## 4 Experiment Analysis
### Experiments on Synthetic Datasets  
In this subsection, the effectiveness of IKDC on the 10 synthetic datasets in Table 2 will be demonstrated. For ACC, NMI, and ARI, IKDC is compared with DPC [25], DBSCAN [24], KNN-DPC [28], SNN-DPC [34], and FCM [54]. The experimental results of the six algorithms on different datasets are presented in Tables 4 and 5. Figures 3-7 can more intensively display the experimental results of the six different algorithms on the Aggregation, Flame, and Jain datasets, where different clusters are distinguished by color. In Figure 7, the solid dots of the same color represent the core domain, and the dots of the same color and different shapes represent the boundary domain of this cluster. Since DIM512 is a high-dimensional dataset, no graph is formed to show its clustering results in this paper.  
As shown in Figures 3a, 4a, 5a, 6a and 7a, the clustering effect of IKDC is improved over the other algorithms on the Aggregation dataset, with DBSCAN having the worst effect. IKDC was 0.024, 0.034, and 0.038 higher than DBSCAN in ACC, NMI, and ARI values, respectively. As shown in Figures 3b, 4b, 5b, 6b and 7b, for the Flame dataset, IKDC, DPC, DBSCAN, and KNN-DPC all perform well, and FCM has the worst clustering result. As shown in Figures 3c, 4c, 5c, 6c and 7c, for dataset Jain, the clustering results of both IKDC and SNN-DPC are superior. As shown in Table 4, on the Spiral dataset, IKDC, DPC, DBSCAN, KNN-DPC, and SNN-DPC all have good clustering effects, and only FCM has the worst clustering effect. Compared with FCM, IKDC improved the ACC, NMI, and ARI values by 0.66, 1, and 1.006, respectively. This shows that after introducing the fuzzy domain, IKDC is more effective.  
From Table 5, it can be concluded that IKDC outperforms the other five algorithms in clustering on the DIM512 dataset with higher dimensionality. In comparison with FCM with the worst clustering effect, the ACC, NMI, and ARI values of IKDC are improved by 0.223, 0.296, and 0.314. Therefore, IKDC has a better clustering effect in high-dimensional space.  
From Tables 4 and 5, it can be concluded that IKDC outperforms the other five clustering algorithms for the remaining five datasets, especially when the datasets are unevenly distributed and of high dimensionality.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Instances** & **Dimensions** & **Clusters** \\ \hline Aggregation & 788 & 2 & 7 \\ Flame & 240 & 2 & 2 \\ Jain & 373 & 2 & 2 \\ Pathbased & 300 & 2 & 3 \\ R15 & 600 & 2 & 15 \\ Spiral & 312 & 2 & 3 \\ D31 & 3100 & 2 & 31 \\ DIM512 & 1024 & 512 & 16 \\ S2 & 5000 & 2 & 15 \\ Compound & 399 & 2 & 6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Synthetic datasets.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **Instances** & **Dimensions** & **Clusters** \\ \hline Wine & 178 & 13 & 3 \\ WDBC & 569 & 30 & 2 \\ Seeds & 210 & 7 & 3 \\ Libras & 360 & 90 & 15 \\ Ionosphere & 351 & 34 & 2 \\ Waveform & 5000 & 21 & 3 \\ Waveform (noise) & 5000 & 40 & 3 \\ Spectrometer & 531 & 102 & 48 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Real datasets.  
Figure 4: Clustering effect of the KNN-DPC algorithm on Aggregation, Flame and Jain.  
Figure 5: Clustering effect of the SNN-DPC algorithm on Aggregation, Flame, and Jain.  
Figure 3: Clustering effect of the DBSCAN algorithm on Aggregation, Flame, and Jain.