \\  & K-means & 0.93389 & 0.93124 & 0.9287 \\  & K-means plus & 0.93502 & 0.93403 & 0.93219 \\  & Noise K-means & 0.9295 & 0.9275 & 0.9231 \\  & FCM & 0.91112 & 0.90662 & 0.90296 \\  & K-means & 0.9277 & 0.92535 & 0.92255 \\  & K-means plus & 0.92871 & 0.92672 & 0.92334 \\  & Noise K-means & 0.93896 & 0.93689 & 0.93457 \\  & FCM & 0.91979 & 0.91682 & 0.91311 \\  & K-means & 0.93673 & 0.93565 & 0.93424 \\  & K-means plus & 0.93708 & 0.9354 & 0.93195 \\  & Noise K-means & 0.91192 & 0.90933 & 0.90561 \\  & FCM & 0.91979 & 0.91682 & 0.91311 \\  & K-means & 0.91125 & 0.91012 & 0.90853 \\  & K-means plus & 0.90963 & 0.90842 & 0.90668 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison results of SC evaluation values. The average running time for each algorithm when running 20 times is shown in Table 7.  
As can be seen from Table 7, the average iteration time of the noise K-means clustering algorithm is longer, because the noise algorithm needs to capture the clustering number of a given dataset and initialize the clustering center. The noise K-means clustering algorithm can obtain the better clustering number of a given GPS data, and much easier to find urban hotspots. It can also obtain the better clustering evaluation results, capture the urban hotspots.