# ConDPC: Data Connectivity-Based Density Peak Clustering
## 4 Experiments and Results
### Experiments on Synthetic Datasets
#### 4.1.2 Results on Synthetic Datasets
As can be seen from Figure 7, the clustering results of ConDPC, DBSCAN, and McDPC are perfect. However, DPC, K-means, and DPC-DBFN have poor clustering results on the dataset. The Halfkernal dataset consists of two surrounding moon-shaped data clusters. The density of the two clusters is similar. When the DPC algorithm selects neighbors, it only considers the Euclidean distance between two points and does not consider the connectivity between the two points. As shown in Figure 2, DPC can find the clustering centers in the two clusters, respectively. However, in the process of neighbor selection, point \(p\) of the external cluster chooses point \(q\) of the internal cluster as its neighbor, resulting in many points of the external cluster being incorrectly assigned to the internal cluster. ConDPC preferentially searches for big neighbors in the connected group where the point resides. Therefore, even if there are big neighbors closer to \(p\) in the internal cluster, they are not considered because they are not in the same connected group as \(p\). As shown in Figure 8, ConDPC selects the cluster centers in the two clusters, respectively, and assigns the remaining points to the corresponding clusters. DBSCAN also achieves a good clustering result. The other algorithms have poor clustering effects. The Halfcirlce dataset consists of one moon-shaped cluster and two rectangle-shaped clusters, which is similar to the semi-enclosed structure as a whole. The three clusters have similar densities. As can be seen from Figure 9, DPC can find the appropriate clustering centers in each cluster. However, when assigning the points to the clusters, some points of the moon-shaped cluster are wrongly assigned to the rectangle-shaped cluster on the right. This is still because the original algorithm directly selects the nearest big neighbor to a given point without considering the connectivity between the two points when searching for the neighbor. ConDPC preferentially searches for big neighbors in the connected group where the point resides. Therefore, even if there are big neighbors in the rectangle-shaped cluster that are closer to a point in the moon-shaped cluster, they are not considered because they are not in the same connected group as the point. Figure 7: Results on Twocircle. (**a**) ConDPC, (**b**) DPC, (**c**) K-means, (**d**) DBSCAN, (**e**) DPC-DBFN, (**f**) McDPC. As shown in Figure 9, ConDPC selects the cluster center points in the three clusters, respectively, and assigns the remaining points to the corresponding clusters. DBSCAN also  
Figure 8: Results on HalfKernal. (**a**) ConDPC, (**b**) DPC, (**c**) K-means, (**d**) DBSCAN, (**e**) DPC-DBFN, (**f**) McDPC. Figure 9: Results on HalfCircle. (**a**) ConDPC, (**b**) DPC, (**c**) K-means, (**d**) DBSCAN, (**e**) DPC-DBFN, (**f**) McDPC. achieves a good clustering result. K-means and the last two improved algorithms produce similar poor results. The Threecircle dataset is made up of three nested circles. The inner circle is denser than the outer circle. It can be seen from Figure 10 that: (1) DPC algorithm fails to correctly select the clustering center; (2) DPC algorithm fails to correctly assign the remaining points to the cluster. The DPC algorithm selects one cluster center in the inner circle with the largest density, two cluster centers in the middle circle, and no cluster center in the outer circle with the sparsest density. When the other points are assigned to the clusters, some points in the middle circular cluster are incorrectly assigned to the inner circular cluster. ConDPC can find the appropriate cluster center in each cluster because it modifies the calculation method of neighbor distance. In addition, ConDPC preferentially searches for big neighbors in the same connected group, so the neighbors are searched correctly and assigned to the corresponding cluster. As can be seen from Figure 10, the clustering results of ConDPC, DBSCAN, and McDPC are perfect. Both DPC and K-means get bad clustering results.