DATA CLUSTERING BASED ON FUZZY C-MEANS AND CHAOTIC WHALE OPTIMIZATION ALGORITHMS

Yıl 2019, Cilt: 37 Sayı: 4, 1107 - 1128, 01.12.2019

Hatice Arslan Metin Toz

Öz

Clustering is the process of sub-grouping data according to certain distance and similarity criteria. One of the most commonly used clustering algorithms in the literature is the Fuzzy C-Means (FCM) algorithm based on the fuzzy clustering principle. Although FCM is an efficient algorithm, random selection of initial cluster centers is a disadvantage since it easier trap the algorithm into local optimum. This problem can be solved by approaching the clustering problem as an optimization problem. In this article, Whale Optimization Algorithm (WOA), a global optimization algorithm developed by inspiration from hunting behaviors of humpback whales, has been improved with chaos maps using an adaptive normalization method and chaotic WOA algorithms are proposed. They are then hybridized with FCM algorithm. The performances of the proposed chaotic optimization algorithms are tested with thirteen different benchmark functions. Results are evaluated with means and standard deviations of the objective function values and with the Wilcoxon Sign Rank Test at 0.05 significance level. The clustering performances of the proposed hybrid algorithms measured according to the objective function, the Rand Index and the Adjusted Rand Index values and compared with the K-Means, FCM and some of the other hybrid algorithms for six different data sets selected from the UCI Repository database. In addition, the new hybrid clustering algorithms are improved by using Chebyshev distance function instead of the classical Euclidean distance for the FCM algorithm in order to increase their data clustering performances. As a result, it has been seen that the used chaos functions improve the optimization performance of WOA algorithm, integrating chaotic WOA algorithms with FCM algorithm enhances the disadvantages of FCM algorithm and changing the distance function increases clustering performance of the proposed algorithms.

Anahtar Kelimeler

Data clustering, WOA, FCM, optimization, chaos.

Kaynakça

• [1] S. Mirjalili and A. Lewis (2016) The Whale Optimization Algorithm. Adv. Eng. Softw 95:51–67.
• [2] D. H. Wolpert and W. G. Macready (1997) No free lunch theorems for optimization IEEE Trans. Evol. Comput. 1(1): 67–82.
• [3] S. Kirkpatrick, C. D. Gelatt and M. P. Vecchi (2007) Optimization by Simulated Annealing Science, New Series 220(4598):671–680.
• [4] E. Rashedi, H. Nezamabadi-pour, and S. Saryazdi (2009) GSA: A Gravitational Search Algorithm Information Sciences 179(13):2232–2248.
• [5] O. K. Erol and I. Eksin (2006) A new optimization method: Big Bang-Big Crunch Advance Engineering Software 37(2):106–111.
• [6] B. Webster and P. Bernhard (2003) A local search optimization algorithm based on natural principles of gravitation Melbourne, FL. Florida Institute of Technology, pp 18.
• [7] A. Hatamlou (2013) Black hole: A new heuristic optimization approach for data clustering Information Science 222:175–184.
• [8] K.-C. Wu and C.-J. Ting (2010) A beam search algorithm for minimizing reshuffle operations at container yards Int. Conf. Logist. Marit. Syst. 2000:703–710.
• [9] J. H. Holland (1992) Genetic Algorithms Scientific American 66–72.
• [10] J. R. Koza and R. Poll (2005) GENETIC PROGRAMMING Introductory Tutorials in Optimization, Decision Support and Search Methodology, Chapter 5, Kluwer Press, pp. 127–164.
• [11] Eiben A.E., Smith J.E. (2003) Evolution Strategies. In: Introduction to Evolutionary Computing. Natural Computing Series. Springer, Berlin, Heidelberg.
• [12] Baluja S (1994), Population-Based Incremental Learning: A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning, Cmu-Cs-94-163, 1–41.
• [13] D. Simon (2008) Biogeography-based optimization IEEE Trans. Evol. Comput 12(6):702–713.
• [14] J. Kennedy and R. Eberhart (1995) Particle swarm optimization Neural Networks IEEE Int. Conf. 4:1942–1948.
• [15] M. Dorigo, M. Birattari, and T. Stutzle (2006) Ant colony optimization IEEE Computational Intelligence Magazine 1(4):28–39.
• [16] Dervis Karaboga (2010) Artificial bee colony algorithm. Scholarpedia, 5(3):6915.
• [17] S. Mirjalili, S. M. Mirjalili, and A. Lewis (2014) Grey Wolf Optimizer Advance Engineering Software 69:46–61.
• [18] Pan, X., Xue, L. & Li, R. Neural Comput & Applic (2018). https://doi.org/10.1007/s00521-018-3449-6 Accessed 18 February 2019.
• [19] S. Mirjalili (2015) Advances in Engineering Software The Ant Lion Optimizer Adv. Eng. Softw. 83:80–98.
• [20] S. Mirjalili (2016) Knowledge-Based Systems SCA : A Sine Cosine Algorithm for solving optimization problems Knowledge-Based Systems 96:120–133.
• [21] E. Alba and B. Dorronsoro (2005) The exploration/exploitation tradeoff in dynamic cellular genetic algorithms IEEE Trans. Evol. Comput. 9(2):126–142.
• [22] S. Mirjalili and A. H. Gandomi (2017) Chaotic gravitational constants for the gravitational search algorithm Appl. Soft Comput. J. 53:407–419.
• [23] J. Zhang, Y. Yang, and Q. Zhang (2009) The Particle Swarm Optimization Algorithm Based on Dynamic Chaotic Perturbations and its Application to K-Means 2009 Int. Conf. Comput. Intell. Secur. pp. 282–286.
• [24] Y. Wang and M. Yao (2009) A new Hybrid Genetic Algorithm Based on Chaos and PSO IEEE International Conference on Intelligent Computing and Intelligent Systems, Shanghai, China, https://doi.org/10.1109/ICICISYS.2009.5357766 Accessed 18 February 2019.
• [25] B. Alatas, E. Akin, and A. B. Ozer (2009) Chaos embedded particle swarm optimization algorithms Chaos, Solitons and Fractals 40(4)4:1715–1734.
• [26] B. Alatas (2010) Chaotic bee colony algorithms for global numerical optimization Expert Syst. Appl. 37(8):5682–5687.
• [27] B. Alatas (2010) Chaotic harmony search algorithms Appl. Math. Comput. 216(9):2687–2699.
• [28] H. Yan, Z. Lv, Y. Zhao, G. Qiao, L. Xiao, and Z. Yang (2014) Chaos Genetic Algorithm Optimization Design Based on Linear Motor Chaos Genet. Algorithm Optim. Des. Based Linear Mot. 2:2265–2268.
• [29] M. Javidi and R. Hosseinpourfard (2015) Chaos genetic algorithm instead genetic algorithm Int. Arab J. Inf. Technol. 12(2):163–168.
• [30] L. D. S. Coelho and V. C. Mariani (2012) Firefly algorithm approach based on chaotic Tinkerbell map applied to multivariable PID controller tuning Comput. Math. with Appl. 64(8):2371–2382.
• [31] J. Mingjun and T. Huanwen (2004) Application of chaos in simulated annealing Chaos, Solitons and Fractals 21(4):933–941.
• [32] G. Zhenyu, C. Bo, Y. Min, and C. Binggang (2006) Self-adaptive chaos differential evolution Adv. Nat. Comput. 1:972–975.
• [33] G. G. Wang, L. Guo, A. H. Gandomi, G. S. Hao, and H. Wang (2014) Chaotic Krill Herd algorithm Inf. Sci. (Ny). 274:17–34.
• [34] Tanyıldızı E, Cigal T (2017) Kaotik Haritalı Balina Optimizasyon Algoritmaları 29(1):309–319.
• [35] W. Z. Sun and J. S. Wang (2017) Elman Neural Network Soft-Sensor Model of Conversion Velocity in Polymerization Process Optimized by Chaos Whale Optimization Algorithm IEEE Access https://doi.org/10.1109/ACCESS.2017.2723610 Accessed 18 February 2019.
• [36] D. Oliva, M. Abd El Aziz, and A. Ella Hassanien (2017) Parameter estimation of photovoltaic cells using an improved chaotic whale optimization algorithm Appl. Energy 200:141–154.
• [37] S. Karthikeyan and T. Christopher (2014) A Hybrid Clustering Approach using Artificial Bee Colony ( ABC ) and Particle Swarm Optimization 100(15):1–6.
• [38] X. H. Han, L. Quan, X. Y. Xiong, M. Almeter, J. Xiang, and Y. Lan (2017) A novel data clustering algorithm based on modified gravitational search algorithm Eng. Appl. Artif. Intell. 61:1–7.
• [39] J. C. Dunn (1973) A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters J. Cybern. 3(3):32–57.
• [40] J. C. Bezdek, R. Ehrlich, and W. Full (1984) FCM: The fuzzy c-means clustering algorithm Comput. Geosci. 10(2–3):191–203.
• [41] S. J. Nanda and G. Panda (2014) A survey on nature inspired metaheuristic algorithms for partitional clustering Swarm Evol. Comput.16:1–18.
• [42] G. Gan, J. Wu, and Z. Yang (2009) A genetic fuzzy k-Modes algorithm for clustering categorical data Expert Syst. Appl. 36(2) PART 1:1615–1620.
• [43] U. Maulik and I. Saha (2010) Automatic fuzzy clustering using modified differential evolution for image classification IEEE Trans. Geosci. Remote Sens. 48(9):3503–3510.
• [44] B. Zhao (2007) An ant colony clustering algorithm Proceedings of the Sixth International Conference on Machine Learning and Cybernetics, Hong Kong, China, pp. 19–22.
• [45] T. a. Runkler and C. Katz (2006) Fuzzy Clustering by Particle Swarm Optimization 2006 IEEE Int. Conf. Fuzzy Syst. 3:601–608.
• [46] W. Zhu, J. Jiang, C. Song, and L. Bao (2012) Clustering algorithm based on fuzzy c-means and artificial fish swarm Procedia Eng. 29:3307–3311.
• [47] H. Izakian and A. Abraham (2011) Fuzzy C-means and fuzzy swarm for fuzzy clustering problem Expert Syst. Appl. 38(3):1835–1838.
• [48] E. Esme and B. Karlik (2016) Fuzzy c-means based support vector machines classifier for perfume recognitio Appl. Soft Comput. J. 46:452–458.
• [49] M. Lichman UCI Machine Learning Repository http://archive.ics.uci.edu/ml. Accessed: 18 February 2019.
• [50] J. Feng, J. Zhang, X. Zhu, and W. Lian (2017) A novel chaos optimization algorithm Multimedia Tools and Applications 76(16):17405–17436.
• [51] J. Derrac, S. García, D. Molina, and F. Herrera (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms Swarm Evol. Comput. 1(1):3–18.
• [52] M. Kabak, F. Sağlam, and A. Aktaş (2017) Farkli Uzaklik Hesaplama Yaklaşimlarinin Topsis Üzeri Kullanilabi̇li̇rli̇ği̇ni̇n İncelenmesi̇ Gazi Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 32(1):35–43.
• [53] D. J. Bora and A. K. Gupta (2014) Effect of Different Distance Measures on the Performance of K-Means Algorithm : An Experimental Study in Matlab Int. J. Comput. Sci. Inf. Technol. 5(2):2501–2506.
• [54] J. Arora (2016) Hybrid FCM PSO Algorithm with CityBlock Distance pp. 2609–2614.
• [55] W. M. Rand (1971) Objective Criteria for the Evaluation of Clustering Methods Author ( s ): William M . Rand Source : Journal of the American Statistical Association 66 (336):846.
• [56] L. Hubert and P. Arabie (1985) Comparing partitions J. Classif. 2(1):193–218.