# A Novel K-Means Clustering Algorithm with a Noise Algorithm for Capturing Urban Hotspots
## 4 Experiment Results and Analysis
### Visual Presentation of Urban Hotspots  
In order to more intuitively display the capture of urban hotspots by clustering algorithm, a visual presentation in Amap system is used in this paper. That is, the captured cluster center location information is input into the map system through Amap API in order to realize the visual presentation of the captured urban hotspots. The obtained experiment results for the Aracaju (Brazil), San Francisco (USA), Rome (Italy), Chongqing (China), and Beijing (China) are shown in Figures 9-12. Figure 8: The SSE convergence curve for taxi GPS data (Beijing (China)). Figure 7: The SSE convergence curve for taxi GPS data (Chongqing (China)). Figure 10: The city hotspot markers for the city taxi GPS data found by the K-means method: (**a**) Aracaju (Brazil), (**b**) San Francisco (USA), (**c**) Rome (Italy), (**d**) Chongqing (China), (**e**) Beijing (China). Figure 9: The city hotspot markers for the city taxi GPS data found by the FCM method: (**a**) Aracaju (Brazil), (**b**) San Francisco (USA), (**c**) Rome (Italy), (**d**) Chongqing (China), (**e**) Beijing (China). Figure 11: The city hotspot markers for the city taxi GPS data found by the K-means plus method: (**a**) Aracaju (Brazil), (**b**) San Francisco (USA), (**c**) Rome (Italy), (**d**) Chongqing (China), (**e**) Beijing (China). Figure 12: The city hotspot markers for the city taxi GPS data found by the noise-based K-means method: (**a**) Aracaju (Brazil), (**b**) San Francisco (USA), (**c**) Rome (Italy), (**d**) Chongqing (China), (**e**) Beijing (China). As can be seen from Figures 9-12, the spatial distributions of urban hotspots have been captured by the FCM, K-means and K-means plus clustering algorithms for the given taxi GPS data of Aracaju (Brazil), San Francisco (USA), Rome (Italy), Chongqing (China) and Beijing (China) is different. The aggregation degree of taxi operation varies significantly between different cities. From the city hotspot marking results of the taxis GPS data in the five cities obtained by FCM in Figure 9, it can be seen that the clustering effect is not ideal and that there are serious dispersion and local optimum phenomena. For example, the clustering results of San Francisco (USA) demonstrate local optimum phenomena and multiple hotspots are close together, which results in an uneven distribution of urban hotspots and deviation from urban hotspots. Thus, a potentially planned road cannot benefit many people with this approach. From the city hotspot marking results of the taxis GPS data in five cities obtained by K-means clustering in Figure 10, it can be seen that the clustering centers and numbers of clusters are not very reasonable and do not show optimal results. There are multiple local optimum phenomena, such as the serious phenomenon that multiple hotspots are close together in Rome (Italy) and Beijing (China). The phenomenon occurs such that some marker points are not clustered, so that a planned road cannot benefit a large number of people. As can be seen from the city hotspot marking results of the taxis GPS data in five cities obtained by K-means plus clustering in Figure 11, the obtained clustering effect is better than that obtained with FCM and K-means clustering. The clustering centers and number of clusters in most cities are optimal, but there is a local optimal phenomenon in Rome (Italy), which shows multiple hotspots together. A road planned with this approach could benefit many people. As can be seen from the city hotspot marking results of the taxis GPS data in five cities obtained by the noise-based K-means clustering in Figure 12, the obtained clustering effect is better than that obtained with FCM, K-means, and K-means plus clustering. The clustering centers and numbers of clusters for all five cities are the best here, and there are no groups of hotspots that are close together.