JACIII Vol.23 No.3 pp. 592-601
doi: 10.20965/jaciii.2019.p0592


Interval Type-2 Fuzzy Possibilistic C-Means Clustering Based on Granular Gravitational Forces and Particle Swarm Optimization

Hung Quoc Truong, Long Thanh Ngo, and Long The Pham

Le Quy Don Technical University (LQDTU)
236 Hoang Quoc Viet Road, Bac Tu Liem District, Hanoi 100000, Vietnam

Corresponding author

December 12, 2018
February 19, 2019
May 20, 2019
fuzzy possibilistic C-means clustering, interval type-2 fuzzy sets, granular computing, granular gravitational clustering, particle swarm optimization

The interval type-2 fuzzy possibilistic C-means clustering (IT2FPCM) algorithm improves the performance of the fuzzy possibilistic C-means clustering (FPCM) algorithm by addressing high degrees of noise and uncertainty. However, the IT2FPCM algorithm continues to face drawbacks including sensitivity to cluster centroid initialization, slow processing speed, and the possibility of being easily trapped in local optima. To overcome these drawbacks and better address noise and uncertainty, we propose an IT2FPCM method based on granular gravitational forces and particle swarm optimization (PSO). This method is based on the idea of gravitational forces grouping the data points into granules and then processing clusters on a granular space using a hybrid algorithm of the IT2FPCM and PSO algorithms. The proposed method also determines the initial centroids by merging granules until the number of granules is equal to the number of clusters. By reducing the elements in the granular space, the proposed algorithms also significantly improve performance when clustering large datasets. Experimental results are reported on different datasets compared with other approaches to demonstrate the advantages of the proposed method.

Cite this article as:
H. Truong, L. Ngo, and L. Pham, “Interval Type-2 Fuzzy Possibilistic C-Means Clustering Based on Granular Gravitational Forces and Particle Swarm Optimization,” J. Adv. Comput. Intell. Intell. Inform., Vol.23, No.3, pp. 592-601, 2019.
Data files:
  1. [1] J. C. Bezdek, R. Ehrlich, and W. Full, “FCM: The Fuzzy C-Means Clustering Algorithm,” Computers & Geosciences, Vol.10, Issues 2-3, pp. 191-203, 1984.
  2. [2] R. Krishnapuram and J. M. Keller, “A possibilistic approach to clustering,” IEEE Trans. on Fuzzy Systems, Vol.1, No.2, pp. 98-110, 1993.
  3. [3] N. R. Pal, K. Pal, and J. C. Bezdek, “A mixed C-Means clustering model,” The 6th IEEE Int. Conf. on Fuzzy Systems, Vol.1, pp. 11-21, 1997.
  4. [4] S. Askari, N. Montazerin, and M. H. Fazel Zarandi, “Generalized possibilistic fuzzy C-Means with novel cluster validity indices for clustering noisy data,” Applied Soft Computing, Vol.53, pp. 262-283, 2017.
  5. [5] S. Askari, N. Montazerin, M. H. Fazel Zarandi, and E. Hakimi, “Generalized entropy based possibilistic fuzzy c-means for clustering noisy data and its convergence proof,” Neurocomputing, Vol.219, pp. 186-202, 2017.
  6. [6] M. B. Ferraro and P. Giordani, “Possibilistic and fuzzy clustering methods for robust analysis of non-precise data,” Int. J. of Approximate Reasoning, Vol.88, pp. 23-38, 2017.
  7. [7] J. Aparajeeta, P. K. Nanda, and N. Das, “Modified Possibilistic fuzzy C–means algorithms for segmentation of magnetic resonance image,” Applied Soft Computing, Vol.41, pp. 104-119, 2016.
  8. [8] N. N. Karnik and J. M. Mendel, “Operations on type-2 sets,” Fuzzy Sets and Systems, Vol.122, No.2, pp. 327-348, 2001.
  9. [9] C. Hwang and F. C.-H. Rhee, “Uncertain fuzzy clustering: interval type-2 fuzzy approach to C-Means,” IEEE Trans. on Fuzzy Systems, Vol.15, No.1, pp. 107-120, 2007.
  10. [10] M. H. F. Zarandi, M. Zarinbal, and I. B. Turksen, “Type–II fuzzy possibilistic C-mean clustering,” IFSA-EUSFLAT 2009, pp. 30-35, 2009.
  11. [11] J. P. Sarkar, I. Saha, and U. Maulik, “Rough Possibilistic Type-2 Fuzzy C-Means clustering for MR brain image segmentation,” Applied Soft Computing, Vol.46, pp. 527-536, 2016.
  12. [12] E. Rubio, O. Castillo, and P. Melin, “A new Interval Type-2 Fuzzy Possibilistic C-Means clustering algorithm,” 2015 Annual Conf. of the North American Fuzzy Information Processing Society (NAFIPS) held jointly with 2015 5th World Conf. on Soft Computing (WConSC), pp. 1-5, 2015.
  13. [13] E. Rubio and O. Castillo, “Optimization of the Interval Type-2 Fuzzy C-Means using Granular Swarm Optimization,” Proc. of the 10th Nano Bio Info Chemistry (NaBIC) Symp., pp. 10-15, 2013.
  14. [14] W. Pedrycz, “Granular Computing for Data Analytics: A Manifesto of Human-Centric Computing,” IEEE/CAA J. of Automatica Sinica, Vol.5, No.6, pp. 1025-1034, 2018.
  15. [15] W. Pedrycz, “From fuzzy data analysis and fuzzy regression to granular fuzzy data analysis,” Fuzzy Sets and Systems, Vol.274, pp. 12-17, 2015.
  16. [16] A. Bargiela and W. Pedrycz, “Toward a Theory of Granular Computing for Human-Centered Information Processing,” IEEE Trans. on Fuzzy Systems, Vol.16, No.2, pp. 320-330, 2008.
  17. [17] W. Pedrycz, “Granular computing – The emerging paradigm,” J. of Uncertain Systems, Vol.1, No.1, pp. 38-61, 2007.
  18. [18] W. Pedrycz and A. Bargiela, “An Optimization of Allocation of Information Granularity in the Interpretation of Data Structures: Toward Granular Fuzzy Clustering,” IEEE Trans. on Systems, Man, and Cybernetics, Part B (Cybernetics), Vol.42, No.3, pp. 582-590, 2012.
  19. [19] A. Bargiela, W. Pedrycz, and K. Hirota, “Granular Prototyping in Fuzzy Clustering,” IEEE Trans. on Fuzzy Systems, Vol.12, No.5, pp. 697-709, 2004.
  20. [20] A. Gacek and W. Pedrycz, “Clustering Granular Data and Their Characterization with Information Granules of Higher Type,” IEEE Trans. on Fuzzy Systems, Vol.23, No.4, pp. 850-860, 2015.
  21. [21] R. J. Kuo, P. Y. Su, F. E. Zulvia, and C. C. Lin, “Integrating cluster analysis with granular computing for imbalanced data classification problem – A case study on prostate cancer prognosis,” Computers & Industrial Engineering, Vol.125, pp. 319-332, 2018.
  22. [22] X. Wang, X. Liu, and L. Zhang, “A rapid fuzzy rule clustering method based on granular computing,” Applied Soft Computing, Vol.24, pp. 534-542, 2014.
  23. [23] H. Q. Truong, L. T. Ngo, and W. Pedrycz, “Granular Fuzzy Possibilistic C-Means Clustering approach to DNA microarray problem,” Knowledge-Based Systems, Vol.133, pp. 53-65, 2017.
  24. [24] M. A. Sanchez, O. Castillo, J. R. Castro, and P. Melin, “Fuzzy granular gravitational clustering algorithm for multivariate data,” Information Sciences, Vol.279, pp. 498-511, 2014.
  25. [25] M. Alswaitti, M. K. Ishak, and N. A. M. Isa, “Optimized gravitational-based data clustering algorithm,” Engineering Applications of Artificial Intelligence, Vol.73, pp. 126-148, 2018.
  26. [26] J. Kennedy and R. Eberhart, “Particle Swarm Optimization,” Proc. of Int. Conf. Neural Network, Vol.4, pp. 1942-1948, 1995.
  27. [27] R. Eberhart and J. Kennedy, “A new optimizer using particle swarm theory,” Proc. 6th Int. Symp. Micro Machine and Human Science (MHS), pp. 39-43, 1995.
  28. [28] J. Gou, Y.-X. Lei, W.-P. Guo, C. Wang, Y.-Q. Cai, and W. Luo, “A novel improved particle swarm optimization algorithm based on individual difference evolution,” Applied Soft Computing, Vol.57, pp. 468-481, 2017.
  29. [29] K. V. Shihabudheen, M. Mahesh, and G. N. Pillai, “Particle swarm optimization based extreme learning neuro-fuzzy system for regression and classification,” Expert Systems with Applications, Vol.92, pp. 474-484, 2018.
  30. [30] M. Alswaitti, M. Albughdadi, and N. A. M. Isa, “Density-based particle swarm optimization algorithm for data clustering,” Expert Systems with Applications, Vol.91, pp. 170-186, 2018.
  31. [31] T. X. Pham, P. Siarry, and H. Oulhadj, “Integrating fuzzy entropy clustering with an improved PSO for MRI brain image segmentation,” Applied Soft Computing, Vol.65, pp. 230-242, 2018.
  32. [32] H. Izakian and A. Abraham, “Fuzzy C-Means and fuzzy swarm for fuzzy clustering problem,” Expert Systems with Applications, Vol.38, No.3, pp. 1835-1838, 2011.
  33. [33] J. Zang and K. Song, “Trembling Particle Swarm Optimization for Modified Possibilistic C-Means in Image Segmentation,” 2nd WRI Global Congress on Intelligent Systems, Vol.2, pp. 119-122, 2010.

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