Research Article
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Year 2019, Volume: 48 Issue: 3, 859 - 882, 15.06.2019
https://doi.org/10.15672/HJMS.2019.655

Abstract

References

  • Alam, S., Dobbie, G., Koh, Y.S., Riddle, P., and Rehman, S.U. Research on particle swarm optimization based clustering: A systematic review of literature and techniques, Swarm and Evolutionary Computation 17, 1-13, 2014.
  • Bandyopadhyay, S. and Maulik, U. An evolutionary technique based on K-Means algorithm for optimal clustering in RN, Information Sciences 146 (1), 221-237, 2002.
  • Baykasolu, A. and Akpinar, . Weighted Superposition Attraction (WSA): A swarm intel- ligence algorithm for optimization problems Part 1: Unconstrained optimization, Applied Soft Computing 56, 520-540, 2017.
  • Baykasolu, A. and Akpinar, . Weighted Superposition Attraction (WSA): A swarm intelli- gence algorithm for optimization problems Part 2: Constrained optimization, Applied Soft Computing 37, 396-415, 2015.
  • Baykasolu, A. and Ozsoydan, F.B. Dynamic optimization in binary search spaces via weighted superposition attraction algorithm, Expert Systems with Applications 96 157-174, 2018.
  • Belacel, N., Hansen, P., and Mladenovic, N. Fuzzy J-Means: a new heuristic for fuzzy clustering, Pattern Recognition 35 (10), 2193-2200, 2002.
  • Bezdek, J.C., Fuzzy Mathematics in Pattern Classification, Cornell University: Ithaca, NY, 1973.
  • Bezdek, J.C., Ehrlich, R., and Full, W. FCM: The fuzzy c-means clustering algorithm, Computers and Geosciences 10 (2), 191-203, 1984.
  • Bezdek, J.C. Pattern Recognition with Fuzzy Objective Function Algorithms (Plenum Press, New York, 1981).
  • Bezdek, J.C. Cluster Validity with Fuzzy Sets, Journal of Cybernetics 3 (3), 58-73, 1973.
  • Blackwell, T., Branke, J., and Li, X., Particle swarms for dynamic optimization problems, in Swarm Intelligence, Springer. p. 193-217, 2008.
  • Blackwell, T. and Branke, J., Multi-swarm Optimization in Dynamic Environments, in Ap- plications of Evolutionary Computing: EvoWorkshops, Springer Berlin Heidelberg: Berlin, Heidelberg. p. 489-500, 2004.
  • Chen, M.-Y. and Linkens, D.A. Rule-base self-generation and simplification for data-driven fuzzy models. in 10th IEEE International Conference on Fuzzy Systems, 2001.
  • Derrac, J., García, S., Molina, D., and Herrera, F. A practical tutorial on the use of nonpara- metric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms, Swarm and Evolutionary Computation 1 (1), 3-18, 2011.
  • Filho, T.M.S., Pimentel, B.A., Souza, R.M.C.R., and Oliveira, A.L.I. Hybrid methods for fuzzy clustering based on fuzzy c-means and improved particle swarm optimization, Expert Systems with Applications 42 (17), 6315-6328, 2015.
  • Forgy, E.W. Cluster analysis of multivariate data: efficiency versus interpretability models, Biometrics 61 (3), 768-769, 1965.
  • Fukuyama, Y. and Sugeno, M. A new method of choosing the number of clusters for the fuzzy c-mean method. in Proc. 5th Fuzzy Syst. Symp, 1989.
  • Graves, D. and Pedrycz, W. Kernel-based fuzzy clustering and fuzzy clustering: A compar- ative experimental study, Fuzzy Sets and Systems 161 (4), 522-543, 2010.
  • Güngör, Z. and Ünler, A. K-harmonic means data clustering with simulated annealing heuristic, Applied Mathematics and Computation 184 (2), 199-209, 2007.
  • Hayes-Roth, B. and Hayes-Roth, F. Concept learning and the recognition and classification of exemplars, Journal of Verbal Learning and Verbal Behavior 16 (3), 321-338, 1977.
  • José-García, A. and Gómez-Flores, W. Automatic clustering using nature-inspired meta- heuristics: A survey, Applied Soft Computing 41, 192-213, 2016.
  • Kao, Y.-T., Zahara, E., and Kao, I.W. A hybridized approach to data clustering, Expert Systems with Applications 34 (3), 1754-1762, 2008
  • Li, C., Zhou, J., Kou, P., and Xiao, J. A novel chaotic particle swarm optimization based fuzzy clustering algorithm, Neurocomputing 83, 98-109, 2012.
  • Lichman, M., UCI Machine Learning Repository, University of California, School of Infor- mation and Computer Sciences, Irvine, CA, 2013.
  • Nanda, S.J. and Panda, G. A survey on nature inspired metaheuristic algorithms for par- titional clustering, Swarm and Evolutionary Computation 16 (Supplement C), 1-18, 2014.
  • Nayak, J., Naik, B., Behera, H.S., and Abraham, A. Hybrid chemical reaction based meta- heuristic with fuzzy c-means algorithm for optimal cluster analysis, Expert Systems with Applications 79, 282-295, 2017.
  • Özbakr, L. and Turna, F. Clustering performance comparison of new generation meta- heuristic algorithms, Knowledge-Based Systems 130, 1-16, 2017.
  • Pakhira, M.K., Bandyopadhyay, S., and Maulik, U. A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification, Fuzzy Sets and Systems 155 (2), 191-214, 2005.
  • Pal, N.R., Pal, K., Keller, J.M., and Bezdek, J.C. A possibilistic fuzzy c-means clustering algorithm, IEEE transactions on fuzzy systems 13 (4), 517-530, 2005.
  • Pimentel, B.A. and de Souza, R.M.C.R. A multivariate fuzzy c-means method, Applied Soft Computing 13 (4), 1592-1607, 2013.
  • Pimentel, B.A. and de Souza, R.M.C.R. A weighted multivariate Fuzzy C-Means method in interval-valued scientific production data, Expert Systems with Applications 41 (7), 3223- 3236, 2014.
  • Sabzekar, M. and Naghibzadeh, M. Fuzzy c-means improvement using relaxed constraints support vector machines, Applied Soft Computing 13 (2), 881-890, 2013.
  • Shelokar, P.S., Jayaraman, V.K., and Kulkarni, B.D. An ant colony approach for clustering, Analytica Chimica Acta 509 (2), 187-195, 2004.
  • Siegler, R.S. Three aspects of cognitive development, Cognitive psychology 8 (4), 481-520, 1976.
  • Xie, X.L. and Beni, G. A validity measure for fuzzy clustering, IEEE Transactions on pattern analysis and machine intelligence 13 (8), 841-847, 1991.
  • Zhang, L., Pedrycz, W., Lu, W., Liu, X., and Zhang, L. An interval weighed fuzzy c-means clustering by genetically guided alternating optimization, Expert Systems with Applications 41 (13), 5960-5971, 2014.
  • Zhang, C., Ouyang, D., and Ning, J. An artificial bee colony approach for clustering, Expert Systems with Applications 37 (7), 4761-4767, 2010.
  • Zhao, F., Fan, J., and Liu, H. Optimal-selection-based suppressed fuzzy c-means clustering algorithm with self-tuning non local spatial information for image segmentation, Expert Systems with Applications 41 (9), 4083-4093, 2014.

Improving fuzzy c-means clustering via quantum-enhanced weighted superposition attraction algorithm

Year 2019, Volume: 48 Issue: 3, 859 - 882, 15.06.2019
https://doi.org/10.15672/HJMS.2019.655

Abstract

Fuzzy clustering has become an important research field in pattern recognition and data analysis. As supporting unsupervised mode of learning, fuzzy clustering brings about unique opportunities to reveal structural relationships in data. Fuzzy c-means clustering is one of the widely preferred clustering algorithms in the literature. However, fuzzy c-means clustering algorithm has a major drawback that it can get trapped at some local optima. In order to overcome this shortcoming, this study employs a new generation metaheuristic algorithm. Weighted Superposition Attraction Algorithm (WSA) is a novel swarm intelligence-based method that draws inspiration from the superposition principle of physics in combination with the attracted movement of agents. Due to its high converging capability and practicality, WSA algorithm has been employed in order to enhance performance of fuzzy-c means clustering. Comprehensive experimental study has been conducted on publicly available datasets obtained from UCI machine learning repository. The results point out significant improvements over the traditional fuzzy c-means algorithm.

References

  • Alam, S., Dobbie, G., Koh, Y.S., Riddle, P., and Rehman, S.U. Research on particle swarm optimization based clustering: A systematic review of literature and techniques, Swarm and Evolutionary Computation 17, 1-13, 2014.
  • Bandyopadhyay, S. and Maulik, U. An evolutionary technique based on K-Means algorithm for optimal clustering in RN, Information Sciences 146 (1), 221-237, 2002.
  • Baykasolu, A. and Akpinar, . Weighted Superposition Attraction (WSA): A swarm intel- ligence algorithm for optimization problems Part 1: Unconstrained optimization, Applied Soft Computing 56, 520-540, 2017.
  • Baykasolu, A. and Akpinar, . Weighted Superposition Attraction (WSA): A swarm intelli- gence algorithm for optimization problems Part 2: Constrained optimization, Applied Soft Computing 37, 396-415, 2015.
  • Baykasolu, A. and Ozsoydan, F.B. Dynamic optimization in binary search spaces via weighted superposition attraction algorithm, Expert Systems with Applications 96 157-174, 2018.
  • Belacel, N., Hansen, P., and Mladenovic, N. Fuzzy J-Means: a new heuristic for fuzzy clustering, Pattern Recognition 35 (10), 2193-2200, 2002.
  • Bezdek, J.C., Fuzzy Mathematics in Pattern Classification, Cornell University: Ithaca, NY, 1973.
  • Bezdek, J.C., Ehrlich, R., and Full, W. FCM: The fuzzy c-means clustering algorithm, Computers and Geosciences 10 (2), 191-203, 1984.
  • Bezdek, J.C. Pattern Recognition with Fuzzy Objective Function Algorithms (Plenum Press, New York, 1981).
  • Bezdek, J.C. Cluster Validity with Fuzzy Sets, Journal of Cybernetics 3 (3), 58-73, 1973.
  • Blackwell, T., Branke, J., and Li, X., Particle swarms for dynamic optimization problems, in Swarm Intelligence, Springer. p. 193-217, 2008.
  • Blackwell, T. and Branke, J., Multi-swarm Optimization in Dynamic Environments, in Ap- plications of Evolutionary Computing: EvoWorkshops, Springer Berlin Heidelberg: Berlin, Heidelberg. p. 489-500, 2004.
  • Chen, M.-Y. and Linkens, D.A. Rule-base self-generation and simplification for data-driven fuzzy models. in 10th IEEE International Conference on Fuzzy Systems, 2001.
  • Derrac, J., García, S., Molina, D., and Herrera, F. A practical tutorial on the use of nonpara- metric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms, Swarm and Evolutionary Computation 1 (1), 3-18, 2011.
  • Filho, T.M.S., Pimentel, B.A., Souza, R.M.C.R., and Oliveira, A.L.I. Hybrid methods for fuzzy clustering based on fuzzy c-means and improved particle swarm optimization, Expert Systems with Applications 42 (17), 6315-6328, 2015.
  • Forgy, E.W. Cluster analysis of multivariate data: efficiency versus interpretability models, Biometrics 61 (3), 768-769, 1965.
  • Fukuyama, Y. and Sugeno, M. A new method of choosing the number of clusters for the fuzzy c-mean method. in Proc. 5th Fuzzy Syst. Symp, 1989.
  • Graves, D. and Pedrycz, W. Kernel-based fuzzy clustering and fuzzy clustering: A compar- ative experimental study, Fuzzy Sets and Systems 161 (4), 522-543, 2010.
  • Güngör, Z. and Ünler, A. K-harmonic means data clustering with simulated annealing heuristic, Applied Mathematics and Computation 184 (2), 199-209, 2007.
  • Hayes-Roth, B. and Hayes-Roth, F. Concept learning and the recognition and classification of exemplars, Journal of Verbal Learning and Verbal Behavior 16 (3), 321-338, 1977.
  • José-García, A. and Gómez-Flores, W. Automatic clustering using nature-inspired meta- heuristics: A survey, Applied Soft Computing 41, 192-213, 2016.
  • Kao, Y.-T., Zahara, E., and Kao, I.W. A hybridized approach to data clustering, Expert Systems with Applications 34 (3), 1754-1762, 2008
  • Li, C., Zhou, J., Kou, P., and Xiao, J. A novel chaotic particle swarm optimization based fuzzy clustering algorithm, Neurocomputing 83, 98-109, 2012.
  • Lichman, M., UCI Machine Learning Repository, University of California, School of Infor- mation and Computer Sciences, Irvine, CA, 2013.
  • Nanda, S.J. and Panda, G. A survey on nature inspired metaheuristic algorithms for par- titional clustering, Swarm and Evolutionary Computation 16 (Supplement C), 1-18, 2014.
  • Nayak, J., Naik, B., Behera, H.S., and Abraham, A. Hybrid chemical reaction based meta- heuristic with fuzzy c-means algorithm for optimal cluster analysis, Expert Systems with Applications 79, 282-295, 2017.
  • Özbakr, L. and Turna, F. Clustering performance comparison of new generation meta- heuristic algorithms, Knowledge-Based Systems 130, 1-16, 2017.
  • Pakhira, M.K., Bandyopadhyay, S., and Maulik, U. A study of some fuzzy cluster validity indices, genetic clustering and application to pixel classification, Fuzzy Sets and Systems 155 (2), 191-214, 2005.
  • Pal, N.R., Pal, K., Keller, J.M., and Bezdek, J.C. A possibilistic fuzzy c-means clustering algorithm, IEEE transactions on fuzzy systems 13 (4), 517-530, 2005.
  • Pimentel, B.A. and de Souza, R.M.C.R. A multivariate fuzzy c-means method, Applied Soft Computing 13 (4), 1592-1607, 2013.
  • Pimentel, B.A. and de Souza, R.M.C.R. A weighted multivariate Fuzzy C-Means method in interval-valued scientific production data, Expert Systems with Applications 41 (7), 3223- 3236, 2014.
  • Sabzekar, M. and Naghibzadeh, M. Fuzzy c-means improvement using relaxed constraints support vector machines, Applied Soft Computing 13 (2), 881-890, 2013.
  • Shelokar, P.S., Jayaraman, V.K., and Kulkarni, B.D. An ant colony approach for clustering, Analytica Chimica Acta 509 (2), 187-195, 2004.
  • Siegler, R.S. Three aspects of cognitive development, Cognitive psychology 8 (4), 481-520, 1976.
  • Xie, X.L. and Beni, G. A validity measure for fuzzy clustering, IEEE Transactions on pattern analysis and machine intelligence 13 (8), 841-847, 1991.
  • Zhang, L., Pedrycz, W., Lu, W., Liu, X., and Zhang, L. An interval weighed fuzzy c-means clustering by genetically guided alternating optimization, Expert Systems with Applications 41 (13), 5960-5971, 2014.
  • Zhang, C., Ouyang, D., and Ning, J. An artificial bee colony approach for clustering, Expert Systems with Applications 37 (7), 4761-4767, 2010.
  • Zhao, F., Fan, J., and Liu, H. Optimal-selection-based suppressed fuzzy c-means clustering algorithm with self-tuning non local spatial information for image segmentation, Expert Systems with Applications 41 (9), 4083-4093, 2014.
There are 38 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Adil Baykasoğlu 0000-0002-4952-7239

İlker Gölcük 0000-0002-8430-7952

Fehmi Burçin Özsoydan 0000-0002-6368-4425

Publication Date June 15, 2019
Published in Issue Year 2019 Volume: 48 Issue: 3

Cite

APA Baykasoğlu, A., Gölcük, İ., & Özsoydan, F. B. (2019). Improving fuzzy c-means clustering via quantum-enhanced weighted superposition attraction algorithm. Hacettepe Journal of Mathematics and Statistics, 48(3), 859-882. https://doi.org/10.15672/HJMS.2019.655
AMA Baykasoğlu A, Gölcük İ, Özsoydan FB. Improving fuzzy c-means clustering via quantum-enhanced weighted superposition attraction algorithm. Hacettepe Journal of Mathematics and Statistics. June 2019;48(3):859-882. doi:10.15672/HJMS.2019.655
Chicago Baykasoğlu, Adil, İlker Gölcük, and Fehmi Burçin Özsoydan. “Improving Fuzzy C-Means Clustering via Quantum-Enhanced Weighted Superposition Attraction Algorithm”. Hacettepe Journal of Mathematics and Statistics 48, no. 3 (June 2019): 859-82. https://doi.org/10.15672/HJMS.2019.655.
EndNote Baykasoğlu A, Gölcük İ, Özsoydan FB (June 1, 2019) Improving fuzzy c-means clustering via quantum-enhanced weighted superposition attraction algorithm. Hacettepe Journal of Mathematics and Statistics 48 3 859–882.
IEEE A. Baykasoğlu, İ. Gölcük, and F. B. Özsoydan, “Improving fuzzy c-means clustering via quantum-enhanced weighted superposition attraction algorithm”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, pp. 859–882, 2019, doi: 10.15672/HJMS.2019.655.
ISNAD Baykasoğlu, Adil et al. “Improving Fuzzy C-Means Clustering via Quantum-Enhanced Weighted Superposition Attraction Algorithm”. Hacettepe Journal of Mathematics and Statistics 48/3 (June 2019), 859-882. https://doi.org/10.15672/HJMS.2019.655.
JAMA Baykasoğlu A, Gölcük İ, Özsoydan FB. Improving fuzzy c-means clustering via quantum-enhanced weighted superposition attraction algorithm. Hacettepe Journal of Mathematics and Statistics. 2019;48:859–882.
MLA Baykasoğlu, Adil et al. “Improving Fuzzy C-Means Clustering via Quantum-Enhanced Weighted Superposition Attraction Algorithm”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, 2019, pp. 859-82, doi:10.15672/HJMS.2019.655.
Vancouver Baykasoğlu A, Gölcük İ, Özsoydan FB. Improving fuzzy c-means clustering via quantum-enhanced weighted superposition attraction algorithm. Hacettepe Journal of Mathematics and Statistics. 2019;48(3):859-82.