Association Rule Mining through Combining Hybrid Water Wave Optimization Algorithm with Levy Flight
Abstract
:1. Introduction
- (1)
- Levy flight is used in the WWO algorithm’s location update process to improve the variety of solutions and prevent it from being stuck on the local optimal solution.
- (2)
- A hybrid strategy is proposed to help the algorithm balance exploration and exploitation. A hybrid algorithm with greater global search capability was obtained by hybridizing ACO, BA, and CS with LWWO, respectively.
- (3)
- The proposed hybrid LWWO–ARM method generates rules directly. Different from traditional ARM algorithms, the proposed method does not generate frequent item sets, reducing the computational overhead of the algorithm, which improves its applicability in practical cases.
2. Theory Background
2.1. Association Rule Mining
- (1)
- Support
- (2)
- Confidence
2.2. Brief Introduction to WWO
- (1)
- Propagation.
- (2)
- Refraction.
- (3)
- Breaking.
2.3. Brief View of Levy Flight
3. Proposed Approach
3.1. Integrating Levy Flight with WWO
Algorithm 1: Pseudo-Code of LWWO |
Input: population () and maximum number of iterations (); Output: 1: Randomly Initialize a population of n waves and the parameters () 2: While stop criterion is not satisfied do 3: for each do 4: propagate to a new using Equation (3) 5: if then 6: if then 7: using Equation (11) 8: 9: Replace 10: else 11: 12: if then 13: Refract to a new using Equations (5) and (6) 14: Update the wavelengths using Equation (4) 15: Return |
3.2. The Hybrid Strategy for LWWO
Algorithm 2: Pseudo-Code of the proposed hybrid algorithm based on LWWO |
Input: population and maximum number of iterations, datasets; Output: rules stored in HashSet, the support and confidence stored in HashMap to an Excel table 1: Scan the datasets and count the number of attribute items 2: Convert the transactions in the datasets into a 0-1 matrix 3: Randomly Initialize the population and the parameters of algorithm A 4: Iterations = 5: While do 6: for each individual in the population do 7: Compute the fitness values for individuals in the population 8: Update the individuals in the population by location update formula of algorithm A 9: Binarize the updated individuals using sigmoid activation function using Equation (13) 10: Evaluate individuals in the population, deposit the individuals that meet the rules in HashSet, deposit the corresponding support and confidence in HashMap 11: end for 12: 13: end while 14: Use the population after algorithm A iterations as the initial population of algorithm B 15: Initialize the parameters for algorithm B; 16: while t < T2 do 17: for each individual in the population do 18: Compute the fitness values for individuals in the population 19: Update the individuals in the population by location update formula of algorithm B 20: Binarize the updated individuals using sigmoid activation function using Equation (13). 21: Evaluate individuals in the population, deposit the individuals that meet the rules in HashSet, deposit the corresponding support and confidence in HashMap 22: end for 23: 24: end while 25: Count the execution time of hybrid algorithm and the number of rules searched |
3.3. The Hybrid Algorithms for Association Rule Mining
3.4. Rule Encoding
3.5. The Fitness Function
4. Experimental Results and Discussion
4.1. Datasets
4.2. Parameters Settings
- 500 for the total number of iterations (T);
- 60 for population size;
- 0.7 for support weight ();
- 0.3 for confidence weight ();
- 0.1 for the minimum support ();
- 0.5 for the minimum confidence ().
4.3. Evaluation Standard
4.4. Performance Comparison
4.5. Comprehensive Evaluation
5. Summary and Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
ARM | association rule mining |
WWO | water wave optimization algorithm |
LWWO | water wave optimization algorithm with Levy flight |
FIM | frequent item sets mining |
ACO | ant colony optimization algorithm |
BSO | bee swarm optimization algorithm |
BA | bat algorithm |
CS | cuckoo search algorithm |
PeSOA | penguin search optimization algorithm |
PSO | particle swarm optimization algorithm |
ABC | artificial bee colony algorithm |
WMSA | water moth search algorithm |
SCWWO | sine cosine water wave optimization algorithm |
SCA | sine cosine algorithm |
FD | functional dependency |
LWWO–ACO | water wave optimization algorithm with Levy flight hybrid with ant colony optimization algorithm |
LWWO–BA | water wave optimization algorithm with Levy flight hybrid with bat algorithm |
LWWO–CS | water wave optimization algorithm with Levy flight hybrid with cuckoo search algorithm |
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I1 | I2 | I3 | I4 | I5 | |||||
---|---|---|---|---|---|---|---|---|---|
1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |
Dataset | Rows | Columns |
---|---|---|
Iris | 150 | 19 |
Heart | 303 | 52 |
Ecoli | 336 | 34 |
Breast | 699 | 20 |
Flare | 1389 | 39 |
Led7 | 3200 | 24 |
Support Weight () | Confidence Weight () | Evaluation Indicators | ACO | BA | CS | WWO | LWWO |
---|---|---|---|---|---|---|---|
0.1 | 0.9 | Rule_num | 166 | 1671 | 1356 | 775 | 1665 |
Avg_conf | 0.9569 | 0.9497 | 0.8505 | 0.9635 | 0.9497 | ||
0.2 | 0.8 | Rule_num | 487 | 1331 | 736 | 619 | 1319 |
Avg_conf | 0.9852 | 0.9329 | 0.9431 | 0.9557 | 0.9329 | ||
0.3 | 0.7 | Rule_num | 387 | 1573 | 1672 | 733 | 1531 |
Avg_conf | 0.9564 | 0.9494 | 0.9255 | 0.9449 | 0.9494 | ||
0.4 | 0.6 | Rule_num | 214 | 1834 | 868 | 743 | 1743 |
Avg_conf | 0.8941 | 0.9246 | 0.9506 | 0.9349 | 0.9246 | ||
0.5 | 0.5 | Rule_num | 149 | 1633 | 1702 | 822 | 1621 |
Avg_conf | 0.9646 | 0.9376 | 0.9583 | 0.9529 | 0.9376 | ||
0.6 | 0.4 | Rule_num | 234 | 1539 | 2266 | 722 | 1712 |
Avg_conf | 0.9529 | 0.9364 | 0.9167 | 0.9250 | 0.9364 | ||
0.7 | 0.3 | Rule_num | 470 | 1833 | 1795 | 876 | 1867 |
Avg_conf | 0.9694 | 0.9363 | 0.8562 | 0.9481 | 0.9363 | ||
0.8 | 0.2 | Rule_num | 190 | 1382 | 653 | 786 | 1368 |
Avg_conf | 0.9558 | 0.9133 | 0.8365 | 0.9675 | 0.9133 | ||
0.9 | 0.1 | Rule_num | 229 | 1288 | 451 | 775 | 1257 |
Avg_conf | 0.8904 | 0.8886 | 0.9109 | 0.9635 | 0.8886 |
Number of Records | WWO | LWWO | LWWO–ACO | LWWO–BA | LWWO–CS |
---|---|---|---|---|---|
400 | 331 | 174 | 418 | 382 | 342 |
800 | 552 | 281 | 767 | 702 | 629 |
1200 | 791 | 387 | 1136 | 1079 | 923 |
1600 | 1042 | 552 | 1472 | 1384 | 1167 |
2000 | 1271 | 711 | 1837 | 1672 | 1389 |
2400 | 1498 | 834 | 2092 | 1952 | 1661 |
2800 | 1809 | 976 | 2388 | 2218 | 1937 |
3200 | 2085 | 1137 | 2634 | 2495 | 2243 |
Dataset | Algorithm | Time(ms) | Num | Sup | Conf | Fitness |
---|---|---|---|---|---|---|
Iris | WWO | 163 | 39 | 0.128 | 0.804 | 0.601 |
LWWO | 78 | 53 | 0.159 | 0.833 | 0.631 | |
LWWO–ACO | 236 | 97 | 0.252 | 0.846 | 0.668 | |
LWWO–BA | 229 | 272 | 0.248 | 0.867 | 0.681 | |
LWWO–CS | 193 | 263 | 0.304 | 0.856 | 0.690 | |
Heart | WWO | 381 | 81 | 0.188 | 0.722 | 0.562 |
LWWO | 258 | 113 | 0.217 | 0.756 | 0.594 | |
LWWO–ACO | 692 | 168 | 0.226 | 0.794 | 0.624 | |
LWWO–BA | 674 | 334 | 0.224 | 0.803 | 0.629 | |
LWWO–CS | 564 | 242 | 0.235 | 0.824 | 0.647 | |
Ecoli | WWO | 194 | 124 | 0.303 | 0.792 | 0.645 |
LWWO | 86 | 173 | 0.325 | 0.799 | 0.657 | |
LWWO–ACO | 256 | 272 | 0.332 | 0.816 | 0.671 | |
LWWO–BA | 237 | 513 | 0.336 | 0.815 | 0.671 | |
LWWO–CS | 201 | 371 | 0.339 | 0.826 | 0.680 | |
Breast | WWO | 586 | 65 | 0.307 | 0.797 | 0.650 |
LWWO | 323 | 76 | 0.332 | 0.806 | 0.664 | |
LWWO–ACO | 769 | 127 | 0.346 | 0.818 | 0.676 | |
LWWO–BA | 756 | 391 | 0.365 | 0.823 | 0.686 | |
LWWO–CS | 622 | 376 | 0.359 | 0.819 | 0.681 | |
Flare | WWO | 822 | 252 | 0.127 | 0.827 | 0.617 |
LWWO | 484 | 364 | 0.156 | 0.831 | 0.629 | |
LWWO–ACO | 1336 | 619 | 0.172 | 0.863 | 0.656 | |
LWWO–BA | 1261 | 1099 | 0.180 | 0.904 | 0.687 | |
LWWO–CS | 1056 | 781 | 0.193 | 0.930 | 0.709 | |
Led7 | WWO | 2085 | 155 | 0.151 | 0.786 | 0.596 |
LWWO | 1137 | 179 | 0.168 | 0.837 | 0.636 | |
LWWO–ACO | 2634 | 271 | 0.197 | 0.852 | 0.656 | |
LWWO–BA | 2495 | 938 | 0.224 | 0.851 | 0.663 | |
LWWO–CS | 2143 | 896 | 0.286 | 0.868 | 0.693 |
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He, Q.; Tu, J.; Ye, Z.; Wang, M.; Cao, Y.; Zhou, X.; Bai, W. Association Rule Mining through Combining Hybrid Water Wave Optimization Algorithm with Levy Flight. Mathematics 2023, 11, 1195. https://doi.org/10.3390/math11051195
He Q, Tu J, Ye Z, Wang M, Cao Y, Zhou X, Bai W. Association Rule Mining through Combining Hybrid Water Wave Optimization Algorithm with Levy Flight. Mathematics. 2023; 11(5):1195. https://doi.org/10.3390/math11051195
Chicago/Turabian StyleHe, Qiyi, Jin Tu, Zhiwei Ye, Mingwei Wang, Ye Cao, Xianjing Zhou, and Wanfang Bai. 2023. "Association Rule Mining through Combining Hybrid Water Wave Optimization Algorithm with Levy Flight" Mathematics 11, no. 5: 1195. https://doi.org/10.3390/math11051195