Year 2019,
, 859 - 882, 15.06.2019
Adil Baykasoğlu
,
İlker Gölcük
,
Fehmi Burçin Özsoydan
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,
, 859 - 882, 15.06.2019
Adil Baykasoğlu
,
İlker Gölcük
,
Fehmi Burçin Özsoydan
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.