Conceptualization, S.Z. and K.L.; methodology, S.Z.; software, S.Z.; validation, S.Z. and K.L.; formal analysis, S.Z.; investigation, S.Z.; resources, S.Z.; data curation, S.Z.; writing—original draft preparation, S.Z.; writing—review and editing, S.Z. and K.L.; visualization, S.Z. and K.L.; supervision, K.L. All authors have read and agreed to the published version of the manuscript.
Figure 1. Raw data distribution and core domain range.
Figure 1. Raw data distribution and core domain range.
Figure 2. The detailed steps of K-induction similarity.
Figure 2. The detailed steps of K-induction similarity.
Figure 3. Clustering effect of the DBSCAN algorithm on Aggregation, Flame, and Jain.
Figure 3. Clustering effect of the DBSCAN algorithm on Aggregation, Flame, and Jain.
Figure 4. Clustering effect of the KNN-DPC algorithm on Aggregation, Flame and Jain.
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 5. Clustering effect of the SNN-DPC algorithm on Aggregation, Flame, and Jain.
Figure 6. Clustering effect of the FCM algorithm on Aggregation, Flame, and Jain.
Figure 6. Clustering effect of the FCM algorithm on Aggregation, Flame, and Jain.
Figure 7. Clustering effect of the IKDC algorithm on Aggregation, Flame, and Jain.
Figure 7. Clustering effect of the IKDC algorithm on Aggregation, Flame, and Jain.
Figure 8. Influence of own parameters on experimental results.
Figure 8. Influence of own parameters on experimental results.
Table 1. Symbols and descriptions.
Table 1. Symbols and descriptions.
SymbolDescriptionXDglobal sample pointsX′a subset of sample points in the universexii-th sample pointρilocal density of sample point iδidistance from xi to the closest point with higher density than itθisolation partitionCrPthe core domain of the r-th clusterCrBthe boundary domain of the r-th clusterCrNthe noise domain of the r-th clusterTable 2. Synthetic datasets.
Table 2. Synthetic datasets.
DatasetInstancesDimensionsClustersAggregation78827Flame24022Jain37322Pathbased30023R15600215Spiral31223D313100231DIM512102451216S25000215Compound39926Table 3. Real datasets.
DatasetInstancesDimensionsClustersWine178133WDBC569302Seeds21073Libras3609015Ionosphere351342Waveform5000213Waveform (noise)5000403Spectrometer53110248Table 4. ACC, NMI, and ARI of six algorithms on different synthetic datasets.
Table 4. ACC, NMI, and ARI of six algorithms on different synthetic datasets.
AlgorithmACCNMIARIAlgorithmACCNMIARIAggregation Spiral IKDC1.0001.0001.000IKDC1.0001.0001.000DPC0.9950.9920.990DPC1.0001.0001.000DBSCAN0.9730.9580.958DBSCAN1.0001.0001.000KNN-DPC0.9970.9920.996KNN-DPC1.0001.0001.000SNN-DPC0.9780.9550.959SNN-DPC1.0001.0001.000FCM0.7780.8250.684FCM0.3400.000-0.006Flame D31 IKDC1.0001.0001.000IKDC0.9700.9620.953DPC1.0001.0001.000DPC0.9680.9580.936DBSCAN1.0001.0001.000DBSCAN0.9680.9570.935KNN-DPC1.0001.0001.000KNN-DPC0.9700.9600.940SNN-DPC0.9980.8990.950SNN-DPC0.9740.9630.974FCM0.8500.4420.488FCM0.8910.8620.936Jain DIM512 IKDC1.0001.0001.000IKDC0.9660.9510.956DPC0.9810.9760.970DPC0.9440.9400.935DBSCAN0.9280.8950.890DBSCAN0.8510.7740.749KNN-DPC0.9700.9600.940KNN-DPC0.9180.8970.890SNN-DPC1.0001.0001.000SNN-DPC0.9390.8960.926FCM0.7780.8310.707FCM0.7430.6550.6428Table 5. ACC, NMI, and ARI of six algorithms on different synthetic datasets.
Table 5. ACC, NMI, and ARI of six algorithms on different synthetic datasets.
AlgorithmACCNMIARIAlgorithmACCNMIARIPathbased S2 IKDC0.9800.9200.916IKDC0.9660.9510.956DPC0.7530.5550.472DPC0.9440.9400.935DBSCAN0.8230.7310.613DBSCAN0.8510.7740.749KNN-DPC0.7600.5610.561KNN-DPC0.9180.8970.890SNN-DPC0.9770.9010.929SNN-DPC0.9390.8960.926FCM0.7470.5500.465FCM0.7410.6900.694R15 Compound IKDC1.0001.0001.000IKDC0.8850.9130.899DPC0.9970.9940.993DPC0.8320.8730.833DBSCAN0.9930.9890.986DBSCAN0.8400.8280.844KNN-DPC0.9970.9940.993KNN-DPC0.8700.5520.809SNN-DPC0.9970.9940.993SNN-DPC0.8570.8530.835FCM0.9970.9650.993FCM0.5010.6190.406Table 6. ACC, NMI, and ARI of six algorithms on different real datasets.
Table 6. ACC, NMI, and ARI of six algorithms on different real datasets.
AlgorithmACCNMIARIAlgorithmACCNMIARIIonosphere Waveform IKDC1.0001.0001.000IKDC0.9800.9840.955DPC1.0001.0001.000DPC0.9680.9580.936DBSCAN1.0001.0001.000DBSCAN0.5240.1520.135KNN-DPC1.0001.0001.000KNN-DPC0.6350.2180.223SNN-DPC0.9980.8990.950SNN-DPC0.5980.3260.311FCM0.8500.4420.488FCM0.6280.3740.353Wine Waveform (noise) IKDC0.9520.8730.852IKDC0.9830.9790.959DPC0.8820.7100.627DPC0.9690.9580.936DBSCAN0.9100.7530.741DBSCAN0.9680.9570.935KNN-DPC0.9040.7430.727KNN-DPC0.9700.9600.940SNN-DPC0.9660.8780.899SNN-DPC0.9740.9630.974FCM0.9490.8500.834FCM0.8910.8620.936Table 7. ACC, NMI, and ARI of different clustering algorithms on different real datasets.
Table 7. ACC, NMI, and ARI of different clustering algorithms on different real datasets.
AlgorithmACCNMIARIAlgorithmACCNMIARILibras Spectrometer IKDC0.5030.5430.401IKDC0.9790.9750.975DPC0.4200.5140.345DPC0.9680.9580.936DBSCAN0.4580.6260.309DBSCAN0.9680.9570.935KNN-DPC0.4970.6340.361KNN-DPC0.9700.9600.940SNN-DPC0.4940.6610.393SNN-DPC0.9740.9630.974FCM0.1830.2160.069FCM0.8910.8620.936WDBC Seeds IKDC0.9170.7200.751IKDC0.9340.7630.830DPC0.8300.3730.373DPC0.9100.7160.742DBSCAN0.6310.5300.530DBSCAN0.6240.4230.487KNN-DPC0.8700.7660.436KNN-DPC0.9140.7340.766SNN-DPC0.8740.5350.650SNN-DPC0.9240.7540.789FCM0.9280.6090.631FCM0.9000.6910.727
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