1 Introduction
1.1 Literature review
1.2 The gap
1.3 The contribution
1.4 The structure of the paper
2 Related work
2.1 The basic theory of DBSCAN
2.2 The arithmetic optimization algorithm
2.3 The opposition-based learning
3 The proposed OBLAOA
4 The improved DBSCAN with OBLAOA
5 Numerical simulation
5.1 The benchmark functions
Function | Description | Range |
---|---|---|
\(F_{1}\) | \(f(x)= x_1^2 + {10^6}*\sum \limits _{i = 2}^D {x_i^2}\) | [− 100,100] |
\(F_{2}\) | \(f(x) = \sum \limits _{i = 1}^D {(x_i^2 - 10*\cos (2\pi {x_i})}\) | [− 100,100] |
\(F_{3}\) | \(f(x) = \sum \limits _{i = 1}^D {{{({{10}^6})}^{\frac{{i - 1}}{{D - 1}}}}*x_i^2}\) | [− 100,100] |
\(F_{4}\) | \(f(x) = {|{{{\left( {\sum \limits _{i = 1}^D {x_i^2} } \right) }^2} - {{\left( {\sum \limits _{i = 1}^D {{x_i}} } \right) }^2}} |^{1/2}} + \left( {0.5*\sum \limits _{i = 1}^D {x_i^2} + \sum \limits _{i = 1}^D {{x_i}} } \right) /D + 0.5\) | [− 100,100] |
\(F_{5}\) | \(f(x)= \sum \limits _{i = 1}^{D - 1} {(100*{{(x_i^2 - {x_{i + 1}})}^2} + {{({x_i} - 1)}^2})}\) | [− 100,100] |
\(F_{6}\) | \(f(x)= \sum \limits _{i = 1}^D {\frac{{x_i^2}}{{4000}}} - \prod \limits _{i = 1}^D {\cos \left( {\frac{{{x_i}}}{{\sqrt{i} }}} \right) + 1}\) | [− 100,100] |
\(F_{7}\) | \(f(x)= - 20*\exp ( - 0.2*\sqrt{\frac{1}{D}\sum \limits _{i = 1}^D {x_i^2} } ) - \exp \left( {\frac{1}{D}\sum \limits _{i = 1}^D {\cos (2\pi {x_i})} } \right) + 20 + e\) | [− 100,100] |
\(F_{8}\) | \(f(x)= {|{\sum \limits _{i = 1}^D {x_i^2} - D} |^{1/4}} + \left( {0.5\sum \limits _{i = 1}^D {x_i^2} + \sum \limits _{i = 1}^D {{x_i}} } \right) /D + 0.5\) | [− 100,100] |
5.2 The setting of experimental parameters
\(F_1\) | \(F_2\) | |||||||
---|---|---|---|---|---|---|---|---|
Avg | Best | Std | h | Avg | Best | Std | h | |
AOA | 2.94e+9 | 1.08e-3 | 3.10e+18 | 1 | 1.94e+3 | 1.77e+3 | 2.11e+4 | 1 |
DAOA | 1.04e+10 | 1.04e-10 | 3.97e+16 | 1 | 2.02e+3 | 2.17e+3 | 2.57e+3 | 1 |
IAOA | 2.95e+7 | 2.20e-198 | 3.43e+17 | 1 | 203.06 | 0 | 1.3e+5 | 1 |
ENGWO | 9.90e+9 | 9.85e-9 | 2.38e+16 | 1 | 2.31e+3 | 2.28e+3 | 1.5e+3 | 1 |
WSSA | 1.30e+10 | 1.30e-10 | 5.26e-9 | 1 | 2.59e+3 | 2.58e+3 | 869.1 | 1 |
OBLAOA | 2.62e+7 | 0 | 3.38e-17 | 0 | 179.94 | 0 | 2.11e+4 | 0 |
\(F_3\) | \(F_4\) | |||||||
---|---|---|---|---|---|---|---|---|
Avg | Best | Std | h | Avg | Best | Std | h | |
AOA | 218.02 | 200.89 | 2.59e+3 | 1 | 4.16e+4 | 9.31e+5 | 1.52e+11 | 1 |
DAOA | 559.48 | 468.61 | 28.37 | 1 | 7.74e+4 | 5.01e+5 | 2.23e+11 | 1 |
IAOA | 114.78 | 109.62 | 490.39 | 1 | 3.49e+5 | 3.29e+5 | 8.46e+10 | 1 |
ENGWO | 453.99 | 450.90 | 35.45 | 1 | 1.64e+5 | 1.35e+5 | 8.83e+10 | 1 |
WSSA | 559.48 | 559.48 | 0 | 1 | 5.95e+6 | 5.92e+6 | 1.50e+10 | 1 |
OBLAOA | 106.76 | 106.76 | 1.10e+13 | 0 | 2.37e+5 | 1.99e+5 | 9.47e+10 | 0 |
\(F_5\) | \(F_6\) | |||||||
---|---|---|---|---|---|---|---|---|
Avg | Best | h | Std | Avg | Best | Std | h | |
AOA | 2.71e+7 | 2.17e+3 | 3.40e+14 | 1 | 2.14e+3 | 2.86e+3 | 2.29e+3 | 1 |
DAOA | 6.04e+7 | 5.01e+3 | 3.77e+14 | 1 | 2.18e+3 | 2.05e+3 | 4.16e+3 | 1 |
IAOA | 1.53e+5 | 1700 | 1.10e+14 | 1 | 1.62e+3 | 1600 | 3.52e+3 | 1 |
ENGWO | 2.11e+7 | 2.09e+7 | 5.89e+12 | 1 | 2.14e+3 | 2.13e+3 | 330.07 | 1 |
WSSA | 2.85e+7 | 2.75e+7 | 2.85e+13 | 1 | 2.35e+3 | 2.35e+3 | 0.02 | 1 |
OBLAOA | 106.76 | 1700 | 1.10e+13 | 0 | 1.62e+3 | 1600 | 2.35e+3 | 0 |
\(F_{7}\) | \(F_{8}\) | |||||||
---|---|---|---|---|---|---|---|---|
Avg | Best | Std | h | Avg | Best | Std | h | |
AOA | 1.24e+07 | 1.42e+6 | 3.72e+13 | 1 | 0.29 | 3.19e+3 | 3.03e+3 | 1 |
DAOA | 1.67e+7 | 6.06e+6 | 4.70e+12 | 1 | 3.98e+3 | 3.68e+3 | 2.40e+4 | 1 |
IAOA | 06.89e+5 | 5.8e+5 | 6.84e11 | 1 | 3.33e+3 | 3.33+e3 | 1.10e+4 | 1 |
ENGWO | 7.42e+6 | 7.05e+06 | 7.08e+11 | 1 | 4.18e+3 | 4.13e+3 | 716.21 | 1 |
WSSA | 1.74e+6 | 1.74e+7 | 3.08e-36 | 1 | 4.4e+3 | 4.4e+3 | 0.32 | 1 |
OBLAOA | 3.23e+5 | 1.40e+5 | 8.19e+11 | 0 | 3.04 | 2.99e+3 | 9.45 | 0 |
\(F_1\) | \(F_2\) | |||||||
---|---|---|---|---|---|---|---|---|
Avg | Best | Std | h | Avg | Best | Std | h | |
AOA | 3.36e+10 | 3.2e-10 | 4.7e+17 | 1 | 5.7e+3 | 3.3e+3 | 4.9e+4 | 1 |
DAOA | 3.7e+10 | 3.6e-10 | 7.6e+15 | 1 | 5.7e+3 | 5.4e+3 | 3.5e+4 | 1 |
IAOA | 9.9e+7 | 2.2e-160 | 3e+18 | 1 | 109 | 0 | 3.2e+5 | 1 |
ENGWO | 3.2e+10 | 3.2e-10 | 1.04e+17 | 1 | 5.8e+3 | 5.7e+3 | 1.26e+3 | 1 |
WSSA | 3.7e+10 | 3.7e-10 | 1.3e-8 | 1 | 6.2e+3 | 6.2e+3 | 5.6e+22 | 1 |
OBLAOA | 7.7e+7 | 2.6e-177 | 2.8e+18 | 0 | 108 | 0 | 1.25e+5 | 0 |
\(F_3\) | \(F_4\) | |||||||
---|---|---|---|---|---|---|---|---|
Avg | Best | Std | h | Avg | Best | Std | h | |
AOA | 1.2e+3 | 12e+3 | 3.6e+3 | 1 | 1.24e+6 | 1.06e+6 | 9.2e+11 | 1 |
DAOA | 1.7e+3 | 1.62e+3 | 11 | 1 | 5.6e+6 | 3.6e+6 | 1.03e+13 | 1 |
IAOA | 341 | 333 | 4e+9 | 1 | 4.5e+5 | 4.17e+5 | 4.2e+11 | 1 |
ENGWO | 1.56e+3 | 01.56e+3 | 34 | 1 | 4.05e+6 | 4.01e+6 | 2.23e+11 | 1 |
WSSA | 1.69e+3 | 1.69e+3 | 0 | 1 | 1.45e+7 | 1.45e+7 | 1.6e+14 | 1 |
OBLAOA | 305 | 300 | 4e+3 | 0 | 4.5e+5 | 3.5e+5 | 4.5e+11 | 0 |
\(F_5\) | \(F_6\) | |||||||
---|---|---|---|---|---|---|---|---|
Avg | Best | Std | h | Avg | Best | Std | h | |
AOA | 8.1e+7 | 2.8e+4 | 4.5e+15 | 1 | 3.55e+3 | 3.35e+3 | 2.98e+3 | 1 |
DAOA | 2.2e+8 | 3.17e+6 | 1.13e+13 | 1 | 3.83e+3 | 3.56e+3 | 1.14e+3 | 1 |
IAOA | 4.9e+5 | 1700 | 1.13e+14 | 1 | 1.66e+3 | 1600 | 2.4e+4 | 1 |
ENGWO | 1.26e+8 | 1.25e+8 | 2.78e+13 | 1 | 3.71e+3 | 3.7e+3 | 405 | 1 |
WSSA | 1.84e+8 | 1.814e+8 | 1.08e+14 | 1 | 1.84e+8 | 1.81e+8 | 1.08e+14 | 1 |
OBLAOA | 4.7e+5 | 1700 | 1.13e+14 | 0 | 1.64e+3 | 1600 | 1.45e+4 | 0 |
\(F_{7}\) | \(F_{8}\) | |||||||
---|---|---|---|---|---|---|---|---|
Avg | Best | Std | h | Avg | Best | Std | h | |
AOA | 6.9e+7 | 1.06e+7 | 3.49e+15 | 1 | 7.6e+3 | 7.32e+3 | 4.78e+4 | 1 |
DAOA | 1.8e+8 | 6.12e+7 | 2.53e+15 | 1 | 7.65e+3 | 7.32e+3 | 4.99e+4 | 1 |
IAOA | 1.53e+7 | 1.45e+7 | 8.6e+13 | 1 | 6.74e+3 | 6.62e+3 | 7.3774e+4 | 1 |
ENGWO | 5.55e+7 | 5.46e+7 | 5.37e+13 | 1 | 8.19e+3 | 8.19e+3 | 1.06e+4 | 1 |
WSSA | 2.12e+8 | 2.12e+8 | 1.11e+11 | 1 | 8.72e+3 | 8.71e+3 | 1.24e+03 | 1 |
OBLAOA | 2.86e+6 | 7.6e+5 | 1.89e+14 | 0 | 6.6e+3 | 2.99e+3 | 5.05e+4 | 0 |
Engineering problem A: Welded Beam Design, WBD | ||||
---|---|---|---|---|
Avg | Best | Std | h | |
AOA | 101.40 | 2.47 | 2.46e+6 | 1 |
DAOA | 158.78 | 2.3768 | 34.54e+6 | 1 |
IAOA | 1217 | 2.85 | 1.32e+7 | 1 |
ENGWO | 1922 | 4.38 | 32.85e+7 | 1 |
WSSA | 335 | 235.41 | 352.12e+6 | 1 |
OBLAOA | 158.78 | 2.37 | 4.54e+6 | 0 |
Engineering problem B: compression spring design, CSD | ||||
---|---|---|---|---|
Avg | Best | Std | h | |
AOA | 12.33 | 6.44 | 16.22 | 1 |
DAOA | 11.75 | 7.12 | 137.92 | 1 |
IAOA | 9.15 | 9.82 | 129.11 | 1 |
ENGWO | 28.98 | 16.86 | 120.95 | 1 |
WSSA | 33.31 | 26.25 | 380.73 | 1 |
OBLAOA | 12.09 | 4.25 | 129.1167 | 0 |
Engineering problem C: design problems of I-beam, IBP | ||||
---|---|---|---|---|
Avg | Best | Std | h | |
AOA | 189.42 | 187.63 | 3.68 | 1 |
DAOA | 190.63 | 187.28 | 10.41 | 1 |
IAOA | 192.97 | 187 | 24.34 | 1 |
ENGWO | 188.05 | 187.73 | 1.48 | 1 |
WSSA | 188.73 | 186.73 | 5.46 | 1 |
OBLAOA | 189.47 | 186.42 | 5.43 | 0 |
5.3 Analysis of the results
6 Experiment and performance evaluation
6.1 The datasets
Dataset | Instance | Dimension | Cluster |
---|---|---|---|
Aggregation | 788 | 3 | 7 |
Compound | 399 | 3 | 6 |
Jain | 373 | 3 | 2 |
Iris | 150 | 5 | 3 |
Spiral | 251 | 3 | 3 |
Pathbased | 300 | 2 | 5 |
Wpbc | 198 | 34 | 2 |
Synthesis | 1980 | 3 | 5 |
R15 | 341 | 3 | 9 |
Vehicel | 846 | 19 | 4 |
6.2 The error index
6.3 Experiment settings
Dataset | EPS | MinPts |
---|---|---|
Aggregation | [1.0,3.0] | [2,25] |
Compound | [1.2,2.8] | [2,15] |
Jain | [2.4,3.3] | [4,16] |
Iris | [0.5,1.8] | [0,30] |
Spiral | [1.1,4.0] | [0,10] |
Pathbased | [1.6,2.1] | [2,6] |
Wpbc | [0.5,1.2] | [2,12] |
Synthesis | [0.5,6.6] | [2,10] |
R15 | [0.5,1.2] | [0,20] |
Vehicel | [0.3,1.1] | [3,12] |
6.4 Experimental results of the optimization algorithm
Dataset | Algorithm | Evaluation index | |||
---|---|---|---|---|---|
Accuracy | DBI | RI | SIL | ||
Aggregation | WOA-DBSCAN | 0.9949 | 0.3651 | 1 | 0.6813 |
SSA-DBSCAN | 0.9949 | 0.3651 | 1 | 0.6813 | |
WSSA-DBSCAN | 0.9949 | 0.3651 | 1 | 0.6813 | |
ENGWO-DBSCAN | 0.9949 | 0.3651 | 1 | 0.6813 | |
AOA-DBSCAN | 0.9949 | 0.3651 | 1 | 0.6813 | |
dAOA-DBSCAN | 0.9949 | 0.3651 | 1 | 0.6813 | |
IAOA-DBSCAN | 0.9949 | 0.3651 | 1 | 0.6813 | |
OBLAOA-DBSCAN | 0.9949 | 0.3651 | 1 | 0.6813 | |
Compound | WOA-DBSCAN | 0.7443 | 0.4221 | 0.8916 | 0.6488 |
SSA-DBSCAN | 0.7757 | 0.4334 | 0.9083 | 0.5890 | |
WSSA-DBSCAN | 0.7453 | 0.4218 | 0.8922 | 0.6411 | |
ENGWO-DBSCAN | 0.8321 | 1.0888 | 0.9324 | 0.1298 | |
AOA-DBSCAN | 0.7966 | 1.0815 | 0.9171 | 0.1041 | |
dAOA-DBSCAN | 0.8375 | 1.0888 | 0.9347 | 0.1341 | |
IAOA-DBSCAN | 0.7966 | 1.0815 | 0.9171 | 0.1041 | |
OBLAOA-DBSCAN | 0.8538 | 1.0941 | 0.9415 | 0.1488 | |
Jain | WOA-DBSCAN | 0.6728 | 0.4920 | 0.8517 | 0.4272 |
SSA-DBSCAN | 0.6518 | 0.4828 | 0.8427 | 0.4047 | |
WSSA-DBSCAN | 0.6518 | 0.4828 | 0.8427 | 0.4047 | |
ENGWO-DBSCAN | 0.6728 | 0.4920 | 0.8517 | 0.4272 | |
AOA-DBSCAN | 0.6834 | 0.4999 | 0.8562 | 0.4355 | |
dAOA-DBSCAN | 0.6834 | 0.4999 | 0.8562 | 0.4355 | |
IAOA-DBSCAN | 0.7151 | 0.5037 | 0.8700 | 0.4064 | |
OBLAOA-DBSCAN | 0.7151 | 0.5037 | 0.8700 | 0.4064 | |
Iris | WOA-DBSCAN | 0.9800 | 0.3773 | 0.9911 | 0.6642 |
SSA-DBSCAN | 0.9400 | 0.3760 | 0.9740 | 0.7148 | |
WSSA-DBSCAN | 0.9600 | 0.3765 | 0.9825 | 0.7272 | |
ENGWO-DBSCAN | 1 | 0.3654 | 1 | 0.7478 | |
AOA-DBSCAN | 0.9400 | 0.3760 | 0.9740 | 0.7148 | |
dAOA-DBSCAN | 0.9400 | 0.3760 | 0.9740 | 0.7148 | |
IAOA-DBSCAN | 0.9600 | 0.3765 | 0.9825 | 0.7272 | |
OBLAOA-DBSCAN | 1 | 0.3654 | 1 | 0.7478 | |
Spiral | WOA-DBSCAN | 1 | 2.2296 | 1 | –0.1081 |
SSA-DBSCAN | 1 | 2.2296 | 1 | –0.1081 | |
WSSA-DBSCAN | 1 | 2.2296 | 1 | –0.1081 | |
ENGWO-DBSCAN | 1 | 2.2296 | 1 | –0.1081 | |
AOA-DBSCAN | 1 | 2.2296 | 1 | –0.1081 | |
dAOA-DBSCAN | 1 | 2.2296 | 1 | –0.1081 | |
IAOA-DBSCAN | 1 | 2.2296 | 1 | –0.1081 | |
OBLAOA-DBSCAN | 1 | 2.2296 | 1 | –0.1081 |
Dataset | Algorithm | Evaluation index | |||
---|---|---|---|---|---|
Accuracy | DBI | RI | SIL | ||
WOA-DBSCAN | 0.8100 | 0.9482 | 0.8129 | 0.4349 | |
SSA-DBSCAN | 0.8100 | 0.9482 | 0.8129 | 0.4349 | |
WSSA-DBSCAN | 0.8100 | 0.9482 | 0.8129 | 0.4349 | |
Pathbased | ENGWO-DBSCAN | 0.8100 | 0.9482 | 0.8129 | 0.4349 |
AOA-DBSCAN | 0.8233 | 0.9482 | 0.8158 | 0.4515 | |
dAOA-DBSCAN | 0.8233 | 0.9482 | 0.8158 | 0.4515 | |
IAOA-DBSCAN | 0.8233 | 0.9482 | 0.8158 | 0.4515 | |
OBLAOA-DBSCAN | 0.8233 | 0.9482 | 0.8158 | 0.4515 | |
WOA-DBSCAN | 0.1314 | 0.3792 | 0.6699 | 0.0751 | |
SSA-DBSCAN | 0.2595 | 0.4859 | 0.7075 | 0.1425 | |
WSSA-DBSCAN | 0.2595 | 0.4859 | 0.7075 | 0.1425 | |
Wpbc | ENGWO-DBSCAN | 0.8913 | 0.7829 | 0.9505 | 0.3282 |
AOA-DBSCAN | 0.8270 | 0.7552 | 0.9221 | 0.2937 | |
dAOA-DBSCAN | 0.8270 | 0.7552 | 0.9221 | 0.2937 | |
IAOA-DBSCAN | 0.8913 | 0.7829 | 0.9505 | 0.3282 | |
OBLAOA-DBSCAN | 0.9346 | 0.8023 | 0.9700 | 0.3447 | |
WOA-DBSCAN | 0.9884 | 0.1926 | 0.9956 | 0.8542 | |
SSA-DBSCAN | 0.9860 | 0.2152 | 0.9930 | 0.8606 | |
WSSA-DBSCAN | 0.9884 | 0.1926 | 0.9956 | 0.8542 | |
Synthesis | ENGWO-DBSCAN | 0.9970 | 0.1791 | 0.9985 | 0.8534 |
AOA-DBSCAN | 0.9970 | 0.1791 | 0.9985 | 0.8534 | |
dAOA-DBSCAN | 0.9970 | 0.1791 | 0.9985 | 0.8534 | |
IAOA-DBSCAN | 0.9860 | 0.2152 | 0.9930 | 0.8606 | |
OBLAOA-DBSCAN | 0.9998 | 0.1787 | 0.9999 | 0.8517 | |
WOA-DBSCAN | 1 | 0.3044 | 1 | 0.8966 | |
SSA-DBSCAN | 0.9971 | 0.3047 | 0.9986 | 0.8946 | |
WSSA-DBSCAN | 1 | 0.3044 | 1 | 0.8966 | |
R15 | ENGWO-DBSCAN | 1 | 0.3044 | 1 | 0.8966 |
AOA-DBSCAN | 1 | 0.3044 | 1 | 0.8966 | |
dAOA-DBSCAN | 1 | 0.3044 | 1 | 0.8966 | |
IAOA-DBSCAN | 1 | 0.3044 | 1 | 0.8966 | |
OBLAOA-DBSCAN | 1 | 0.3044 | 1 | 0.8966 | |
WOA-DBSCAN | 0.4823 | 1.5198 | 0.9605 | 0.1637 | |
SSA-DBSCAN | 0.9561 | 1.5527 | 0.9835 | 0.1772 | |
WSSA-DBSCAN | 0.9561 | 1.5527 | 0.9835 | 0.1772 | |
Vehicle | ENGWO-DBSCAN | 0.9624 | 1.5534 | 0.9859 | 0.1790 |
AOA-DBSCAN | 0.9561 | 1.5527 | 0.9835 | 0.1772 | |
dAOA-DBSCAN | 0.9248 | 1.5301 | 0.9718 | 0.1701 | |
IAOA-DBSCAN | 0.9624 | 1.5534 | 0.9859 | 0.1790 | |
OBLAOA-DBSCAN | 0.9656 | 1.5541 | 0.9871 | 0.1808 |
Dataset | Algorithm | Evaluation index | |||
---|---|---|---|---|---|
NMI | Homogeneity | Completeness | Vmeasure | ||
Aggregation | WOA-DBSCAN | 1 | 1 | 1 | 1 |
SSA-DBSCAN | 1 | 1 | 1 | 1 | |
WSSA-DBSCAN | 1 | 1 | 1 | 1 | |
ENGWO-DBSCAN | 1 | 1 | 1 | 1 | |
AOA-DBSCAN | 1 | 1 | 1 | 1 | |
dAOA-DBSCAN | 1 | 1 | 1 | 1 | |
IAOA-DBSCAN | 1 | 1 | 1 | 1 | |
OBLAOA-DBSCAN | 1 | 1 | 1 | 1 | |
Compound | WOA-DBSCAN | 0.8073 | 0.9531 | 0.6838 | 0.7963 |
SSA-DBSCAN | 0.8021 | 0.8928 | 0.7207 | 0.7976 | |
WSSA-DBSCAN | 0.8061 | 0.9478 | 0.6856 | 0.7956 | |
ENGWO-DBSCAN | 0.8736 | 0.9434 | 0.8089 | 0.8710 | |
AOA-DBSCAN | 0.8364 | 0.9118 | 0.7672 | 0.8333 | |
dAOA-DBSCAN | 0.8796 | 0.9488 | 0.8154 | 0.8770 | |
IAOA-DBSCAN | 0.8364 | 0.9118 | 0.7672 | 0.8333 | |
OBLAOA-DBSCAN | 0.9049 | 0.9729 | 0.8417 | 0.9026 | |
Jain | WOA-DBSCAN | 0.5987 | 0.6584 | 0.5409 | 0.5939 |
SSA-DBSCAN | 0.5781 | 0.6435 | 0.5194 | 0.5748 | |
WSSA-DBSCAN | 0.5781 | 0.6435 | 0.5194 | 0.5748 | |
ENGWO-DBSCAN | 0.5987 | 0.6584 | 0.5409 | 0.5939 | |
AOA-DBSCAN | 0.6062 | 0.6660 | 0.5518 | 0.6035 | |
dAOA-DBSCAN | 0.6062 | 0.6660 | 0.5518 | 0.6035 | |
IAOA-DBSCAN | 0.6353 | 0.6894 | 0.5855 | 0.6332 | |
OBLAOA-DBSCAN | 0.6353 | 0.6894 | 0.5855 | 0.6332 | |
Iris | WOA-DBSCAN | 0.9702 | 0.9703 | 0.9701 | 0.9702 |
SSA-DBSCAN | 0.9306 | 0.9311 | 0.9300 | 0.9306 | |
WSSA-DBSCAN | 0.9488 | 0.9490 | 0.9486 | 0.9488 | |
ENGWO-DBSCAN | 1 | 1 | 1 | 1 | |
AOA-DBSCAN | 0.9306 | 0.9311 | 0.9300 | 0.9306 | |
dAOA-DBSCAN | 0.9306 | 0.9311 | 0.9300 | 0.9306 | |
IAOA-DBSCAN | 0.9488 | 0.9490 | 0.9486 | 0.9488 | |
OBLAOA-DBSCAN | 1 | 1 | 1 | 1 | |
Spiral | WOA-DBSCAN | 1 | 1 | 1 | 1 |
SSA-DBSCAN | 1 | 1 | 1 | 1 | |
WSSA-DBSCAN | 1 | 1 | 1 | 1 | |
ENGWO-DBSCAN | 1 | 1 | 1 | 1 | |
AOA-DBSCAN | 1 | 1 | 1 | 1 | |
dAOA-DBSCAN | 1 | 1 | 1 | 1 | |
IAOA-DBSCAN | 1 | 1 | 1 | 1 | |
OBLAOA-DBSCAN | 1 | 1 | 1 | 1 |
Dataset | Algorithm | Evaluation index | |||
---|---|---|---|---|---|
NMI | Homogeneity | Completeness | SIL | ||
Pathbased | WOA-DBSCAN | 0.6907 | 0.7114 | 0.6706 | 0.6904 |
SSA-DBSCAN | 0.6907 | 0.7114 | 0.6706 | 0.6904 | |
WSSA-DBSCAN | 0.6907 | 0.7114 | 0.6706 | 0.6904 | |
ENGWO-DBSCAN | 0.6907 | 0.7114 | 0.6706 | 0.6904 | |
AOA-DBSCAN | 0.7012 | 0.7226 | 0.6804 | 0.7009 | |
dAOA-DBSCAN | 0.7012 | 0.7226 | 0.6804 | 0.7009 | |
IAOA-DBSCAN | 0.7012 | 0.7226 | 0.6804 | 0.7009 | |
OBLAOA-DBSCAN | 0.7012 | 0.7226 | 0.6804 | 0.7009 | |
Wpbc | WOA-DBSCAN | 0.1655 | 0.3324 | 0.0824 | 0.1320 |
SSA-DBSCAN | 0.2649 | 0.4102 | 0.1711 | 0.2415 | |
WSSA-DBSCAN | 0.2649 | 0.4102 | 0.1711 | 0.2415 | |
ENGWO-DBSCAN | 0.8199 | 0.8443 | 0.7961 | 0.8195 | |
AOA-DBSCAN | 0.7438 | 0.7817 | 0.7078 | 0.7429 | |
dAOA-DBSCAN | 0.7438 | 0.7817 | 0.7078 | 0.7429 | |
IAOA-DBSCAN | 0.8199 | 0.8443 | 0.7961 | 0.8195 | |
OBLAOA-DBSCAN | 0.8786 | 0.8936 | 0.8637 | 0.8784 | |
Synthesis | WOA-DBSCAN | 0.9674 | 0.9820 | 0.9530 | 0.9673 |
SSA-DBSCAN | 0.9505 | 0.9809 | 0.9386 | 0.9593 | |
WSSA-DBSCAN | 0.9674 | 0.9820 | 0.9530 | 0.9673 | |
ENGWO-DBSCAN | 0.9836 | 0.9914 | 0.9758 | 0.9835 | |
AOA-DBSCAN | 0.9836 | 0.9914 | 0.9758 | 0.9835 | |
dAOA-DBSCAN | 0.9836 | 0.9914 | 0.9758 | 0.9835 | |
IAOA-DBSCAN | 0.9505 | 0.9809 | 0.9386 | 0.9593 | |
OBLAOA-DBSCAN | 0.9934 | 0.9980 | 0.9888 | 0.9934 | |
R15 | WOA-DBSCAN | 1 | 1 | 1 | 1 |
SSA-DBSCAN | 0.9937 | 0.9937 | 0.9937 | 0.9937 | |
WSSA-DBSCAN | 1 | 1 | 1 | 1 | |
ENGWO-DBSCAN | 1 | 1 | 1 | 1 | |
AOA-DBSCAN | 1 | 1 | 1 | 1 | |
dAOA-DBSCAN | 1 | 1 | 1 | 1 | |
IAOA-DBSCAN | 1 | 1 | 1 | 1 | |
OBLAOA-DBSCAN | 1 | 1 | 1 | 1 | |
Vehicle | WOA-DBSCAN | 0.8938 | 0.8953 | 0.8924 | 0.8938 |
SSA-DBSCAN | 0.9436 | 0.9439 | 0.9432 | 0.9436 | |
WSSA-DBSCAN | 0.9436 | 0.9439 | 0.9432 | 0.9436 | |
ENGWO-DBSCAN | 0.9500 | 0.9503 | 0.9497 | 0.9500 | |
AOA-DBSCAN | 0.9436 | 9439 | 0.9432 | 0.9436 | |
dAOA-DBSCAN | 0.9161 | 0.9169 | 0.9154 | 0.9161 | |
IAOA-DBSCAN | 0.9500 | 0.9503 | 0.9497 | 0.9500 | |
OBLAOA-DBSCAN | 0.9535 | 0.9538 | 0.9533 | 0.9585 |
6.5 Experimental results of clustering algorithm
Dataset | Algorithm | Evaluation index | |||
---|---|---|---|---|---|
Accuracy | DBI | RI | SIL | ||
Aggregation | K-means | 0.9226 | 0.8668 | 0.5323 | 0.6729 |
Spectral | 0.9727 | 0.9870 | 0.3853 | 0.6808 | |
Optics | 0.5533 | 0.8301 | 0.9274 | 0.4362 | |
DPC | 0.6586 | 0.3738 | 0.9055 | 0.3023 | |
DBSCAN | 0.9898 | 0.3657 | 0.9993 | 0.5877 | |
OBLAOA-DBSCAN |
0.9949
|
0.3651
|
1
|
0.6813
| |
Compound | K-means | 0.5740* | 0.6115 | 0.8234 | 0.5329 |
Spectral | 0.5789 | 0.5692 | 0.8462 | 0.606 | |
Optics | 0.4286 | 0.9662 | 0.9302 | 0.0496 | |
DPC | 0.2130 |
0.4052
| 0.8444 | 0.3998 | |
DBSCAN | 0.8450* | 1.0888 | 0.9347 | 0.1341 | |
OBLAOA-DBSCAN |
0.8538
| 1.0941 |
0.9415
|
0.1488
| |
Jain | K-means | 0.7748 | 0.3923 | 0.6501 |
0.6722
|
Spectral | 0.7105 |
0.3879
| 0.5875 | 0.6466 | |
Optics | 0.1930 | 0.5667 | 0.6876 | 0.3049 | |
DPC | 0.6793 | 2.1268 | 0.5624 | 0.0688 | |
DBSCAN | 0.6834 | 0.4999 | 0.8562 | 0.4355 | |
OBLAOA-DBSCAN |
0.7151
| 0.5037 |
0.8700
| 0.4064 | |
Iris | K-means | 0.8830* | 0.3960 | 0.8997 | 0.7242 |
Spectral | 0.9933 | 0.3824 | 0.9910 | 0.7540 | |
Optics | 0.6600 | 0.6453 | 0.7719 | 0.6943 | |
DPC | 0.9067 | 0.3902 | 0.8923 | 0.7023 | |
DBSCAN | 0.6400* |
0.3654
|
1
|
0.7478
| |
OBLAOA-DBSCAN |
1
|
0.3654
|
1
|
0.7478
| |
Spiral | K-means | 0.3720 | 0.6149 | 0.5156 | 0.5492 |
Spectral | 0.2815 | 0.5707 | 0.5339 | 0.5415 | |
Optics | 0.9760 | 2.1960 | 0.9888 | –0.0206 | |
DPC |
1
|
2.2296
|
1
|
–0.1081
| |
DBSCAN |
1
|
2.2296
|
1
|
–0.1081
| |
OBLAOA-DBSCAN |
1
|
2.2296
|
1
|
–0.1081
| |
Pathbased | K-means | 0.7500 | 0.4437 | 0.7319 | 0.7482 |
Spectral | 0.7500 | 0.4437 | 0.7319 | 0.7482 | |
Optics | 0.6167 | 1.3392 | 0.7499 | 0.2123 | |
DPC | 0.6467 | 0.8539 | 0.6769 | 0.4039 | |
DBSCAN | 0.8100 | 0.9482 | 0.8129 | 0.4349 | |
OBLAOA-DBSCAN |
0.8233
|
0.9482
|
0.8158
|
0.4515
| |
Wpbc | K-means | 0.6010 | 1 | 0.5180 | 0.2872 |
Spectral | 0.6041 | 1.4287 | 0.5201 | 0.0796 | |
Optics | 0.7020 | 1.6713 | 0.5795 | 0.3222 | |
DPC | 0.6670 | 0.2529 | 0.6308 | 0.5213 | |
DBSCAN | 0.8270 | 0.7552 | 0.9221 | 0.2937 | |
OBLAOA-DBSCAN |
0.9346
|
0.8023
|
0.9700
|
0.3447
| |
Synthesis | K-means | 0.6074 | 0.5452 | 0.7573 | 0.6496 |
Spectral | 0.8025 | 0.2735 | 0.9018 | 0.7964 | |
Optics | 0.9788 | 0.3227 | 0.9989 | 0.8517 | |
DPC | 0.9829 | 0.3680 | 0.9965 | 0.7789 | |
DBSCAN | 0.9884 | 0.1926 | 0.9956 | 0.8542 | |
OBLAOA-DBSCAN |
0.9998
|
0.1787
|
0.9999
|
0.8517
| |
R15 | K-means | 0.8106 | 0.4353 | 0.9598 | 0.6844 |
Spectral | 0.8409 | 0.3953 | 0.9659 | 0.7473 | |
Optics | 0.1202 | 1.0480 | 0.2310 | 0.5570 | |
DPC | 0.9941 | 0.3500 | 0.9973 | 0.8398 | |
DBSCAN |
1
|
0.3044
|
1
|
0.8966
| |
OBLAOA-DBSCAN |
1
|
0.3044
|
1
|
0.8966
| |
Vehicle | K-means | 0.2920 | 1.4350 | 0.6530 | 0.3075 |
Spectral | 0.3014 |
0.7864
| 0.6903 |
0.3264
| |
Optics | 0.2577 | 0.9972 | 0.2625 | 0.2327 | |
DPC | 0.3262 | 0.8936 | 0.5118 | 0.0943 | |
DBSCAN | 0.9309 | 1.5369 | 0.9741 | 0.1717 | |
OBLAOA-DBSCAN |
0.9656
| 1.7856 |
0.9871
| 0.1808 |
Dataset | Algorithms | Evaluation Index | |||
---|---|---|---|---|---|
NMI | Homogeneity | Completeness | Vmeasure | ||
Aggregation | K-means | 0.8509* | 0.7911 | 0.8722 | 0.8297 |
Spectral | 0.9927 | 0.9912 | 0.9942 | 0.9927 | |
Optics | 0.8833 | 0.9766 | 0.7990 | 0.8789 | |
DPC | 0.9769* | 0.8221 | 0.7950 | 0.8083 | |
DBSCAN | 0.9960 | 0.9954 | 0.9966 | 0.9960 | |
OBLAOA-DBSCAN |
1
|
1
|
1
|
1
| |
Compound | K-means | 0.6604 | 0.6351 | 0.6867 | 0.6599 |
Spectral | 0.7236 | 0.6890 | 0.7600 | 0.7228 | |
Optics | 0.8317 | 0.9104 | 0.7598 | 0.8283 | |
DPC | 0.7597 | 0.7639 | 0.7559 | 0.7597 | |
DBSCAN | 0.8796 | 0.9488 | 0.8154 | 0.8770 | |
OBLAOA-DBSCAN |
0.9049
|
0.9729
|
0.8417
|
0.9026
| |
Jain | K-means | 0.3690* | 0.3375 | 0.4070 | 0.3690 |
Spectral | 0.3072 | 0.2804 | 0.3367 | 0.3060 | |
Optics | 0.2216 | 0.3209 | 0.1530 | 0.2072 | |
DPC | 0.6183* | 0.1048 | 0.1264 | 0.1146 | |
DBSCAN | 0.6062 | 0.6660 | 0.5518 | 0.6035 | |
OBLAOA-DBSCAN |
0.6353
|
0.6894
|
0.5855
|
0.6332
| |
Iris | K-means | 7.7766* | 0.7650 | 0.7515 | 0.7582 |
Spectral | 0.9702 | 0.9703 | 0.9701 | 0.9702 | |
Optics | 0.7220 | 0.9063 | 0.5752 | 0.7037 | |
DPC | 0.8350* | 0.7960 | 0.8156 | 0.8057 | |
DBSCAN |
1
|
1.0000
|
1
|
1
| |
OBLAOA-DBSCAN |
1
|
1.0000
|
1
|
1
| |
Spiral | K-means | 0.0636 | 0.0619 | 0.0654 | 0.0636 |
Spectral | 0.0586 | 0.0579 | 0.0594 | 0.0586 | |
Optics | 0.9582 | 0.9597 | 0.9567 | 0.9582 | |
DPC |
1
|
1
|
1
|
1
| |
DBSCAN |
1
|
1
|
1
|
1
| |
OBLAOA-DBSCAN |
1
|
1
|
1
|
1
| |
Pathbased | K-means | 0.5463* | 0.5846 | 0.5140 | 0.5470 |
Spectral | 0.5482 | 0.5846 | 0.5140 | 0.5470 | |
Optics | 0.6398 | 0.7799 | 0.5248 | 0.6274 | |
DPC | 0.5390* | 0.4845 | 0.3597 | 0.4129 | |
DBSCAN | 0.6907 | 0.7114 | 0.6706 | 0.6904 | |
OBLAOA-DBSCAN |
0.7012
|
0.7226
|
0.6804
|
0.7009
| |
Wpbc | K-means | 0.0270 | 0.0241 | 0.0302 | 0.0268 |
Spectral | 0.4389 | 0.5421 | 0.3553 | 0.4293 | |
Optics | 0.0089 | 0.0124 | 0.0064 | 0.0084 | |
DPC | 0.0104 | 0.0432 | 0.0025 | 0.0047 | |
DBSCAN | 0.7438 | 0.7817 | 0.7078 | 0.7429 | |
OBLAOA-DBSCAN |
0.8786
|
0.8936
|
0.8637
|
0.8784
| |
Synthesis | K-means | 0.6313 | 0.8546 | 0.4734 | 0.6309 |
Spectral | 0.8209 | 0.7201 | 0.9346 | 0.8140 | |
Optics | 0.9826 | 0.9801 | 0.9852 | 0.9826 | |
DPC | 0.9726 | 0.9619 | 0.9835 | 0.9726 | |
DBSCAN | 0.9674 | 0.9820 | 0.9530 | 0.9673 | |
OBLAOA-DBSCAN |
0.9934
|
0.9980
|
0.9888
|
0.9934
| |
R15 | K-means | 0.9942* | 0.8839 | 0.9182 | 0.9007 |
Spectral | 0.9441 | 0.9225 | 0.9630 | 0.9439 | |
Optics | 0.2991 | 0.1244 | 0.7190 | 0.2122 | |
DPC | 0.9933* | 0.9874 | 0.9874 | 0.9874 | |
DBSCAN |
1
|
1
|
1
|
1
| |
OBLAOA-DBSCAN |
1
|
1
|
1
|
1
| |
Vehicle | K-means | 0.0999 | 0.0997 | 1 | 0.0999 |
Spectral | 0.3927 | 0.3489 | 0.4420 | 0.3900 | |
Optics | 0.0351 | 0.0078 | 0.1585 | 0.0148 | |
DPC | 0.1106 | 0.0770 | 0.1587 | 0.1037 | |
DBSCAN | 0.9208 | 0.9215 | 0.9202 | 0.9208 | |
OBLAOA-DBSCAN |
0.9535
|
0.9538
|
0.9533
|
0.9585
|