A selfish herd optimization algorithm based on the simplex method for clustering analysis

Abstract

Clustering analysis is a popular data analysis technology that has been successfully applied in many fields, such as pattern recognition, machine learning, image processing, data mining, computer vision and fuzzy control. Clustering analysis has made great progress in these fields. The purpose of clustering analysis is to classify data according to their intrinsic attributes such that data that have the same characteristics are in the same class and data that differ are in different classes. Currently, the k-means clustering algorithm is one of the most commonly used clustering methods because it is simple and easy to implement. However, its performance largely depends on the initial solution, and it easily falls into locally optimal solutions during the execution of the algorithm. To overcome the shortcomings of k-means clustering, many scholars have used meta-heuristic optimization algorithms to solve data clustering problems and have obtained satisfactory results. Therefore, in this paper, a selfish herd optimization algorithm based on the simplex method (SMSHO) is proposed. In SMSHO, the simplex method replaces mating operations to generate new prey individuals. The incorporation of the simplex method increases the population diversity of algorithm, thereby improving the global searching ability of algorithm. Twelve clustering datasets are selected to verify the performance of SMSHO in solving clustering problems. The SMSHO is compared with ABC, BPFPA, DE, k-means, PSO, SMSSO and SHO. The experimental results show that SMSHO has faster convergence speed, higher accuracy and higher stability than the other algorithms.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31
Fig. 32
Fig. 33
Fig. 34
Fig. 35
Fig. 36
Fig. 37
Fig. 38
Fig. 39
Fig. 40
Fig. 41
Fig. 42
Fig. 43
Fig. 44
Fig. 45
Fig. 46
Fig. 47
Fig. 48
Fig. 49
Fig. 50
Fig. 51
Fig. 52
Fig. 53
Fig. 54
Fig. 55
Fig. 56
Fig. 57
Fig. 58
Fig. 59
Fig. 60
Fig. 61
Fig. 62
Fig. 63
Fig. 64
Fig. 65
Fig. 66
Fig. 67
Fig. 68
Fig. 69
Fig. 70
Fig. 71
Fig. 72
Fig. 73
Fig. 74
Fig. 75
Fig. 76

References

  1. 1.

    Unglert K, Radic V, Jellinek AM (2016) Principal component analysis vs. self-organizing maps combined with hierarchical clustering for pattern recognition in volcano seismic spectra. J Volcanol Geotherm Res 320(15):58–74. https://doi.org/10.1016/j.jvolgeores.2016.04.014

    Article  Google Scholar 

  2. 2.

    Diaz-Rozo J, Bielza C, Larranaga P (2017) Machine learning-based CPS for clustering high throughput machining cycle conditions. Proc Manuf 10:997–1008. https://doi.org/10.1016/j.promfg.2017.07.091

    Article  Google Scholar 

  3. 3.

    GeethaRamani R, Balasubramanian L (2018) Macula segmentation and fovea localization employing image processing and heuristic based clustering for automated retinal screening. Comput Methods Programs Biomed 160:153–163. https://doi.org/10.1016/j.cmpb.2018.03.020

    Article  Google Scholar 

  4. 4.

    Thomas MC, Zhu W, Romagnoli JA (2018) Data mining and clustering in chemical process databases for monitoring and knowledge discovery. J Process Control 67:160–175. https://doi.org/10.1016/j.jprocont.2017.02.006

    Article  Google Scholar 

  5. 5.

    Campos V, Sastre F, Yagües M, Bellver M, Giró-i-Nieto X, Torres J (2017) Distributed training strategies for a computer vision deep learning algorithm on a distributed GPU cluster. Proc Comput Sci 108:315–324. https://doi.org/10.1016/j.procs.2017.05.074

    Article  Google Scholar 

  6. 6.

    Ngo LT, Dang TH, Pedrycz W (2018) Towards interval-valued fuzzy set-based collaborative fuzzy clustering algorithms. Pattern Recogn 81:404–416. https://doi.org/10.1016/j.patcog.2018.04.006

    Article  Google Scholar 

  7. 7.

    Nanda SJ, Panda G (2014) A survey on nature inspired meta-heuristic algorithms for partitional clustering. Swarm Evolut Comput 16:1–18. https://doi.org/10.1016/j.swevo.2013.11.003

    Article  Google Scholar 

  8. 8.

    Xu R, Wunsch D (2005) Survey of clustering algorithms. IEEE Trans Neural Network 16(3):645–678. https://doi.org/10.1109/TNN.2005.845141

    Article  Google Scholar 

  9. 9.

    Zalik KR (2008) An efficient k-means clustering algorithm. Pattern Recognition Letter. https://doi.org/10.1016/j.patrec.2008.02.014

    Article  Google Scholar 

  10. 10.

    Borobia A, Canogar R (2017) The real nonnegative inverse eigenvalue problem is NP-hard. Linear Algebra Appl 522(1):127–139. https://doi.org/10.1016/j.laa.2017.02.010

    MathSciNet  Article  MATH  Google Scholar 

  11. 11.

    Zhao Yanchang, Song Junde (2001) GDILC: a grid-based density-isoline clustering algorithm. International Conferences on Info-Tech and Info-Net. Proceedings (Cat. No.01EX479) 3: 140–145. Beijing, China. https://doi.org/https://doi.org/10.1109/ICII.2001.983048

  12. 12.

    Merwe VD, Engelbrecht AP (2003) Data clustering using particle swarm optimization. In: Proceedings of IEEE Congress on Evolutionary Computation. Vol. 03. pp 215-220. https://doi.org/https://doi.org/10.1109/CEC.2003.1299577

  13. 13.

    Ozturk C, Karaboga D (2008) Classification by neural networks and clustering with artificial bee colony algorithm. In: Proceedings of the 6th International Symposium on Intelligent and Manufacturing Systems, Features, Strategies and Innovation. Sakarya, Turkey

  14. 14.

    Ramadas M, Abraham A, Kumar S (2019) FSDE-Forced Strategy Differential Evolution used for data clustering. J King Saud Univ Comput Inf Sci 31(1):52–61. https://doi.org/10.1016/j.jksuci.2016.12.005

    Article  Google Scholar 

  15. 15.

    Zhang S, Zhou Y (2015) Grey wolf optimizer based on powell local optimization method for clustering analysis. Discret Dyn Nat Soc. https://doi.org/10.1155/2015/481360

    Article  Google Scholar 

  16. 16.

    Wang R, Zhou Y, Qiao S, Huang K (2016) Flower pollination algorithm with bee pollinator for cluster analysis. Inform Process Lett 116(1):1–14. https://doi.org/10.1016/j.ipl.2015.08.007

    Article  Google Scholar 

  17. 17.

    Zhou Y, Zhou Y, Luo Q, Abdel-Basset M (2017) A simplex method-based social spider optimization algorithm for clustering Analysis. Eng Appl Artif Intell 64:67–82. https://doi.org/10.1016/j.engappai.2017.06.004

    Article  Google Scholar 

  18. 18.

    Han XiaoHong, Quan L, Xiong XiaoYan, Almeter M, Xiang J, Lan Y (2017) A novel data clustering algorithm based on modified gravitational search algorithm. Eng Appl Artif Intell 61:1–7. https://doi.org/10.1016/j.engappai.2016.11.003

    Article  Google Scholar 

  19. 19.

    Alswaitti M, Albughdadi M, Isa NAM (2018) Density-based particle swarm optimization algorithm for data clustering. Expert Syst Appl 91:170–186. https://doi.org/10.1016/j.eswa.2017.08.050

    Article  Google Scholar 

  20. 20.

    Jadhav AN, Gomathi N (2018) WGC: Hybridization of exponential grey wolf optimizer with whale optimization for data clustering. Alex Eng J 57(3):1569–1584. https://doi.org/10.1016/j.aej.2017.04.013

    Article  Google Scholar 

  21. 21.

    Boushaki SI, Kamel N, Bendjeghaba O (2018) A new quantum chaotic cuckoo search algorithm for data clustering. Expert Syst Appl 96:358–372

    Article  Google Scholar 

  22. 22.

    Abualigah LM, Khader AT, Hanandeh ES, Gandomi AH (2017) A novel hybridization strategy for krill herd algorithm applied to clustering techniques. Appl Soft Comput 60:423–435. https://doi.org/10.1016/j.asoc.2017.06.059

    Article  Google Scholar 

  23. 23.

    Amiri E, Mahmoudi S (2016) Efficient protocol for data clustering by fuzzy Cuckoo optimization algorithm. Appl Soft Compu 41:15–21. https://doi.org/10.1016/j.asoc.2015.12.008

    Article  Google Scholar 

  24. 24.

    Fausto F, Cuevas E, Valdivia A, González A (2017) A global optimization algorithm inspired in the behavior of selfish herds. Biosystems 160:39–55. https://doi.org/10.1016/j.biosystems.2017.07.010

    Article  Google Scholar 

  25. 25.

    Ma M, Luo Q, Zhou Y, Chen X, Li L (2015) An improved animal migration optimization algorithm for clustering analysis. Discrete dyn Nat Soc. https://doi.org/10.1155/2015/194792

    Article  Google Scholar 

  26. 26.

    Hamilton WD (1971) Geometry to the selfish herd. J Theory Biol 31(2):295–311. https://doi.org/10.1016/0022-5193(71)90189-5

    Article  Google Scholar 

  27. 27.

    Blake CL, Merz CJ (2007) UCI repository of machine learning databases. http://archive.ics.uci.edu/ml/datasets.html. Accessed 2007

  28. 28.

    Taher N, Babak A (2010) An efficient hybrid approach based on PSO ACO and k-means for cluster analysis. Appl Soft Comput 10(1):183–197. https://doi.org/10.1016/j.asoc.2009.07.001

    Article  Google Scholar 

  29. 29.

    Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugenics 7 Part 2. https://doi.org/10.1111/j.1469-1809.1936.tb02137.x

    Article  Google Scholar 

  30. 30.

    Niknam T, Olamaie J, Amiri B (2008) A hybrid evolutionary algorithm based on ACO and SA for cluster analysis. J Appl Sci 8(15):2695–2702. https://doi.org/10.3923/jas.2008.2695.2702

    Article  Google Scholar 

  31. 31.

    Zou W, Zhu Y, Chen H, Sui X (2010) A clustering approach using cooperative artificial bee colony algorithm. Discrete dyn Nat Soc. https://doi.org/10.1155/2010/459796

    MathSciNet  Article  MATH  Google Scholar 

  32. 32.

    Derrac J, Gracie S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1:3–18. https://doi.org/10.1016/j.swevo.2011.02.002

    Article  Google Scholar 

  33. 33.

    Nelder JA, Mead R (1965) A simplex method for function minimization. Comput J 30:308–313. https://doi.org/10.1093/comjnl/7.4.308

    MathSciNet  Article  MATH  Google Scholar 

  34. 34.

    Qi X (1994) Theoretical analysis of evolutionary algorithms with an infinite population size in continuous space part i: basic properties of selection and mutation. IEEE Trans Neural Netw 5(1):102–119. https://doi.org/10.1109/72.265965

    Article  Google Scholar 

  35. 35.

    Maulik U, Bandyopadhyay S (2000) Genetic algorithm-based clustering technique. Pattern Recogn 33(9):1455–1465. https://doi.org/10.1016/S0031-3203(99)00137-5

    Article  Google Scholar 

  36. 36.

    Likas A, Vlassis N, Verbeek JJ (2003) The global k-means clustering algorithm. Pattern Recogn 36(2):451–461. https://doi.org/10.1016/S0031-3203(02)00060-2

    Article  Google Scholar 

  37. 37.

    Yang Y, Cai J, Yang H, Zhang J, Zhao X (2020) TAD: A trajectory clustering algorithm based on spatial-temporal density analysis. Expert Syst Appl 139:112846. https://doi.org/10.1016/j.eswa.2019.112846

    Article  Google Scholar 

  38. 38.

    Osamy W, Salim A, Khedr AM (2020) An information entropy based-clustering algorithm for heterogeneous wireless sensor networks. Wireless Netw 26:1869–1886. https://doi.org/10.1007/s11276-018-1877-y

    Article  Google Scholar 

  39. 39.

    Bui Q-T, Vo B, Do H-A, Hung NQV, Snasel V (2020) F-Mapper: a Fuzzy Mapper clustering algorithm. Knowl-Based Syst 189:105107. https://doi.org/10.1016/j.knosys.2019.105107

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions. This paper has been awarded by the National Natural Science Foundation of China (61941113, 82074580), the Fundamental Research Fund for the Central Universities (30918015103, 30918012204), supported by Science and Technology on Information System Engineering Laboratory (No: 05202004), Nanjing Science and Technology Development Plan Project (201805036), China Academy of Engineering Consulting Research Project (2019-ZD-1-02-02), National Social Science Foundation (18BTQ073), State Grid Technology Project (5211XT190033). The authors gratefully acknowledge financial support from China Scholarship Council (CSC NO. 201906840057).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Yongli Wang.

Ethics declarations

Conflict of interest

The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zhao, R., Wang, Y., Xiao, G. et al. A selfish herd optimization algorithm based on the simplex method for clustering analysis. J Supercomput (2021). https://doi.org/10.1007/s11227-020-03597-0

Download citation

Keywords

  • Clustering analysis
  • Selfish herd optimization algorithm
  • Simplex method
  • Global searching ability
  • Meta-heuristic optimization algorithm