An application of the whale optimization algorithm with Levy flight strategy for clustering of medical datasets
Clustering, which is handled by many researchers, is separating data into clusters without supervision. In clustering, the data are grouped using similarities or differences between them. Many traditional and heuristic algorithms are used in clustering problems and new techniques continue to be developed today. In this study, a new and effective clustering algorithm was developed by using the Whale Optimization Algorithm (WOA) and Levy flight (LF) strategy that imitates the hunting behavior of whales. With the developed WOA-LF algorithm, clustering was performed using ten medical datasets taken from the UCI Machine Learning Repository database. The clustering performance of the WOA-LF was compared with the performance of k-means, k-medoids, fuzzy c-means and the original WOA clustering algorithms. Application results showed that WOA-LF has more successful clustering performance in general and can be used as an alternative algorithm in clustering problems.
[1] Evirgen, F. (2016). Analyze the optimal solutions of optimization problems by means of fractional gradient based system using VIM. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 6(2), 75-83.
[2] Evirgen, F. (2017). Conformable fractional gradient based dynamic system for constrained optimization problem. Special issue of the 3rd International Conference on Computational and Experimental Science and Engineering (ICCESEN 2016),1066- 1069.
[3] Evirgen, F. and Yavuz, M. (2018). An alternative approach for nonlinear optimization problem with Caputo-Fabrizio derivative. ITM Web of Conferences,01009.
[4] Cui, D. (2017). Application of whale optimization algorithm in reservoir optimal operation. Advances in Science and Technology of Water Resources, 37(3), 72-79.
[5] Zhang, C., Ouyang, D., and Ning, J. (2010). An artificial bee colony approach for clustering. Expert systems with applications, 37(7), 4761-4767.
[6] Selim, S. Z. and Alsultan, K. (1991). A simulated annealing algorithm for the clustering problem. Pattern recognition, 24(10), 1003-1008.
[7] Maulik, U. and Mukhopadhyay, A. (2010). Simulated annealing based automatic fuzzy clustering combined with ANN classification for analyzing microarray data. Computers & operations research, 37(8), 1369-1380.
[8] Maulik, U. and Bandyopadhyay, S. (2000). Genetic algorithm-based clustering technique. Pattern recognition, 33(9), 1455-1465.
[9] Shelokar, P., Jayaraman, V. K., and Kulkarni, B. D. (2004). An ant colony approach for clustering. Analytica Chimica Acta, 509(2), 187-195.
[10] Van der Merwe, D. and Engelbrecht, A. P. (2003). Data clustering using particle swarm optimization. The 2003 Congress on Evolutionary Computation, 2003. CEC'03.,215-220.
[11] Cura, T. (2012). A particle swarm optimization approach to clustering. Expert Systems with Applications, 39(1), 1582-1588.
[12] Karaboga, D. and Ozturk, C. (2011). A novel clustering approach: Artificial Bee Colony (ABC) algorithm. Applied soft computing, 11(1), 652-657.
[13] Armano, G. and Farmani, M. R. (2014). Clustering analysis with combination of artificial bee colony algorithm and k-means technique. International Journal of Computer Theory and Engineering, 6, 141-145.
[14] Karthikeyan, S. and Christopher, T. (2014). A hybrid clustering approach using artificial bee colony (ABC) and particle swarm optimization. International Journal of Computer Applications, 100(15).
[15] Mane, S. U. and Gaikwad, P. G. (2014). Hybrid particle swarm optimization (HPSO) for data clustering. International Journal of Computer Applications, 97(19).
[16] Mirjalili, S. and Lewis, A. (2016). The whale optimization algorithm. Advances in engineering software, 95, 51-67.
[17] Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization. Proceedings of ICNN'95-international conference on neural networks,1942-1948.
[18] Storn, R. and Price, K. (1997). Differential evolution–a simple and efficient heuristic for globaloptimization over continuous spaces. Journal of global optimization, 11(4), 341-359.
[19] Rashedi, E., Nezamabadi-Pour, H., and Saryazdi, S. (2009). GSA: a gravitational search algorithm. Information sciences, 179(13), 2232-2248.
[20] Yao, X., Liu, Y., and Lin, G. (1999). Evolutionary programming made faster. IEEE Transactions on Evolutionary computation, 3(2), 82-102.
[21] Nasiri, J. and Khiyabani, F. M. (2018). A whale optimization algorithm (WOA) approach for clustering. Cogent Mathematics & Statistics, 5(1), 1483565.
[22] Canayaz, M. and Özdağ, R. (2017). Data clustering based on the whale optimization. Middle East Journal of Technic, 2(2), 178-187.
[23] Al-Temeemy, A. A., Spencer, J., and Ralph, J. (2010). Levy flights for improved ladar scanning. 2010 IEEE International Conference on Imaging Systems and Techniques,225-228.
[24] Chen, Y. (2010). Research and simulation on Levy flight model for DTN. 2010 3rd International Congress on Image and Signal Processing,4421- 4423.
[25] Pereyra, M. A. and Batatia, H. (2010). A Levy flight model for ultrasound in skin tissues. 2010 IEEE International Ultrasonics Symposium,2327-2331.
[26] Terdik, G. and Gyires, T. (2008). Lévy flights and fractal modeling of internet traffic. IEEE/ACM Transactions on Networking, 17(1), 120-129.
[27] Sutantyo, D. K., Kernbach, S., Levi, P., and Nepomnyashchikh, V. A. (2010). Multi-robot searching algorithm using Lévy flight and artificial potential field. 2010 IEEE Safety Security and Rescue Robotics,1-6.
[28] Rhee, I., Shin, M., Hong, S., Lee, K., Kim, S. J., and Chong, S. (2011). On the levy-walk nature of human mobility. IEEE/ACM transactions on networking, 19(3), 630-643.
[29] Edwards, A. M., Phillips, R. A., Watkins, N. W., Freeman, M. P., Murphy, E. J., Afanasyev, V., et al. (2007). Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees and deer. Nature, 449(7165), 1044-1048.
[30] Viswanathan, G. M., Afanasyev, V., Buldyrev, S., Murphy, E., Prince, P., and Stanley, H. E. (1996). Lévy flight search patterns of wandering albatrosses. Nature, 381(6581), 413-415.
[31] Yang, X.-S. and Deb, S. (2013). Multiobjective cuckoo search for design optimization. Computers & Operations Research, 40(6), 1616-1624.
[32] Yang, X.-S. (2010). Firefly algorithm, Levy flights and global optimization. Research and development in intelligent systems XXVI. Springer, 209-218.
[33] Murphy, P. and Aha, D. (1994). UCI repository of machine learning. University of California, Department of Information and Computer Science.
[34] Ozdamar, K. (2002). Paket programlari ile istatistiksel veri analizi-1. Kaan Kitabevi, Eskisehir.
[35] Tatlıdil, H. (1996). Uygulamalı Çok Değişkenli İstatistiksel Analiz. Cem Ofset Ltd. Şti, Ankara.
[36] Hair Jr, J., Anderson, R., and Tatham, R. (1998). Multivariate data analysis.NJ: PrenticeYHall Inc, Upper Saddle River.
[37] Lorr, M. (1983). Cluster analysis for socialscientists.Jossey-Bass Incorporated Pub.
[38] Boushaki, S. I., Kamel, N., and Bendjeghaba, O. (2018). A new quantum chaotic cuckoo search algorithm for data clustering. Expert Systems with Applications, 96, 358-372.
[39] Frigui, H. and Krishnapuram, R. (1999). A robust competitive clustering algorithm with applications in computer vision. Ieee transactions on pattern analysis and machine intelligence, 21(5), 450-465.
[40] Karakoyun, M. (2015). Kurbağa sıçrama algoritmasının kümeleme problemlerine uygulanması. Master Thesis. Selçuk University.
[41] Sharma, S. (1996). Applied multivariate techniques.
[42] Tabak, J. (2014). Geometry: the language of space and form. Infobase Publishing.
[43] MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations. Proceedings of the fifth Berkeley symposium on mathematical statistics and probability,281-297.
[44] Han, J. and Kamber, M. (2010). Data mining: concepts and techniques. [Nachdr.], Amsterdam: Elsevier/Morgan Kaufmann, 11, 6.
[45] Tan, P.-N., Steinbach, M., and Kumar, V. (2006). Classification: basic concepts, decision trees, and model evaluation. Introduction to data mining, 1, 145-205.
[46] Xu, R. and Wunsch, D. (2005). Survey of clustering algorithms. IEEE Transactions on neural networks, 16(3), 645-678.
[47] Dodge, Y. (2012). Statistical data analysis based on the L1-norm and related methods. Birkhäuser.
[48] Dinçer, Ş. E. (2006). Veri madenciliğinde K-means algoritması ve tıp alanında uygulanması. Master Thesis. Kocaeli University.
[49] Karakoyun, M., Saglam, A., Baykan, N. A., and Altun, A. A. (2017). Non-locally color image segmentation for remote sensing images in different color spaces by using data-clustering methods. 5th International Conference on Advanced Technology & Sciences (ICAT'17), 6-12.
[50] Höppner, F., Klawonn, F., Kruse, R., and Runkler, T. (1999). Fuzzy cluster analysis: methods for classification, data analysis and image recognition. John Wiley & Sons.
[51] Moertini, V. (2002). Introduction to Five DataClustering Algorithms Clustering Algorithm. Integral, 7(2).
[52] Goldbogen, J. A., Friedlaender, A. S., Calambokidis, J., Mckenna, M. F., Simon, M., and Nowacek, D. P. (2013). Integrative approaches to the study of baleen whale diving behavior, feeding performance, and foraging ecology. BioScience, 63(2), 90-100.
[53] Tanyıldızı, E. and Cigalı, T. (2017). Kaotik Haritalı Balina Optimizasyon Algoritmaları. Fırat Üniversitesi Mühendislik Bilimleri Dergisi, 29(1), 307-317.
[54] Pavlyukevich, I. (2007). Lévy flights, non-local search and simulated annealing. Journal of Computational Physics, 226(2), 1830-1844.
[55] Reynolds, A. M. and Frye, M. A. (2007). Free-flight odor tracking in Drosophila is consistent with an optimal intermittent scale-free search. PloS one, 2(4), e354.
[56] Shlesinger, M. F. (2006). Search research. Nature, 443(7109), 281-282. [57] Chechkin, A. V., Metzler, R., Klafter, J., and Gonchar, V. Y. (2008). Introduction to the theory of Lévy flights. Anomalous transport, 1, 129.
[58] Yang, X.-S. (2010). Engineering optimization: an introduction with metaheuristic applications. John Wiley & Sons.
[59] Lee, C.-Y. and Yao, X. (2001). Evolutionary algorithms with adaptive lévy mutations. Proceedings of the 2001 congress on evolutionary computation (IEEE Cat. No. 01TH8546), 568-575.