Journal of Computer Applications ›› 2024, Vol. 44 ›› Issue (3): 831-841.DOI: 10.11772/j.issn.1001-9081.2023030351
Special Issue: 先进计算
• Advanced computing • Previous Articles Next Articles
Lin SUN1(), Menghan LIU2
Received:
2023-04-03
Revised:
2023-06-05
Accepted:
2023-06-14
Online:
2023-10-10
Published:
2024-03-10
Contact:
Lin SUN
About author:
LIU Menghan, born in 1996, M. S. candidate. Her research interests include data mining.
Supported by:
通讯作者:
孙林
作者简介:
刘梦含(1996—),女,河南周口人,硕士研究生,主要研究方向:数据挖掘。
基金资助:
CLC Number:
Lin SUN, Menghan LIU. K-means clustering based on adaptive cuckoo optimization feature selection[J]. Journal of Computer Applications, 2024, 44(3): 831-841.
孙林, 刘梦含. 基于自适应布谷鸟优化特征选择的K-means聚类[J]. 《计算机应用》唯一官方网站, 2024, 44(3): 831-841.
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URL: https://www.joca.cn/EN/10.11772/j.issn.1001-9081.2023030351
函数 | 公式 | 变量范围 | 理论最优值 |
---|---|---|---|
Sphere | [-5.12,5.12] D' | 0 | |
Step | [-100,100] D' | 0 | |
Rosenbrock | [-2.048,2.048] D' | 0 | |
Quartic with noise | [-1.28,1.28] D' | 0 | |
Schwefel 2.21 | [-100,100] D' | 0 | |
Schwefel 1.2 | [-100,100] D' | 0 | |
Griewank | [-600,600] D' | 0 | |
Penalized 2 | [-50,50] D' | 0 | |
Ackley | [-30,30] D' | 0 | |
Penalized 1 | [-50,50] D' | 0 |
Tab. 1 Information of ten benchmark functions
函数 | 公式 | 变量范围 | 理论最优值 |
---|---|---|---|
Sphere | [-5.12,5.12] D' | 0 | |
Step | [-100,100] D' | 0 | |
Rosenbrock | [-2.048,2.048] D' | 0 | |
Quartic with noise | [-1.28,1.28] D' | 0 | |
Schwefel 2.21 | [-100,100] D' | 0 | |
Schwefel 1.2 | [-100,100] D' | 0 | |
Griewank | [-600,600] D' | 0 | |
Penalized 2 | [-50,50] D' | 0 | |
Ackley | [-30,30] D' | 0 | |
Penalized 1 | [-50,50] D' | 0 |
函数 | 算法 | best | worst | std | mean |
---|---|---|---|---|---|
f1 | PSO | 1.80E+02 | 1.30E+02 | 1.53E+01 | 1.54E+02 |
ABC | 3.59E+01 | 2.63E+01 | 2.95E+00 | 3.18E+01 | |
CS | 3.73E+00 | 1.34E+00 | 6.39E-01 | 2.24E+00 | |
IDCS | 5.50E+00 | 3.24E+00 | 6.33E-01 | 4.06E+00 | |
f2 | PSO | 1.83E+02 | 1.37E+02 | 1.38E+01 | 1.58E+02 |
ABC | 4.90E+01 | 2.79E+01 | 5.78E+00 | 3.59E+01 | |
CS | 4.40E+00 | 1.64E+00 | 7.18E-01 | 2.85E+00 | |
IDCS | 5.60E+00 | 3.66E+00 | 6.56E-01 | 4.52E+00 | |
f3 | PSO | 1.83E+05 | 1.08E+05 | 2.04E+04 | 1.50E+05 |
ABC | 2.54E+05 | 1.18E+05 | 4.02E+04 | 1.96E+05 | |
CS | 1.01E+03 | 4.67E+02 | 1.50E+02 | 6.97E+02 | |
IDCS | 7.11E+02 | 3.47E+02 | 9.73E+01 | 5.66E+02 | |
f4 | PSO | 4.87E+04 | 2.61E+04 | 6.31E+03 | 3.36E+04 |
ABC | 6.80E+04 | 2.26E+04 | 1.27E+04 | 3.72E+04 | |
CS | 7.17E+01 | 1.83E+01 | 1.65E+01 | 3.76E+01 | |
IDCS | 7.08E+01 | 1.49E+01 | 1.58E+01 | 3.02E+01 | |
f5 | PSO | 4.79E+00 | 3.56E+00 | 3.25E-01 | 4.30E+00 |
ABC | 9.21E+00 | 8.08E+00 | 3.41E-01 | 8.78E+00 | |
CS | 2.11E+00 | 1.63E+00 | 1.58E-01 | 1.86E+00 | |
IDCS | 1.38E+00 | 1.04E+00 | 8.59E-02 | 1.20E+00 | |
f6 | PSO | 7.62E+02 | 3.00E+02 | 1.34E+02 | 4.89E+02 |
ABC | 1.14E+03 | 9.39E+02 | 6.45E+01 | 1.02E+03 | |
CS | 2.09E+02 | 1.22E+02 | 2.58E+01 | 1.69E+02 | |
IDCS | 1.28E+01 | 5.80E+00 | 2.25E+00 | 9.94E+00 | |
f7 | PSO | 1.05E+00 | 1.03E+00 | 6.10E-03 | 1.04E+00 |
ABC | 8.84E-01 | 6.90E-01 | 5.80E-02 | 7.82E-01 | |
CS | 2.55E-01 | 9.85E-02 | 4.49E-02 | 1.53E-01 | |
IDCS | 1.81E-01 | 8.41E-02 | 2.94E-02 | 1.23E-01 | |
f8 | PSO | 3.20E+01 | 2.25E+01 | 2.83E+00 | 2.70E+01 |
ABC | 1.11E+04 | 1.13E+03 | 2.96E+03 | 3.18E+03 | |
CS | 5.96E+00 | 3.12E+00 | 8.56E-01 | 4.79E+00 | |
IDCS | 3.64E+00 | 1.40E+00 | 5.95E-01 | 2.15E+00 | |
f9 | PSO | 8.08E+00 | 7.14E+00 | 2.85E-01 | 7.62E+00 |
ABC | 5.37E+00 | 4.43E+00 | 2.83E-01 | 4.97E+00 | |
CS | 3.48E+00 | 3.10E+00 | 1.16E-01 | 3.32E+00 | |
IDCS | 3.12E+00 | 2.50E+00 | 1.84E-01 | 2.79E+00 | |
f10 | PSO | 4.60E+00 | 3.22E+00 | 3.72E-01 | 3.92E+00 |
ABC | 6.05E+00 | 3.38E+00 | 7.82E-01 | 4.38E+00 | |
CS | 1.89E+00 | 8.95E-01 | 3.52E-01 | 1.41E+00 | |
IDCS | 2.94E-01 | 1.26E-01 | 5.34E-02 | 2.08E-01 |
Tab. 2 Experiment results of four algorithms on 10 benchmark functions with 500 iteration runs in 50 dimensions
函数 | 算法 | best | worst | std | mean |
---|---|---|---|---|---|
f1 | PSO | 1.80E+02 | 1.30E+02 | 1.53E+01 | 1.54E+02 |
ABC | 3.59E+01 | 2.63E+01 | 2.95E+00 | 3.18E+01 | |
CS | 3.73E+00 | 1.34E+00 | 6.39E-01 | 2.24E+00 | |
IDCS | 5.50E+00 | 3.24E+00 | 6.33E-01 | 4.06E+00 | |
f2 | PSO | 1.83E+02 | 1.37E+02 | 1.38E+01 | 1.58E+02 |
ABC | 4.90E+01 | 2.79E+01 | 5.78E+00 | 3.59E+01 | |
CS | 4.40E+00 | 1.64E+00 | 7.18E-01 | 2.85E+00 | |
IDCS | 5.60E+00 | 3.66E+00 | 6.56E-01 | 4.52E+00 | |
f3 | PSO | 1.83E+05 | 1.08E+05 | 2.04E+04 | 1.50E+05 |
ABC | 2.54E+05 | 1.18E+05 | 4.02E+04 | 1.96E+05 | |
CS | 1.01E+03 | 4.67E+02 | 1.50E+02 | 6.97E+02 | |
IDCS | 7.11E+02 | 3.47E+02 | 9.73E+01 | 5.66E+02 | |
f4 | PSO | 4.87E+04 | 2.61E+04 | 6.31E+03 | 3.36E+04 |
ABC | 6.80E+04 | 2.26E+04 | 1.27E+04 | 3.72E+04 | |
CS | 7.17E+01 | 1.83E+01 | 1.65E+01 | 3.76E+01 | |
IDCS | 7.08E+01 | 1.49E+01 | 1.58E+01 | 3.02E+01 | |
f5 | PSO | 4.79E+00 | 3.56E+00 | 3.25E-01 | 4.30E+00 |
ABC | 9.21E+00 | 8.08E+00 | 3.41E-01 | 8.78E+00 | |
CS | 2.11E+00 | 1.63E+00 | 1.58E-01 | 1.86E+00 | |
IDCS | 1.38E+00 | 1.04E+00 | 8.59E-02 | 1.20E+00 | |
f6 | PSO | 7.62E+02 | 3.00E+02 | 1.34E+02 | 4.89E+02 |
ABC | 1.14E+03 | 9.39E+02 | 6.45E+01 | 1.02E+03 | |
CS | 2.09E+02 | 1.22E+02 | 2.58E+01 | 1.69E+02 | |
IDCS | 1.28E+01 | 5.80E+00 | 2.25E+00 | 9.94E+00 | |
f7 | PSO | 1.05E+00 | 1.03E+00 | 6.10E-03 | 1.04E+00 |
ABC | 8.84E-01 | 6.90E-01 | 5.80E-02 | 7.82E-01 | |
CS | 2.55E-01 | 9.85E-02 | 4.49E-02 | 1.53E-01 | |
IDCS | 1.81E-01 | 8.41E-02 | 2.94E-02 | 1.23E-01 | |
f8 | PSO | 3.20E+01 | 2.25E+01 | 2.83E+00 | 2.70E+01 |
ABC | 1.11E+04 | 1.13E+03 | 2.96E+03 | 3.18E+03 | |
CS | 5.96E+00 | 3.12E+00 | 8.56E-01 | 4.79E+00 | |
IDCS | 3.64E+00 | 1.40E+00 | 5.95E-01 | 2.15E+00 | |
f9 | PSO | 8.08E+00 | 7.14E+00 | 2.85E-01 | 7.62E+00 |
ABC | 5.37E+00 | 4.43E+00 | 2.83E-01 | 4.97E+00 | |
CS | 3.48E+00 | 3.10E+00 | 1.16E-01 | 3.32E+00 | |
IDCS | 3.12E+00 | 2.50E+00 | 1.84E-01 | 2.79E+00 | |
f10 | PSO | 4.60E+00 | 3.22E+00 | 3.72E-01 | 3.92E+00 |
ABC | 6.05E+00 | 3.38E+00 | 7.82E-01 | 4.38E+00 | |
CS | 1.89E+00 | 8.95E-01 | 3.52E-01 | 1.41E+00 | |
IDCS | 2.94E-01 | 1.26E-01 | 5.34E-02 | 2.08E-01 |
数据集 | 指标 | K-means | AP | DBSCAN | OPTICS | KCOIC | DCFSK |
---|---|---|---|---|---|---|---|
Zelnik3 | AMI | 0.637 8 | 0.413 4 | 0.476 0 | 0.481 4 | 0.639 1 | 0.755 3 |
NMI | 0.760 1 | 0.563 8 | 0.601 2 | 0.529 9 | 0.700 3 | 0.819 2 | |
RI | 0.888 5 | 0.746 2 | 0.722 9 | 0.735 4 | 0.807 6 | 0.923 3 | |
ARI | 0.466 8 | 0.346 3 | 0.445 4 | 0.459 8 | 0.698 3 | 0.753 4 | |
Compound | AMI | 0.672 4 | 0.700 8 | 0.701 0 | 0.665 3 | 0.672 4 | 0.745 2 |
NMI | 0.669 1 | 0.745 3 | 0.763 8 | 0.675 7 | 0.587 7 | 0.755 9 | |
RI | 0.830 3 | 0.899 0 | 0.903 1 | 0.827 0 | 0.883 4 | 0.918 1 | |
ARI | 0.536 2 | 0.744 2 | 0.756 0 | 0.507 9 | 0.740 2 | 0.763 0 | |
Aggregation | AMI | 0.722 2 | 0.835 5 | 0.659 2 | 0.663 3 | 0.835 9 | 0.834 7 |
NMI | 0.760 8 | 0.841 6 | 0.735 7 | 0.686 9 | 0.849 6 | 0.656 6 | |
RI | 0.886 7 | 0.946 1 | 0.874 0 | 0.849 1 | 0.945 4 | 0.821 4 | |
ARI | 0.635 9 | 0.840 2 | 0.668 9 | 0.524 1 | 0.852 5 | 0.568 4 | |
Path-based | AMI | 0.529 5 | 0.381 8 | 0.536 7 | 0.437 9 | 0.646 8 | 0.527 1 |
NMI | 0.560 6 | 0.549 1 | 0.616 5 | 0.506 9 | 0.548 9 | 0.564 1 | |
RI | 0.758 1 | 0.748 3 | 0.818 6 | 0.722 0 | 0.749 7 | 0.763 0 | |
ARI | 0.483 8 | 0.311 2 | 0.580 4 | 0.432 3 | 0.736 7 | 0.488 4 | |
R15 | AMI | 0.798 9 | 0.639 4 | 0.576 2 | 0.755 8 | 0.837 5 | 0.864 3 |
NMI | 0.848 7 | 0.741 2 | 0.742 5 | 0.850 2 | 0.864 9 | 0.879 7 | |
RI | 0.950 5 | 0.897 5 | 0.750 7 | 0.941 6 | 0.954 9 | 0.971 9 | |
ARI | 0.661 3 | 0.454 6 | 0.263 7 | 0.649 2 | 0.717 8 | 0.772 3 | |
D31 | AMI | 0.836 3 | 0.454 2 | 0.395 0 | 0.800 8 | 0.577 4 | 0.899 1 |
NMI | 0.855 1 | 0.618 3 | 0.792 0 | 0.867 0 | 0.717 9 | 0.904 4 | |
RI | 0.975 7 | 0.818 4 | 0.949 0 | 0.971 3 | 0.903 6 | 0.985 0 | |
ARI | 0.639 3 | 0.204 9 | 0.430 0 | 0.650 6 | 0.341 9 | 0.766 8 |
Tab. 3 Experimental results of six algorithms on six synthesis datasets in four metrics
数据集 | 指标 | K-means | AP | DBSCAN | OPTICS | KCOIC | DCFSK |
---|---|---|---|---|---|---|---|
Zelnik3 | AMI | 0.637 8 | 0.413 4 | 0.476 0 | 0.481 4 | 0.639 1 | 0.755 3 |
NMI | 0.760 1 | 0.563 8 | 0.601 2 | 0.529 9 | 0.700 3 | 0.819 2 | |
RI | 0.888 5 | 0.746 2 | 0.722 9 | 0.735 4 | 0.807 6 | 0.923 3 | |
ARI | 0.466 8 | 0.346 3 | 0.445 4 | 0.459 8 | 0.698 3 | 0.753 4 | |
Compound | AMI | 0.672 4 | 0.700 8 | 0.701 0 | 0.665 3 | 0.672 4 | 0.745 2 |
NMI | 0.669 1 | 0.745 3 | 0.763 8 | 0.675 7 | 0.587 7 | 0.755 9 | |
RI | 0.830 3 | 0.899 0 | 0.903 1 | 0.827 0 | 0.883 4 | 0.918 1 | |
ARI | 0.536 2 | 0.744 2 | 0.756 0 | 0.507 9 | 0.740 2 | 0.763 0 | |
Aggregation | AMI | 0.722 2 | 0.835 5 | 0.659 2 | 0.663 3 | 0.835 9 | 0.834 7 |
NMI | 0.760 8 | 0.841 6 | 0.735 7 | 0.686 9 | 0.849 6 | 0.656 6 | |
RI | 0.886 7 | 0.946 1 | 0.874 0 | 0.849 1 | 0.945 4 | 0.821 4 | |
ARI | 0.635 9 | 0.840 2 | 0.668 9 | 0.524 1 | 0.852 5 | 0.568 4 | |
Path-based | AMI | 0.529 5 | 0.381 8 | 0.536 7 | 0.437 9 | 0.646 8 | 0.527 1 |
NMI | 0.560 6 | 0.549 1 | 0.616 5 | 0.506 9 | 0.548 9 | 0.564 1 | |
RI | 0.758 1 | 0.748 3 | 0.818 6 | 0.722 0 | 0.749 7 | 0.763 0 | |
ARI | 0.483 8 | 0.311 2 | 0.580 4 | 0.432 3 | 0.736 7 | 0.488 4 | |
R15 | AMI | 0.798 9 | 0.639 4 | 0.576 2 | 0.755 8 | 0.837 5 | 0.864 3 |
NMI | 0.848 7 | 0.741 2 | 0.742 5 | 0.850 2 | 0.864 9 | 0.879 7 | |
RI | 0.950 5 | 0.897 5 | 0.750 7 | 0.941 6 | 0.954 9 | 0.971 9 | |
ARI | 0.661 3 | 0.454 6 | 0.263 7 | 0.649 2 | 0.717 8 | 0.772 3 | |
D31 | AMI | 0.836 3 | 0.454 2 | 0.395 0 | 0.800 8 | 0.577 4 | 0.899 1 |
NMI | 0.855 1 | 0.618 3 | 0.792 0 | 0.867 0 | 0.717 9 | 0.904 4 | |
RI | 0.975 7 | 0.818 4 | 0.949 0 | 0.971 3 | 0.903 6 | 0.985 0 | |
ARI | 0.639 3 | 0.204 9 | 0.430 0 | 0.650 6 | 0.341 9 | 0.766 8 |
数据集 | 指标 | ABC+K-means | PSO+K-means | PAM | AICO | CAABC-K-means | RABC-K-means | DCFSK |
---|---|---|---|---|---|---|---|---|
Iris | NMI | 0.713 2 | 0.733 2 | 0.773 9 | 0.790 6 | 0.790 8 | 0.674 1 | 0.733 7 |
ACC | 0.543 2 | 0.530 2 | 0.589 9 | 0.590 0 | 0.590 6 | 0.613 3 | 0.942 0 | |
R | 0.900 0 | 0.920 0 | 0.960 0 | 0.970 0 | 0.970 0 | 0.720 0 | 0.844 3 | |
Wine | NMI | 0.403 0 | 0.532 0 | 0.563 2 | 0.570 4 | 0.572 0 | 0.547 1 | 0.593 9 |
ACC | 0.891 9 | 0.904 3 | 0.928 4 | 0.929 4 | 0.931 1 | 0.865 2 | 0.955 1 | |
R | 0.930 0 | 0.980 0 | 0.960 0 | 0.960 0 | 1.000 0 | 0.845 2 | 1.000 0 | |
Glass | NMI | 0.403 2 | 0.403 6 | 0.482 3 | 0.490 3 | 0.493 2 | 0.563 7 | 0.623 0 |
ACC | 0.593 2 | 0.589 6 | 0.683 3 | 0.690 8 | 0.693 2 | 0.579 4 | 0.550 3 | |
R | 0.830 0 | 0.830 0 | 0.830 0 | 0.880 0 | 0.910 0 | 0.666 7 | 1.000 0 | |
ECOLI | NMI | 0.573 0 | 0.574 0 | 0.560 3 | 0.583 3 | 0.603 2 | 0.631 9 | 0.716 8 |
ACC | 0.843 0 | 0.852 9 | 0.860 0 | 0.870 4 | 0.890 4 | 0.800 6 | 0.890 6 | |
R | 0.840 0 | 0.840 0 | 0.840 0 | 0.850 0 | 0.890 0 | 1.000 0 | 1.000 0 | |
CMC | NMI | 0.790 3 | 0.830 7 | 0.693 4 | 0.749 5 | 0.890 0 | 0.587 3 | 0.844 9 |
ACC | 0.592 4 | 0.591 5 | 0.583 7 | 0.607 5 | 0.620 3 | 0.614 5 | 0.954 5 | |
R | 0.820 0 | 0.790 0 | 0.740 0 | 0.840 0 | 0.940 0 | 0.786 8 | 1.000 0 | |
Musk | NMI | 0.534 0 | 0.593 2 | 0.475 6 | 0.549 9 | 0.599 8 | 0.610 7 | 0.336 0 |
ACC | 0.699 3 | 0.683 4 | 0.683 5 | 0.696 8 | 0.700 0 | 0.739 0 | 0.512 1 | |
R | 0.600 0 | 0.520 0 | 0.500 0 | 0.720 0 | 0.820 0 | 0.920 0 | 1.000 0 |
Tab. 4 Clustering results of seven algorithms on six UCI datasets
数据集 | 指标 | ABC+K-means | PSO+K-means | PAM | AICO | CAABC-K-means | RABC-K-means | DCFSK |
---|---|---|---|---|---|---|---|---|
Iris | NMI | 0.713 2 | 0.733 2 | 0.773 9 | 0.790 6 | 0.790 8 | 0.674 1 | 0.733 7 |
ACC | 0.543 2 | 0.530 2 | 0.589 9 | 0.590 0 | 0.590 6 | 0.613 3 | 0.942 0 | |
R | 0.900 0 | 0.920 0 | 0.960 0 | 0.970 0 | 0.970 0 | 0.720 0 | 0.844 3 | |
Wine | NMI | 0.403 0 | 0.532 0 | 0.563 2 | 0.570 4 | 0.572 0 | 0.547 1 | 0.593 9 |
ACC | 0.891 9 | 0.904 3 | 0.928 4 | 0.929 4 | 0.931 1 | 0.865 2 | 0.955 1 | |
R | 0.930 0 | 0.980 0 | 0.960 0 | 0.960 0 | 1.000 0 | 0.845 2 | 1.000 0 | |
Glass | NMI | 0.403 2 | 0.403 6 | 0.482 3 | 0.490 3 | 0.493 2 | 0.563 7 | 0.623 0 |
ACC | 0.593 2 | 0.589 6 | 0.683 3 | 0.690 8 | 0.693 2 | 0.579 4 | 0.550 3 | |
R | 0.830 0 | 0.830 0 | 0.830 0 | 0.880 0 | 0.910 0 | 0.666 7 | 1.000 0 | |
ECOLI | NMI | 0.573 0 | 0.574 0 | 0.560 3 | 0.583 3 | 0.603 2 | 0.631 9 | 0.716 8 |
ACC | 0.843 0 | 0.852 9 | 0.860 0 | 0.870 4 | 0.890 4 | 0.800 6 | 0.890 6 | |
R | 0.840 0 | 0.840 0 | 0.840 0 | 0.850 0 | 0.890 0 | 1.000 0 | 1.000 0 | |
CMC | NMI | 0.790 3 | 0.830 7 | 0.693 4 | 0.749 5 | 0.890 0 | 0.587 3 | 0.844 9 |
ACC | 0.592 4 | 0.591 5 | 0.583 7 | 0.607 5 | 0.620 3 | 0.614 5 | 0.954 5 | |
R | 0.820 0 | 0.790 0 | 0.740 0 | 0.840 0 | 0.940 0 | 0.786 8 | 1.000 0 | |
Musk | NMI | 0.534 0 | 0.593 2 | 0.475 6 | 0.549 9 | 0.599 8 | 0.610 7 | 0.336 0 |
ACC | 0.699 3 | 0.683 4 | 0.683 5 | 0.696 8 | 0.700 0 | 0.739 0 | 0.512 1 | |
R | 0.600 0 | 0.520 0 | 0.500 0 | 0.720 0 | 0.820 0 | 0.920 0 | 1.000 0 |
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