Model of Optimal Centroids Approach for Multivariate Data Classification

Authors: Pham Van Nha, Le Cam Binh

Abstract:

Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: Analysis of optimization, artificial intelligence-based optimization, optimization for learning and data analysis, global optimization.

References:

[1] M. Hanmandlua, O.P. Verma, S.S., V.K. Madasu. ”Color segmentation by fuzzy co-clustering of chrominance color features,” Neurocomputing, Vol. 120, pp. 235-249, 2013.
[2] V.N. Pham, N.T. Long, W. Pedrycz. ”Interval-valued fuzzy set approach to fuzzy co-clustering for data classification,” Knowledge-Based Systems, Vol. 107, pp. 1-13, 2016.
[3] J. Kennedy, R. Eberhart. ”Particle swarm optimization,” IEEE International Conference on Neural Networks, Vol. 4, pp. 19421948, 1995.
[4] Y. Song, F. Zhang, C. Liu. ”The risk of block chain financial market based on particle swarm optimization,” Journal of Computational and Applied Mathematics, Vol. 37015, Article 112667, 2020.
[5] W. Gao, C. Su. ”Analysis of earnings forecast of blockchain financial products based on particle swarm optimization,” Journal of Computational and Applied Mathematics, Vol. 372, Article 112724., 2020
[6] H. Xiong, B. Qiu, J. Liu. ”An improved multi-swarm particle swarm optimizer for optimizing the electric field distribution of multichannel transcranial magnetic stimulation,” Artificial Intelligence in Medicine, Vol. 104, Article 101790, 2020.
[7] F.E.F. Junior, G.G. Yen. ”Particle swarm optimization of deep neural networks architectures for image classification,” Swarm and Evolutionary Computation, Vol. 49, pp. 62-74, 2019.
[8] T.R. Farshi, J.H. Drake, E. Ozcan. ”A multimodal particle swarm optimization-based approach for image segmentation,” Expert Systems with Applications, Vol. 1491, Article 113233, 2020.
[9] R. Janani, S. Vijayarani. ”Text document clustering using Spectral Clustering algorithm with Particle Swarm Optimization,” Expert Systems with Applications, Vol. 13415, pp. 192-200, 2019.
[10] Zhihua Cui, Jiangjiang Zhang, Di Wu, Xingjuan Cai, Jinjun Chen. ”Hybrid many-objective particle swarm optimization algorithm for green coal production problem,” Information Sciences, Vol. 518, pp. 256-271, 2020.
[11] Md Maruf Hussain, Noriyuki Fujimoto. ”GPU-based parallel multi-objective particle swarm optimization for large swarms and high dimensional problems,” Parallel Computing, Vol. 92, Article 102589, 2020.
[12] Yingcheng Zhou, Zheng Zhao, Daojian Cheng. ”Cluster structure prediction via revised particle-swarm optimization algorithm,” Computer Physics Communications, Vol. 247, Article 106945, 2020.
[13] J.E. Mazur. ”Mathematical Models and the Experimental Analysis of Behavior,” Journal of the Experimental Analysis of Behavior, Vol. 85(2), pp. 275291, 2006.
[14] Y. Zhang, D. Huang, M. Ji, F. Xie. ”Image segmentation using PSO and PCM with Mahalanobis distance,” Expert Systems with Applications, Vol. 38(7), pp. 9036-9040, 2011.
[15] T.X. Pham, P. Siarry, H. Oulhadj. ”Integrating fuzzy entropy clustering with an improved PSO for MRI brain image segmentation,” Applied Soft Computing, Vol. 65, pp. 230-242, 2018.
[16] J.L. Salmeron, S.A. Rahimi, A.M. Navali, A. Sadeghpour. ”Medical diagnosis of Rheumatoid Arthritis using data driven PSOFCM with scarce datasets,” Neurocomputing, Vol. 2325, pp. 104-112, 2017.
[17] C. Hwang, F.C.H. Rhee, ”Uncertain fuzzy clustering: interval type-2 fuzzy approach to C-means,” IEEE Transactions on Fuzzy Systems, Vol. 15(1), pp. 107120, 2007.
[18] H. Xing, H. He, D. Hu, T. Jiang, X. Yu. ”An interval Type-2 fuzzy sets generation method for remote sensing imagery classification,” Computers & Geosciences, Vol. 133, Article 104287, 2019.
[19] D.L. Olson, D. Delen, Advanced Data Mining Techniques, Springer ISBN 3-540-76916-1, 1st edition, page 138, 2008.
[20] M.W.P. David, Evaluation: From Precision, Recall, and F-Measure to ROC, Informedness, Markedness & Correlation, Journal of Machine Learning Technologies, Vol. 2(1), pp. 37-63, 2011.