## 4 Experimental Results and Analysis
### The Settings of Clustering Center and Privacy Budget Parameters
#### 4.2.2 UCI Datasets  
For the UCI datasets, the line graph of the clustering effect of algorithms under different combinations of \(b_{1}\) and \(b_{2}\) changes with privacy budget \(\varepsilon\), as shown in Figure 3, where the label contains \"eu\" indicating the use of Euclidian distance, while \"cos\" indicates the use of cosine distance. As observed in Figure 3a, for dataset seeds, the clustering effect of DP-CDPC using Euclidean distance is better than that of using cosine distance on the whole; when parameter \(b_{1}\) is set as 2 and \(b_{2}\) is set as 1, the clustering effect of reaching the stationary state is better, and the critical value \(\varepsilon\) of reaching the stationary state is 4. In Figure 3b, for the coil dataset, the clustering effect of the DP-CDPC using cosine distance is better than that of using Euclidean distance overall. When cosine distance is adopted, a better clustering performance is achieved after setting the algorithm's parameters to 2 and 0.5, respectively, and the critical value \(\varepsilon\) of reaching the stationary state is 0.5. When Euclidean distance is used, the clustering effect is better when both parameters \(b_{1}\) and \(b_{2}\) are set to 1, and the critical value is 1.5. Figure 3c reveals that, for the movement dataset, cosine distance also leads to a better clustering performance. When cosine distance is used, the clustering effect is better when parameters \(b_{1}\) and \(b_{2}\) are set as 1 and 0.5, respectively, and the critical value is 1. When Euclidean distance is used, the clustering effect is better when both \(b_{1}\) and \(b_{2}\) are set as 1, respectively, and the critical value is 0.5. In Figure 3d, for the dermatology dataset, the effect of cosine distance is also better. In the case of cosine distance, when \(b_{2}\) is 0.5 and \(b_{1}\) is 3, respectively, the algorithm achieves a better clustering performance when reaching  
Figure 2: Clustering effect of synthetic dataset varying with \(\varepsilon\): (**a**) flame; (**b**) spiral; (**c**) compound; (**d**) aggregation; (**e**) R15; and (**f**) D31. the stable state, and the critical value is 0.5. When Euclidean distance is used, the clustering effect is better when both parameters \(b_{1}\) and \(b_{2}\) are set as 1, respectively, and the critical value is 1.5. Figure 3e indicates that, for the banknote dataset, the clustering effect using Euclidean distance is better than that using cosine distance. When the parameters are set as 3 and 1, respectively, the algorithm achieves a better clustering effect in the stationary state, and the critical value of reaching the stationary state is 8. When cosine distance is adopted, \(b_{2}\) is set as 0.5, and \(b_{1}\) is set as 2, the effect is better after reaching the stationary state, and the critical value \(\varepsilon\) is 2. It can be seen from Figure 3f that, for the abalone dataset, the clustering effect using cosine distance is better. When \(b_{2}\) is set as 1 and \(b_{1}\) is set as 1, 2 or 3, respectively, the algorithms present the same trend of change when different amounts of noise are added. After adding noise of the same \(\varepsilon\), the clustering effect of algorithms with different parameter values is not significantly different, and the critical value of \(\varepsilon\) is 0.5. In conclusion, the experiments conducted on both the synthetic datasets and UCI datasets demonstrate that the parameter \(b_{1}\) in the DP-CDPC algorithm can be set to 1, 2, or 3, while the parameter \(b_{2}\) can be set to 0.5 or 1. By choosing an appropriate privacy budget, the DP-CDPC algorithm achieves a balance between privacy protection and clustering effectiveness. For low-dimensional datasets such as seeds, banknote, and the synthetic datasets, the clustering performance is better when using the similarity measured by Euclidean distance.