# ConDPC: Data Connectivity-Based Density Peak Clustering
## 4 Experiments and Results
### Experiments on Synthetic Datasets
#### 4.1.2 Results on Synthetic Datasets  
Firstly, the clustering results on the first kind of dataset are introduced. DPC performs well on this type of dataset, and this group of experiments mainly verifies whether the proposed algorithm can retain the good results of the original DPC algorithm. The Aggregation dataset has seven clusters. There is little difference in density among the seven clusters. The clustering effect of DPC algorithm on Aggregation is good. The similar density and uniform data distribution make the DPC algorithm applicable to this dataset. ConDPC also achieves a good clustering effect on Aggregation. The clustering result of K-means algorithm is poor. DBSCAN misjudges some points as noise points, and the clustering effect is mediocre. The clustering results are shown in Figure 3, and the star shaped points are the cluster centers [34]. The Flame dataset has two clusters. The shape of the two clusters is different and the density distribution is uniform. As can be seen from Figure 4, ConDPC, DPC, and McDPC have the best clustering effects. Figure 3: Results on Aggregation. (**a**) ConDPC, (**b**) DPC, (**c**) K-means, (**d**) DBSCAN, (**e**) DPC-DBFN, (**f**) McDPC. R15 has a total of 15 clusters, as shown in Figure 5. These 15 clusters have similar densities and similar distributions. The DPC algorithm has achieved a good clustering effect on this dataset. The other five algorithms also have good clustering results. Figure 4: Results on Flame. (**a**) ConDPC, (**b**) DPC, (**c**) K-means, (**d**) DBSCAN, (**e**) DPC-DBFN, (**f**) McDPC. Figure 5: Results on R15. (**a**) ConDPC, (**b**) DPC, (**c**) K-means, (**d**) DBSCAN, (**e**) DPC-DBFN, (**f**) McDPC. The clustering effect on the latter two datasets is described below. DPC does not perform well on this kind of data set. This group of experiments mainly verifies the good clustering effect of ConDPC on these datasets. The Jain dataset consists of two lunar data clusters. The density of these two clusters is quite different, so Jain is often used to check the accuracy of the clustering algorithms. The density calculation of DPC does not consider the density difference between different clusters. In the Jain dataset, the density of the bottom cluster is significantly higher than that of the upper cluster. As shown in Figure 6b, DPC finds two center points in the bottom cluster. After ConDPC finds the point with the highest density in a connected group, it will update \(\delta\) value of this point to the maximum value. In this way, the corresponding \(\gamma\) is corrected. As a result, although the density of the upper cluster is sparse, for the point with the largest density in the cluster, its \(\delta\) value is the maximum value, so its \(\gamma\) value increases accordingly, and finally, this point is selected as the clustering center. In this way, ConDPC finds the cluster centers in both clusters and correctly assigns the remaining points to the corresponding clusters. DBSCAN fails to distinguish multiple clusters with large density differences, divides the upper cluster into two, and misjudges a point as a noise point. Only DPC and McDPC implement clustering perfectly, as shown in Figure 6.  
The Twocircle dataset consists of two nested circular clusters. The density of the internal circle cluster is higher than that of the external one. DPC does not consider the difference of different cluster densities and selects two points that are farther apart in the internal circle cluster with a higher density as the cluster centers but does not select the cluster center in the external circle cluster. For the ConDPC algorithm, although the density of the external circle cluster is relatively small, for the point with the largest density in the cluster, its \(\delta\) value is updated to the maximum value, so its \(\gamma\) value increases accordingly, and finally, this point is selected as the clustering center. Figure 6: Results on Jain. (**a**) ConDPC, (**b**) DPC, (**c**) K-means, (**d**) DBSCAN, (**e**) DPC-DBFN, (**f**) McDPC.