Abstract
In most data mining tasks, feature selection (FS) is a necessary preprocessing step that can reduce the dimensionality of the dataset while ensuring adequate classification accuracy. In this paper, a ReliefF-guided novel binary equilibrium optimizer (RG-NBEO) is proposed for feature selection. Based on the binary equilibrium optimizer, two novel mechanisms are employed to improve the evolution performance. First, two novel transfer functions (SSr and VVr) based on the concept of opposition learning are proposed to transform the continuous search space into a binary search space and achieve a good balance between exploration and exploitation. Second, a ReliefF bootstrap** strategy is proposed to add and remove features directionally in the iterative process according to the feature weights. The simulation experiments are first based on the equilibrium optimizer (EO) variants constructed from the classical S- and V-shaped transfer functions. The variant EO with the best performance is selected and compared with five superior swarm intelligence optimization algorithms and six classical filter feature selection algorithms. The performance of the proposed method was tested on 18 standard datasets, and the results of the different algorithms were statistically evaluated using the Wilcoxon rank sum test and the Freidman rank sum test. The results show that this method can effectively improve the classification accuracy in most cases.
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References
Aalaei S, Shahraki H, Rowhanimanesh A et al (2016) Feature selection using genetic algorithm for breast cancer diagnosis: experiment on three different datasets. Iran J Basic Med Sci 19(5):476
Abdel-Basset M, Mohamed R, Mirjalili S (2021) A binary equilibrium optimization algorithm for 0–1 knapsack problems. Comput Ind Eng 151:106946
Abualigah L, Diabat A (2022) Chaotic binary group search optimizer for feature selection. Expert Syst Appl 192:116368
Abualigah LM, Khader AT, Hanandeh ES (2018) A new feature selection method to improve the document clustering using particle swarm optimization algorithm. J Comput Sci 25:456–466
Abualigah L, Alsalibi B, Shehab M et al (2021) A parallel hybrid krill herd algorithm for feature selection. Int J Mach Learn Cybern 12(3):783–806
Agrawal U, Rohatgi V, Katarya R (2022) Normalized mutual information-based equilibrium optimizer with chaotic maps for wrapper-filter feature selection. Expert Syst Appl 207:118107
Ahmadianfar I, Heidari AA, Gandomi AH et al (2021) RUN beyond the metaphor: an efficient optimization algorithm based on Runge Kutta method. Expert Syst Appl 181:115079
Apolloni J, Leguizamón G, Alba E (2016) Two hybrid wrapper-filter feature selection algorithms applied to high-dimensional microarray experiments. Appl Soft Comput 38:922–932
Awadallah MA, Hammouri AI, Al-Betar MA et al (2022) Binary Horse herd optimization algorithm with crossover operators for feature selection. Comput Biol Med 141:105152
Beheshti Z (2020) A time-varying mirrored S-shaped transfer function for binary particle swarm optimization. Inf Sci 512:1503–1542
Cai D, Zhang C, He X (2010) Unsupervised feature selection for multi-cluster data. Proceedings of the 16th ACM SIGKDD international conference on Knowledge discovery and data mining, pp 333–342
Chattopadhyay S, Dey A, Singh PK, et al (2022) A feature selection model for speech emotion recognition using clustering-based population generation with hybrid of equilibrium optimizer and atom search optimization algorithm. Multimed Tools Appl, pp 1–34.
Dhiman G, Oliva D, Kaur A et al (2021) BEPO: a novel binary emperor penguin optimizer for automatic feature selection. Knowl-Based Syst 211:106560
Dorigo M, Birattari M, Stutzle T (2006) Ant colony optimization. IEEE Comput Intell Mag 1(4):28–39
Emary E, Zawbaa HM, Hassanien AE (2016) Binary grey wolf optimization approaches for feature selection. Neurocomputing 172:371–381
Faramarzi A, Heidarinejad M, Stephens B et al (2020) Equilibrium optimizer: a novel optimization algorithm. Knowl-Based Syst 191:105190
Gu Q, Li Z, Han J (2012) Generalized fisher score for feature selection. ar**v preprint ar**v:1202.3725
Guo S, Wang J, Guo M (2020) Z-shaped transfer functions for binary particle swarm optimization algorithm. Comput Intell Neurosci 2020:1–2
Hamidzadeh J (2021) Feature selection by using chaotic cuckoo optimization algorithm with levy flight, opposition-based learning and disruption operator. Soft Comput 25(4):2911–2933
He X, Cai D, Niyogi P (2005) Laplacian score for feature selection. Adv Neural Inf Process Syst, p 18
He Y, Wang J, Zhang X et al (2019) Encoding transformation-based differential evolution algorithm for solving knapsack problem with single continuous variable. Swarm Evol Comput 50:100507
He Y, Hao X, Li W et al (2021) Binary team game algorithm based on modulo operation for knapsack problem with a single continuous variable. Appl Soft Comput 103:107180
He Y, Zhang F, Mirjalili S et al (2022) Novel binary differential evolution algorithm based on Taper-shaped transfer functions for binary optimization problems. Swarm Evol Comput 69:101022
Heidari AA, Mirjalili S, Faris H et al (2019) Harris hawks optimization: algorithm and applications. Future Gener Comput Syst 97:849–872
Hu P, Pan JS, Chu SC (2020) Improved binary grey wolf optimizer and its application for feature selection. Knowl-Based Syst 195:105746
Hu P, Pan JS, Chu SC et al (2022) Multi-surrogate assisted binary particle swarm optimization algorithm and its application for feature selection. Appl Soft Comput 121:108736
Jordan MI, Mitchell TM (2015) Machine learning: trends, perspectives, and prospects. Science 349(6245):255–260
Joshi PM, Verma HK (2021) Binary equilibrium optimizer based weak bus constrained PMU placement. 2021 emerging trends in industry 4.0 (ETI 4.0). IEEE, pp 1–8
Kabir MM, Shahjahan M, Murase K (2012) A new hybrid ant colony optimization algorithm for feature selection. Expert Syst Appl 39(3):3747–3763
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471
Kennedy J, Eberhart RC (1997) A discrete binary version of the particle swarm algorithm. 1997 IEEE international conference on systems, man, and cybernetics. Comput Cybern Simul IEEE 5:4104–4108
Khosravi H, Amiri B, Yazdanjue N et al (2022) An improved group teaching optimization algorithm based on local search and chaotic map for feature selection in high-dimensional data. Expert Syst Appl 204:117493
Kira K, Rendell LA (1992) The feature selection problem: traditional methods and a new algorithm. Aaai. 2(1992a): 129–134
Kononenko I (1994) Estimating attributes: analysis and extensions of RELIEF. European conference on machine learning. Springer, Berlin, Heidelberg, pp 171–182
Li S, Chen H, Wang M et al (2020) Slime mould algorithm: a new method for stochastic optimization. Future Gener Comput Syst 111:300–323
Li Z, He Y, Li Y et al (2021a) A hybrid grey wolf optimizer for solving the product knapsack problem. Int J Mach Learn Cybern 12(1):201–222
Li AD, Xue B, Zhang M (2021b) Improved binary particle swarm optimization for feature selection with new initialization and search space reduction strategies. Appl Soft Comput 106:107302
Liu M, Xu L, Yi J, et al (2018) A feature gene selection method based on ReliefF and PSO. 2018 10th international conference on measuring technology and mechatronics automation (ICMTMA). IEEE, pp 298–301
Maleki N, Zeinali Y, Niaki STA (2021) A k-NN method for lung cancer prognosis with the use of a genetic algorithm for feature selection. Expert Syst Appl 164:113981
Minocha S, Singh B (2022) A novel phishing detection system using binary modified equilibrium optimizer for feature selection. Comput Electr Eng 98:107689
Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27(4):1053–1073
Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61
Mirjalili S, Zhang H, Mirjalili S et al (2020) A novel U-shaped transfer function for binary particle swarm optimisation[M]//Soft Computing for Problem Solving 2019. Springer, Singapore, pp 241–259
Mohmmadzadeh H, Gharehchopogh FS (2021) An efficient binary chaotic symbiotic organisms search algorithm approaches for feature selection problems. J Supercomput 77(8):9102–9144
Nadimi-Shahraki MH, Banaie-Dezfouli M, Zamani H et al (2021) B-MFO: a binary moth-flame optimization for feature selection from medical datasets. Computers 10(11):136
Pashaei E, Pashaei E (2022) An efficient binary chimp optimization algorithm for feature selection in biomedical data classification. Neural Comput Appl 34(8):6427–6451
Peng H, Long F, Ding C (2005) Feature selection based on mutual information criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans Pattern Anal Mach Intell 27(8):1226–1238
Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1(1):33–57
Raileanu LE, Stoffel K (2004) Theoretical comparison between the gini index and information gain criteria. Ann Math Artif Intell 41(1):77–93
Rizk-Allah RM, Hassanien AE (2022) A hybrid equilibrium algorithm and pattern search technique for wind farm layout optimization problem. ISA transactions
Roffo G, Melzi S, Castellani U, et al (2017) Infinite latent feature selection: A probabilistic latent graph-based ranking approach. Proceedings of the IEEE international conference on computer vision, pp 1398–1406
Sadeghian Z, Akbari E, Nematzadeh H (2021) A hybrid feature selection method based on information theory and binary butterfly optimization algorithm. Eng Appl Artif Intell 97:104079
Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Sun L, Kong X, Xu J et al (2019) A hybrid gene selection method based on ReliefF and ant colony optimization algorithm for tumor classification. Sci Rep 9(1):1–14
Sun Y, Pan JS, Hu P, et al (2022) Enhanced equilibrium optimizer algorithm applied in job shop scheduling problem. J Intell Manuf, pp 1–27
Tang J, Alelyani S, Liu H (2014) Feature selection for classification: a review. Data Classif: Algorithms Appl, p 37
Taradeh M, Mafarja M, Heidari AA et al (2019) An evolutionary gravitational search-based feature selection. Inf Sci 497:219–239
Tizhoosh HR (2005) Opposition-based learning: a new scheme for machine intelligence. International conference on computational intelligence for modelling, control and automation and international conference on intelligent agents, web technologies and internet commerce (CIMCA-IAWTIC’06). IEEE 1:695–701
Tubishat M, Abushariah MAM, Idris N et al (2019) Improved whale optimization algorithm for feature selection in Arabic sentiment analysis. Appl Intell 49(5):1688–1707
Turkoglu B, Kaya E (2020) Training multi-layer perceptron with artificial algae algorithm. Eng Sci Technol Int J 23(6):1342–1350
Turkoglu B, Uymaz SA, Kaya E (2022a) Clustering analysis through artificial algae algorithm. Int J Mach Learn Cybern 13(4):1179–1196
Turkoglu B, Uymaz SA, Kaya E (2022b) Binary artificial algae algorithm for feature selection. Appl Soft Comput 120:108630
Varzaneh ZA, Hossein S, Mood SE et al (2022) A new hybrid feature selection based on improved equilibrium optimization. Chemom Intell Lab Syst 228:104618
Wan J, Chen H, Yuan Z et al (2021) A novel hybrid feature selection method considering feature interaction in neighborhood rough set. Knowl-Based Syst 227:107167
Wang GG (2018) Moth search algorithm: a bio-inspired metaheuristic algorithm for global optimization problems. Memet Comput 10(2):151–164
Wang GG, Deb S, Coelho LDS (2018) Earthworm optimisation algorithm: a bio-inspired metaheuristic algorithm for global optimisation problems. Int J Bio-Inspired Comput 12(1):1–22
Wang GG, Deb S, Cui Z (2019) Monarch butterfly optimization. Neural Comput Appl 31(7):1995–2014
Xu Y, Jones GJ, Li JT et al (2007) A study on mutual information-based feature selection for text categorization. J Comput Inf Syst 3(3):1007–1012
Yang Y, Chen H, Heidari AA et al (2021) Hunger games search: visions, conception, implementation, deep analysis, perspectives, and towards performance shifts. Expert Syst Appl 177:114864
Zhang X, Wu G, Dong Z et al (2015) Embedded feature-selection support vector machine for driving pattern recognition. J Franklin Inst 352(2):669–685
Zhang Y, Liu R, Wang X et al (2021) Boosted binary Harris hawks optimizer and feature selection. Eng Comput 37(4):3741–3770
Zhao W, Wang L, Zhang Z (2019) Atom search optimization and its application to solve a hydrogeologic parameter estimation problem. Knowl-Based Syst 163:283–304
Zhao Y, Dong J, Li X et al (2022) A binary dandelion algorithm using seeding and chaos population strategies for feature selection. Appl Soft Comput 125:109166
Zhu H, He Y, Wang X et al (2017) Discrete differential evolutions for the discounted 0–1 knapsack problem. Int J Bio-Inspired Comput 10(4):219–238
Acknowledgements
This work was supported by the Basic Scientific Research Project of Institution of Higher Learning of Liaoning Province (Grant No. LJKZ0293), and the Project by Liaoning Provincial Natural Science Foundation of China (Grant No. 20180550700).
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MZ participated in the data collection, analysis, algorithm simulation, and draft writing. J-SW participated in the concept, design, interpretation and commented on the manuscript. J-NH, H-MS, X-DL and F-JG participated in the critical revision of this paper.
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Zhang, M., Wang, JS., Hou, JN. et al. RG-NBEO: a ReliefF guided novel binary equilibrium optimizer with opposition-based S-shaped and V-shaped transfer functions for feature selection. Artif Intell Rev 56, 6509–6556 (2023). https://doi.org/10.1007/s10462-022-10333-y
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DOI: https://doi.org/10.1007/s10462-022-10333-y