Abstract
Data analysis becomes more important since rapid technology developments. In data analysis, data clustering is one of the very useful approaches. It can reveal important information hiding inside the dataset by organizing the instances based on their similarity. The objectives of data clustering are maximizing dissimilarity between clusters and minimizing dissimilarity within clusters. In order to construct a good clustering results, many clustering algorithms have been proposed, including the metaheuristic-based clustering algorithms. Recently, a new metaheuristic algorithm named gradient evolution has been proposed. This algorithm shows a good performance on solving the optimization problems. Therefore, this paper employs this GE algorithm for solving the clustering problem. In order to obtain a better clustering result, this paper considers multi-objective clustering instead of single-objective clustering. In this paper, the original GE algorithm is improved so then it is suitable for the multi-objective problem. The proposed modification includes the procedure for vector updating and jumping which involves Pareto rank assignment. In addition, it also employs K-means algorithm to provide the final clustering result. The proposed algorithm is verified using some benchmark datasets. It is also compared with some other multi-objective metaheuristic-based clustering algorithms. The experimental results show that the proposed algorithm can obtain better results than other metaheuristic-based algorithms.
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Acharya S, Saha S, Thadisina Y (2015) Multiobjective simulated annealing based clustering of tissue samples for cancer diagnosis. IEEE J Biomed Health Inf 20(2):691–698. https://doi.org/10.1109/jbhi.2015.2404971
Alok A, Saha S, Ekbal A (2015) Semi-supervised clustering for gene-expression data in multiobjective optimization framework. Int J Mach Learn Cybern. https://doi.org/10.1007/s13042-015-0335-8
Arabali A, Ghofrani M, Etezadi-Amoli M, Fadali MS, Baghzouz Y (2013) Genetic-algorithm-based optimization approach for energy management. IEEE Trans Power Deliv 28(1):162–170. https://doi.org/10.1109/TPWRD.2012.2219598
Carrizosa E, Alguwaizani A, Hansen P, Mladenović N (2015) New heuristic for harmonic means clustering. J Glob Optim 63(3):427–443. https://doi.org/10.1007/s10898-014-0175-1
Chen M-S, Han J, Yu PS (1996) Data mining: an overview from a database perspective. IEEE Trans Knowl Data Eng 8(6):866–883
Coello CAC, Lechuga MS (2002) MOPSO: a proposal for multiple objective particle swarm optimization. In: Proceedings of the 2002 congress on evolutionary computation, 2002. CEC ‘02, pp 1051–1056
Collette Y, Siarry P (2004) Multiobjective optimization. Principles and case studies. Springer, Berlin
Cowgill MC, Harvey RJ, Watson LT (1999) A genetic algorithm approach to cluster analysis. Comput Math Appl 37(7):99–108. https://doi.org/10.1016/S0898-1221(99)00090-5
Das S, Abraham A, Konar A (2008) Automatic clustering using an improved differential evolution algorithm. IEEE Trans Syst Man Cybern Part A Syst Hum 38(1):218–237. https://doi.org/10.1109/TSMCA.2007.909595
Davies DL, Bouldin DW (1979) A cluster separation measure. IEEE Trans Pattern Anal Mach Intell 2:224–227. https://doi.org/10.1109/tpami.1979.4766909
Doval D, Mancoridis S, Mitchell BS (1999) Automatic clustering of software systems using a genetic algorithm. In: Proceedings of software technology and engineering practice, 1999. STEP ‘99, pp 73–81
Duc Chinh H, Yadav P, Kumar R, Panda SK (2014) Real-time implementation of a harmony search algorithm-based clustering protocol for energy-efficient wireless sensor networks. IEEE Trans Ind Inf 10(1):774–783. https://doi.org/10.1109/TII.2013.2273739
Dunn JC (1973) A fuzzy relative of the ISODATA process and its use in detecting compact well-separated clusters. J Cybern 3(3):32–57
Georgieva K, Engelbrecht AP (2013) A cooperative multi-population approach to clustering temporal data. In: 2013 IEEE congress on evolutionary computation (CEC), 20–23 June 2013, pp 1983–1991
Hancer E, Ozturk C, Karaboga D (2012) Artificial Bee Colony based image clustering method. In: 2012 IEEE congress on evolutionary computation (CEC), 10–15 June 2012, pp 1–5
Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184. https://doi.org/10.1016/j.ins.2012.08.023
Hatamlou A, Abdullah S, Nezamabadi-pour H (2012) A combined approach for clustering based on K-means and gravitational search algorithms. Swarm Evol Comput 6:47–52. https://doi.org/10.1016/j.swevo.2012.02.003
Horn J, Nafpliotis N, Goldberg DE (1994) A niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of the first IEEE conference on evolutionary computation, 1994. IEEE world congress on computational intelligence, 27–29 Jun 1994, vol 81, pp 82–87
Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31(3):264–323
Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Technical Report TR06, Erciyes Univ. Press, Erciyes
Knowles J, Corne D (1999) The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation. In: Proceedings of the 1999 congress on evolutionary computation, 1999. CEC 99, vol 101, p 105
Kuo RJ, Lin LM (2010) Application of a hybrid of genetic algorithm and particle swarm optimization algorithm for order clustering. Decis Support Syst 49(4):451–462. https://doi.org/10.1016/j.dss.2010.05.006
Kuo RJ, Zulvia FE (2015) The gradient evolution algorithm: a new metaheuristic. Inf Sci 316:246–265. https://doi.org/10.1016/j.ins.2015.04.031
Laumanns M, Rudolph G, Schwefel H-P (1998) A spatial predator-prey approach to multi-objective optimization: a preliminary study. In: Eiben A, Bäck T, Schoenauer M, Schwefel H-P (eds) Parallel problem solving from nature—PPSN V, vol 1498. Lecture Notes in Computer Science. Springer, Berlin, pp 241–249
Lichman M (2013) UCI machine learning repository. University of California, Irvine, School of Information and Computer Sciences. https://archive.ics.uci.edu/ml. Accessed 18 Mar 2015
Liu PX, Meng MQH (2004) Online data-driven fuzzy clustering with applications to real-time robotic tracking. IEEE Trans Fuzzy Syst 12(4):516–523. https://doi.org/10.1109/TFUZZ.2004.832521
Maulik U, Bandyopadhyay S (2000) Genetic algorithm-based clustering technique. Pattern Recognit 33(9):1455–1465. https://doi.org/10.1016/S0031-3203(99)00137-5
Mehdizadeh E, Tavakkoli-Moghaddam R (2007) A hybrid fuzzy clustering PSO algorithm for a clustering supplier problem. In: 2007 IEEE international conference on industrial engineering and engineering management, 2–4 Dec. 2007, pp 1466–1470
Mukhopadhyay A, Maulik U, Bandyopadhyay S (2015) A survey of multiobjective evolutionary clustering. ACM Comput Surv 47(4):1–46. https://doi.org/10.1145/2742642
Nanda SJ, Panda G (2014) A survey on nature inspired metaheuristic algorithms for partitional clustering. Swarm Evol Comput 16:1–18. https://doi.org/10.1016/j.swevo.2013.11.003
Ng HP, Ong SH, Foong KWC, Goh PS, Nowinski WL (2006) Medical image segmentation using K-means clustering and improved watershed algorithm. In: 2006 IEEE southwest symposium on image analysis and interpretation, pp 61–65
Niknam T, Amiri B, Olamaei J, Arefi A (2009) An efficient hybrid evolutionary optimization algorithm based on PSO and SA for clustering. J Zhejiang Univ Sci A 10(4):512–519. https://doi.org/10.1631/jzus.A0820196
Ordin B, Bagirov AM (2015) A heuristic algorithm for solving the minimum sum-of-squares clustering problems. J Glob Optim 61(2):341–361. https://doi.org/10.1007/s10898-014-0171-5
Price KV, Storn RM, Lampinen JA (2005) Differential evolution a practical approach to global optimization. Springer, Berlin
Shi Y, Eberhart RC (1999) Empirical study of particle swarm optimization. In: Proceedings of the 1999 congress on evolutionary computation, Washington D.C., July 6–9, vol 1953, p 1950
Srinivas N, Deb K (1994) Muiltiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3):221–248. https://doi.org/10.1162/evco.1994.2.3.221
Tan PN, Steinbach M, Kumar V (2006) Introduction to data mining. Pearson Education, Inc., Boston
Turi RH (2001) Clustering-based colour image segmentation. Monash, Melbourne
van der Merwe DW, Engelbrecht AP (2003) Data clustering using particle swarm optimization. In: The 2003 congress on evolutionary computation, 2003. CEC ‘03. 8–12 Dec. 2003, vol 211, pp 215–220
Wu Z, Leahy R (1993) An optimal graph theoretic approach to data clustering: theory and its application to image segmentation. IEEE Trans Pattern Anal Mach Intell 15(11):1101–1113. https://doi.org/10.1109/34.244673
Yang C-L, Kuo RJ, Chien C-H, Quyen NTP (2015) Non-dominated sorting genetic algorithm using fuzzy membership chromosome for categorical data clustering. Appl Soft Comput 30:113–122. https://doi.org/10.1016/j.asoc.2015.01.031
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Kuo, R.J., Zulvia, F.E. Multi-objective cluster analysis using a gradient evolution algorithm. Soft Comput 24, 11545–11559 (2020). https://doi.org/10.1007/s00500-019-04620-0
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DOI: https://doi.org/10.1007/s00500-019-04620-0