Abstract
Radial basis function neural networks (RBF NNs) are one of the most useful tools in the classification of the sonar targets. Despite many abilities of RBF NNs, low accuracy in classification, entrapment in local minima, and slow convergence rate are disadvantages of these networks. In order to overcome these issues, the sine-cosine algorithm (SCA) has been used to train RBF NNs in this work. To evaluate the designed classifier, two benchmark underwater sonar classification problems were used. Also, an experimental underwater target classification was developed to practically evaluate the merits of the RBFbased classifier in dealing with high-dimensional real world problems. In order to have a comprehensive evaluation, the classifier is compared with the gradient descent (GD), gravitational search algorithm (GSA), genetic algorithm (GA), and Kalman filter (KF) algorithms in terms of entrapment in local minima, the accuracy of the classification, and the convergence rate. The results show that the proposed classifier provides a better performance than other compared classifiers as it classifies the sonar datasets 2.72% better than the best benchmark classifier, on average.Keywords:
classifiers, radial basis function neural network, sine-cosine algorithm, sonarReferences
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2. Abu-Mouti F.S., El-Hawary M.E. (2012), Overview of Artificial Bee Colony (ABC) algorithm and its applications, 2012 IEEE International Systems Conference SysCon, pp. 1–6, https://doi.org/10.1109/SysCon.2012.6189539
3. Aljarah I., Faris H., Mirjalili S., Al-Madi N. (2016), Training radial basis function networks using biogeography-based optimizer, Neural Computing and Applications, 29(7): 529–553, https://doi.org/10.1007/s00521-016-2559-2
4. Auer P., Burgsteiner H., Maass W. (2008), A learning rule for very simple universal approximators consisting of a single layer of perceptrons, Neural Networks, 21(5): 786–795, https://doi.org/10.1016/j.neunet.2007.12.036
5. Chen S., Hong X., Luk B.L., Harris C.J. (2009), Non-linear system identification using particle swarm optimisation tuned radial basis function models, International Journal of Bio-Inspired Computation, 1(4): 246–258, https://doi.org/10.1504/IJBIC.2009.024723
6. Chen S., Wu Y., Luk B.L. (1999), Combined genetic algorithm optimization and regularized orthogonal least squares learning for radial basis function networks, IEEE Transactions on Neural Networks, 10(5): 1239–1243, https://doi.org/10.1109/72.788663
7. Chun-Tao M., Xiao-Xia L., Li-Yong Z. (2007), Radial basis function neural network based on ant colony optimization, IEEE International Conference on Computational Intelligence and Security Workshops (CISW 2007), pp. 59–62, https://doi.org/10.1109/CISW.2007.4425446
8. Ding S., Xu L., Su C., Jin F. (2012), An optimizing method of RBF neural network based on genetic algorithm, Neural Computing and Applications, 21(2): 333–336, https://doi.org/10.1007/s00521-011-0702-7
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10. Dua D., Graff C. (2019), UCI Machine Learning Repository, Irvine, CA: University of California, School of Information and Computer Science, Connectionist Bench (sonar, mines vs. rocks), http://archive.ics.uci.edu/ml/datasets/Connectionist+Bench+(Sonar,+Mines+vs.+Rocks)
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15. Gorman R.P., Sejnowski T.J. (1998), Analysis of hidden units in a layered network trained to classify sonar targets, Neural Networks, 1(1): 75–89, https://doi.org/10.1016/0893-6080%2888%2990023-8
16. Gutiérrez F.J., Zhao A. (2015), Common data set 2015, Kongsberg GeoAcoustics Ltd.
17. Ho Y.C., Pepyne D.L. (2002), Simple explanation of the No-Free-Lunch theorem and its implications, Journal of Optimization Theory and Applications, 115(3): 549–570, https://doi.org/10.1023/A%3A1021251113462
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25. Mirjalili S. (2016), SCA: a Sine Cosine Algorithm for solving optimization problems, Knowledge-Based Systems, 96: 120–133, https://doi.org/10.1016/j.knosys.2015.12.022
26. Mirjalili S., Hashim S.Z.M., Sardroudi H.M. (2012), Training feedforward neural networks using hybrid particle swarm optimization and gravitational search algorithm, Applied Mathematics and Computation, 218(22): 11125–11137, https://doi.org/10.1016/j.amc.2012.04.069
27. Mirjalili S., Mirjalili S.M., Lewis A. (2014), Let a biogeography-based optimizer train your multi-layer perceptron, Journal of Information Sciences, 269: 188–209, https://doi.org/10.1016/j.ins.2014.01.038
28. Mosavi M.R., Khishe M. (2017), Training a feed-forward neural network using particle swarm optimizer with autonomous groups for sonar target classification, Journal of Circuits, Systems, and Computers (JCSC), 26(11): 1750185:1-1750185:20, https://doi.org/10.1142/S0218126617501857
29. Mosavi M.R., Khishe M., Moridi A. (2016), Classification of sonar target using hybrid particle swarm and gravitational search, Marine Technology, 3(1): 1–13, https://www.sid.ir/en/journal/ViewPaper.aspx?id=532112
30. Neruda R., Kudová P. (2005), Learning methods for radial basis function networks, Future Generation Computer Systems, 21(7): 1131–1142, https://doi.org/10.1016/j.future.2004.03.013
31. Nguyen L.S., Frauendorfer D., Mast M. S., Gatica-Perez D. (2014), Hire me: Computational inference of hirability in employment interviews based on nonverbal behavior, IEEE Transactions on Multimedia, 16(4): 1018–1031, https://doi.org/10.1109/TMM.2014.2307169
32. Park J., Sandberg I.W. (1993), Approximation and radial-basis-function networks, Neural Computation, 5(2): 305–316, https://doi.org/10.1162/neco.1993.5.2.305
33. Preston M. (2004), Resampling sonar echo time series primarily for seabed sediment, United State Patent, US 6,801,474 B2.
34. Vogt M. (1993), Combination of radial basis function neural networks with optimized learning vector quantization, IEEE International Conference on Neural Networks, San Francisco, CA, USA, Vol. 3, pp. 1841–1846, https://doi.org/10.1109/ICNN.1993.298837
35. Wu D. et al. (2010), Prediction of Parkinson’s disease tremor onset using a radial basis function neural network based on particle swarm optimization, International Journal of Neural Systems, 20(02): 109–116, https://doi.org/10.1142/S0129065710002292
36. Yang X.S. (2014), Nature-Inspired Optimization Algorithms, Elsevier.
37. Yu B., He X. (2006), Training radial basis function networks with differential evolution, Proceedings of IEEE International Conference on Granular Computing, pp. 369–372.
38. Yu H., Xie T., Paszczyński S., Wilamowski B.M. (2011), Advantages of radial basis function networks for dynamic system design, IEEE Transactions on Industrial Electronics, 58(12): 5438–5450, https://doi.org/10.1109/TIE.2011.2164773
39. Yu-Qing S., Jun-Fei Q., Hong-Gui H. (2016), Structure design for RBF neural network based on improved K-means algorithm, Chinese Control and Decision Conference (CCDC), Yinchuan, pp. 7035–7040, https://doi.org/10.1109/CCDC.2016.7532265
40. Zhong Y., Huang X., Meng P., Li F. (2014), PSO-RBF neural network PID control algorithm of electric gas pressure regulator, Abstract and Applied Analysis, 2014: article ID 731368, 7 pages, https://doi.org/10.1155/2014/731368
