Applied Sciences, Vol. 13, Pages 322: A Novel Density Peaks Clustering Algorithm with Isolation Kernel and K-Induction

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.

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Figure 2. The detailed steps of K-induction similarity.

Figure 2. The detailed steps of K-induction similarity.

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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.

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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.

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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.

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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.

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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.

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Figure 8. Influence of own parameters on experimental results.

Figure 8. Influence of own parameters on experimental results.

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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 cluster

Table 2. Synthetic datasets.

Table 2. Synthetic datasets.

DatasetInstancesDimensionsClustersAggregation78827Flame24022Jain37322Pathbased30023R15600215Spiral31223D313100231DIM512102451216S25000215Compound39926

Table 3. Real datasets.

DatasetInstancesDimensionsClustersWine178133WDBC569302Seeds21073Libras3609015Ionosphere351342Waveform5000213Waveform (noise)5000403Spectrometer53110248

Table 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-DPC0.9390.8960.926FCM0.7780.8310.707FCM0.7430.6550.6428

Table 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-DPC0.8570.8530.835FCM0.9970.9650.993FCM0.5010.6190.406

Table 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-DPC0.9740.9630.974FCM0.9490.8500.834FCM0.8910.8620.936

Table 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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