Skip to main content
SpringerLink
Log in

A Comprehensive Review of Evaluation and Fitness Measures for Evolutionary Data Clustering

  • Chapter
  • First Online:
Evolutionary Data Clustering: Algorithms and Applications

Part of the book series: Algorithms for Intelligent Systems ((AIS))

Abstract

Data clustering is among the commonly investigated types of unsupervised learning; owing to its ability for capturing the underlying information. Accordingly, data clustering has an increasing interest in various applications involving health, humanities, and industry. Assessing the goodness of clustering has been widely debated across the history of clustering analysis, which led to the emergence of abundant clustering evaluation measures. The aim of clustering evaluation is to quantify the quality of the potential clusters which is often referred to as clustering validation. There are two broad categories of clustering validations; the external and the internal measures. Mainly, they differ by relying on external true-labels of the data or not. This chapter considers the role of evolutionary and swarm intelligence algorithms for data clustering, which showed extreme advantages over the classical clustering algorithms. The main idea of this chapter is to present thoroughly the clustering validation indices that are found in literature, indicating when they were utilized with evolutionary clustering and when used as an objective function.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Abuobieda, Albaraa, Naomie Salim, Yogan Jaya Kumar, and Ahmed Hamza Osman. 2013. An improved evolutionary algorithm for extractive text summarization. In Asian conference on intelligent information and database systems, 78–89. Springer.

    Google Scholar 

  2. Al-Madi, Nailah, Ibrahim Aljarah, and Simone A. Ludwig. 2014. Parallel glowworm swarm optimization clustering algorithm based on mapreduce. In 2014 IEEE symposium on swarm intelligence (SIS), 1–8. IEEE.

    Google Scholar 

  3. Al Shorman, Amaal, Hossam Faris, and Ibrahim Aljarah. 2020. Unsupervised intelligent system based on one class support vector machine and grey wolf optimization for iot botnet detection. Journal of Ambient Intelligence and Humanized Computing 11 (7): 2809–2825.

    Article  Google Scholar 

  4. Aldouri, Yamur K., Hassan Al-Chalabi, and Liangwei Zhang. 2018. Data clustering and imputing using a two-level multi-objective genetic algorithm (GA): A case study of maintenance cost data for tunnel fans. Cogent Engineering 5 (1): 1513304.

    Article  Google Scholar 

  5. Aliniya, Zahra, and Seyed Abolghasem Mirroshandel. 2019. A novel combinatorial merge-split approach for automatic clustering using imperialist competitive algorithm. Expert Systems with Applications 117: 243–266.

    Article  Google Scholar 

  6. Aljarah, Ibrahim, and Simone A. Ludwig. 2012. Parallel particle swarm optimization clustering algorithm based on mapreduce methodology. In 2012 fourth world congress on Nature and biologically inspired computing (NaBIC), 104–111. IEEE.

    Google Scholar 

  7. Aljarah, Ibrahim, and Simone A. Ludwig. 2013. Mapreduce intrusion detection system based on a particle swarm optimization clustering algorithm. In 2013 IEEE congress on evolutionary computation (CEC), 955–962. IEEE.

    Google Scholar 

  8. Aljarah, Ibrahim, and Simone A. Ludwig. 2013. A new clustering approach based on glowworm swarm optimization. In 2013 IEEE congress on evolutionary computation, 2642–2649. IEEE.

    Google Scholar 

  9. Aljarah, Ibrahim, and Simone A. Ludwig. 2013. Towards a scalable intrusion detection system based on parallel pso clustering using mapreduce. In Proceedings of the 15th annual conference companion on genetic and evolutionary computation, 169–170. ACM.

    Google Scholar 

  10. Aljarah, Ibrahim, Majdi Mafarja, Ali Asghar Heidari, Hossam Faris, and Seyedali Mirjalili. 2019. Clustering analysis using a novel locality-informed grey wolf-inspired clustering approach. Knowledge and Information Systems 1–33.

    Google Scholar 

  11. Aljarah, Ibrahim, Majdi Mafarja, Ali Asghar Heidari, Hossam Faris, and Seyedali Mirjalili. 2020. Clustering analysis using a novel locality-informed grey wolf-inspired clustering approach. Knowledge and Information Systems 62 (2): 507–539.

    Article  Google Scholar 

  12. Aljarah, Ibrahim, Majdi Mafarja, Ali Asghar Heidari, Hossam Faris, and Seyedali Mirjalili. 2020. Multi-verse optimizer: Theory, literature review, and application in data clustering. In Nature-inspired optimizers, 123–141. Springer.

    Google Scholar 

  13. Alswaitti, Mohammed, Mohanad Albughdadi, and Nor Ashidi Mat Isa. 2018. Density-based particle swarm optimization algorithm for data clustering. Expert Systems with Applications 91: 170–186.

    Article  Google Scholar 

  14. Andrade, Carlos E., Mauricio G.C. Resende, Howard J. Karloff, and Flávio K. Miyazawa. 2014. Evolutionary algorithms for overlapping correlation clustering. In Proceedings of the 2014 annual conference on genetic and evolutionary computation, 405–412. ACM.

    Google Scholar 

  15. Arroyo, Ángel, Verónica Tricio, Álvaro Herrero, and Emilio Corchado. 2016. Time analysis of air pollution in a spanish region through k-means. In International joint conference SOCO-16-CISIS-16-ICEUTE-16, 63–72. Springer.

    Google Scholar 

  16. Auffarth, Benjamin. 2010. Clustering by a genetic algorithm with biased mutation operator. In IEEE congress on evolutionary computation, 1–8. IEEE.

    Google Scholar 

  17. Azarakhsh, Javad, and Zobeir Raisi. 2019. Automatic clustering using metaheuristic algorithms for content based image retrieval. In Fundamental research in electrical engineering, 83–99. Springer.

    Google Scholar 

  18. Baker, Frank B., and Lawrence J. Hubert. 1975. Measuring the power of hierarchical cluster analysis. Journal of the American Statistical Association 70 (349): 31–38.

    Article  MATH  Google Scholar 

  19. Ball, Geoffrey H., and David J. Hall. 1965. Isodata, a novel method of data analysis and pattern classification. Technical report, Stanford Research Institute, Menlo Park, CA.

    Google Scholar 

  20. Bandyopadhyay, Sanghamitra, and Ujjwal Maulik. 2002. Genetic clustering for automatic evolution of clusters and application to image classification. Pattern Recognition 35 (6): 1197–1208.

    Article  MATH  Google Scholar 

  21. Beale, E.M.L. 1969. Cluster analysis scientific control system.

    Google Scholar 

  22. Benesty, Jacob, Jingdong Chen, Yiteng Huang, and Israel Cohen. 2009. Pearson correlation coefficient. In Noise reduction in speech processing, 1–4. Springer.

    Google Scholar 

  23. Bezdek, James C. 2013. Pattern recognition with fuzzy objective function algorithms. Springer Science & Business Media.

    Google Scholar 

  24. Bezdek, James C., and Nikhil R. Pal. 1998. Some new indices of cluster validity.

    Google Scholar 

  25. Bolshakova, Nadia, and Francisco Azuaje. 2003. Cluster validation techniques for genome expression data. Signal Processing 83 (4): 825–833.

    Article  MATH  Google Scholar 

  26. Caliński, Tadeusz, and Jerzy Harabasz. 1974. A dendrite method for cluster analysis. Communications in Statistics-Theory and Methods 3 (1): 1–27.

    Article  MathSciNet  MATH  Google Scholar 

  27. Chander, Satish, P. Vijaya, and Praveen Dhyani. 2018. Multi kernel and dynamic fractional lion optimization algorithm for data clustering. Alexandria Engineering Journal 57 (1): 267–276.

    Article  Google Scholar 

  28. Charrad, Malika, Mohamed Ben Ahmed, Yves Lechevallier, and Gilbert Saporta. 2009. Determining the number of clusters in CROKI2 algorithm.

    Google Scholar 

  29. Chen, Junyang, Zhiguo Gong, and Weiwen Liu. 2019. A nonparametric model for online topic discovery with word embeddings. Information Sciences 504: 32–47.

    Article  MathSciNet  Google Scholar 

  30. Chen, Min, and Simone A. Ludwig. 2014. Fuzzy clustering using automatic particle swarm optimization. In 2014 IEEE international conference on fuzzy systems (FUZZ-IEEE), 1545–1552. IEEE.

    Google Scholar 

  31. Chen, Min, and Simone A. Ludwig. 2014. Particle swarm optimization based fuzzy clustering approach to identify optimal number of clusters. Journal of Artificial Intelligence and Soft Computing Research 4 (1): 43–56.

    Article  Google Scholar 

  32. Chen, Scott Shaobing, and Ponani S. Gopalakrishnan. 1998. Clustering via the Bayesian information criterion with applications in speech recognition. In Proceedings of the 1998 IEEE international conference on acoustics, speech and signal processing, ICASSP’98 (Cat. No. 98CH36181), vol. 2, 645–648. IEEE.

    Google Scholar 

  33. Cheng, Fan, Su Tingting Cui, Yunyun Niu Yansen, and Xingyi Zhang. 2018. A local information based multi-objective evolutionary algorithm for community detection in complex networks. Applied Soft Computing 69: 357–367.

    Article  Google Scholar 

  34. Chi, Yun, Xiaodan Song, Dengyong Zhou, Koji Hino, and Belle L. Tseng. 2007. Evolutionary spectral clustering by incorporating temporal smoothness. In Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining, 153–162. ACM.

    Google Scholar 

  35. Chou, Chien-Hsing, Su Mu-Chun, and Eugene Lai. 2003. A new cluster validity measure for clusters with different densities. In IASTED international conference on intelligent systems and control, 276–281.

    Google Scholar 

  36. Chovancova, Olga, Lucia Piatrikova, and Adam Dudas. 2019. Improving fuzzy c-means algorithm using particle swarm optimization and fuzzy c-means++. In 2019 international conference on information and digital technologies (IDT), 173–179. IEEE.

    Google Scholar 

  37. Civicioglu, P., U.H. Atasever, C. Ozkan, E. Besdok, A.E. Karkinli, and A. Kesikoglu. 2014. Performance comparison of evolutionary algorithms for image clustering. The International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences 40 (7): 71.

    Article  Google Scholar 

  38. Cobos, Carlos, Leydy Muñoz, Martha Mendoza, Elizabeth León, and Enrique Herrera-Viedma. 2012. Fitness function obtained from a genetic programming approach for web document clustering using evolutionary algorithms. In Ibero-American conference on artificial intelligence, 179–188. Springer.

    Google Scholar 

  39. Cobos, Carlos, Henry Muñoz-Collazos, Richar Urbano-Muñoz, Martha Mendoza, Elizabeth León, and Enrique Herrera-Viedma. 2014. Clustering of web search results based on the cuckoo search algorithm and balanced Bayesian information criterion. Information Sciences 281: 248–264.

    Article  Google Scholar 

  40. Cowgill, Marcus Charles. 1993. Monte Carlo validation of two genetic clustering algorithms.

    Google Scholar 

  41. Cui, Tianyu, Francesco Caravelli, and Cozmin Ududec. 2018. Correlations and clustering in wholesale electricity markets. Physica A: Statistical Mechanics and its Applications 492: 1507–1522.

    Article  Google Scholar 

  42. Czekanowski, Jan. 1932. Coefficient of racial likeness" und durchschnittliche differenz. Anthropologischer Anzeiger (H. 3/4): 227–249.

    Google Scholar 

  43. Dalrymple-Alford, E.C. 1970. Measurement of clustering in free recall. Psychological Bulletin 74 (1): 32.

    Article  Google Scholar 

  44. D’Ambrosio, Antonio, and Willem J. Heiser. 2019. A distribution-free soft-clustering method for preference rankings. Behaviormetrika 46 (2): 333–351.

    Article  Google Scholar 

  45. Das, Swagatam, and Amit Konar. 2009. Automatic image pixel clustering with an improved differential evolution. Applied Soft Computing 9 (1): 226–236.

    Article  Google Scholar 

  46. Das, Swagatam, and Sudeshna Sil. 2010. Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm. Information Sciences 180 (8): 1237–1256.

    Article  MathSciNet  Google Scholar 

  47. Davies, David L., and Donald W. Bouldin. 1979. A cluster separation measure. IEEE Transactions on Pattern Analysis and Machine Intelligence 2: 224–227.

    Article  Google Scholar 

  48. Desgraupes, Bernard. 2013. Clustering indices. University of Paris Ouest-Lab Modal-X 1: 34.

    Google Scholar 

  49. Dice, Lee R. 1945. Measures of the amount of ecologic association between species. Ecology 26 (3): 297–302.

    Article  Google Scholar 

  50. Ding, Yi, and Fu Xian. 2016. Kernel-based fuzzy c-means clustering algorithm based on genetic algorithm. Neurocomputing 188: 233–238.

    Article  Google Scholar 

  51. Duan, Ganglong, Hu Wenxiu, and Zhiguang Zhang. 2016. A novel data clustering algorithm based on modified adaptive particle swarm optimization. International Journal of Signal Processing, Image Processing and Pattern Recognition 9 (3): 179–188.

    Article  Google Scholar 

  52. Duda, Richard O., and Peter E Hart. 1973. Pattern classification and scene analysis. Wiley.

    Google Scholar 

  53. Dunn, Joseph C. 1973. A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters.

    Google Scholar 

  54. Faris, Hossam, Ibrahim Aljarah, and Ja’far Alqatawna. 2015. Optimizing feedforward neural networks using krill herd algorithm for e-mail spam detection. In 2015 IEEE Jordan conference on applied electrical engineering and computing technologies (AEECT), 1–5. IEEE.

    Google Scholar 

  55. Faris, Hossam, Ibrahim Aljarah, Seyedali Mirjalili, Pedro A. Castillo, and Juan J. Merelo. 2016. EvoloPy: An open-source nature-inspired optimization framework in Python. In IJCCI (ECTA), 171–177.

    Google Scholar 

  56. Folino, Francesco, and Clara Pizzuti. 2010. A multiobjective and evolutionary clustering method for dynamic networks. In 2010 international conference on advances in social networks analysis and mining, 256–263. IEEE.

    Google Scholar 

  57. Forestier, Germain, Cédric Wemmert, and Pierre Gançarski. 2010. Background knowledge integration in clustering using purity indexes. In International conference on knowledge science, engineering and management, 28–38. Springer.

    Google Scholar 

  58. Fowlkes, Edward B., and Colin L. Mallows. 1983. A method for comparing two hierarchical clusterings. Journal of the American Statistical Association 78 (383): 553–569.

    Article  MATH  Google Scholar 

  59. Franco, Manuel, and Juana-María Vivo. 2019. Cluster analysis of microarray data. In Microarray bioinformatics, 153–183. Springer.

    Google Scholar 

  60. Frey, T., and H. Van Groenewoud. 1972. A cluster analysis of the D2 matrix of white spruce stands in Saskatchewan based on the maximum-minimum principle. The Journal of Ecology 873–886.

    Google Scholar 

  61. Friedman, Herman P., and Jerrold Rubin. 1967. On some invariant criteria for grouping data. Journal of the American Statistical Association 62 (320): 1159–1178.

    Article  MathSciNet  Google Scholar 

  62. Fukuyama, Yoshiki. 1989. A new method of choosing the number of clusters for the fuzzy c-mean method. In Proceedings of the 5th fuzzy systems symposium, 1989, 247–250.

    Google Scholar 

  63. Georgieva, Kristina S., and Andries P. Engelbrecht. 2013. Dynamic differential evolution algorithm for clustering temporal data. In International conference on large-scale scientific computing, 240–247. Springer.

    Google Scholar 

  64. Gnanadesikan, R., J.W. Harvey, and J.R. Kettenring. 1993. Mahalanobis metrics for cluster analysis. Sankhyā: The Indian Journal of Statistics, Series A 494–505.

    Google Scholar 

  65. Gong, Xiaofei, Jie Zhang, and Yijie Shi. 2018. Research on data filling algorithm based on improved k-means and information entropy. In 2018 IEEE 4th international conference on computer and communications (ICCC), 1774–1778. IEEE.

    Google Scholar 

  66. Guan, Chun, Kevin Kam Fung Yuen, and Frans Coenen. 2019. Particle swarm optimized density-based clustering and classification: Supervised and unsupervised learning approaches. Swarm and Evolutionary Computation 44: 876–896.

    Article  Google Scholar 

  67. Gurrutxaga, Ibai, Iñaki Albisua, Olatz Arbelaitz, José I. Martín, Javier Muguerza, Jesús M. Pérez, and Iñigo Perona. 2010. SEP/COP: An efficient method to find the best partition in hierarchical clustering based on a new cluster validity index. Pattern Recognition 43 (10): 3364–3373.

    Article  MATH  Google Scholar 

  68. Gutoski, Matheus, Manassés Ribeiro, Nelson Marcelo Romero Aquino, Leandro Takeshi Hattori, André Eugênio Lazzaretti, and Heitor Silvério Lopes. 2018. Feature selection using differential evolution for unsupervised image clustering. In International conference on artificial intelligence and soft computing, 376–385. Springer.

    Google Scholar 

  69. Halkidi, Maria, and Michalis Vazirgiannis. 2001. Clustering validity assessment: Finding the optimal partitioning of a data set. In Proceedings 2001 IEEE international conference on data mining, 187–194. IEEE.

    Google Scholar 

  70. Halkidi, Maria, Michalis Vazirgiannis, and Yannis Batistakis. 2000. Quality scheme assessment in the clustering process. In European conference on principles of data mining and knowledge discovery, 265–276. Springer.

    Google Scholar 

  71. Hamming, Richard W. 1950. Error detecting and error correcting codes. The Bell System Technical Journal 29 (2): 147–160.

    Article  MathSciNet  MATH  Google Scholar 

  72. Han, Jiawei, Micheline Kamber, and Jian Pei. 2011. Getting to know your data. Data Mining: Concepts and Techniques 3 (744): 39–81.

    Google Scholar 

  73. Hancer, Emrah. 2020. A new multi-objective differential evolution approach for simultaneous clustering and feature selection. Engineering Applications of Artificial Intelligence 87: 103307.

    Article  Google Scholar 

  74. Handl, Julia, and Joshua Knowles. 2007. An evolutionary approach to multiobjective clustering. IEEE Transactions on Evolutionary Computation 11 (1): 56–76.

    Article  Google Scholar 

  75. Hartigan, John A. 1975. Clustering algorithms. New York, NY: Wiley Inc.

    MATH  Google Scholar 

  76. Hasan, Mohammad Nazmol, Masuma Binte Malek, Anjuman Ara Begum,Moizur Rahman, Md. Mollah, and Nurul Haque. 2019. Assessment of drugs toxicity and associated biomarker genes using hierarchical clustering. Medicina 55 (8): 451.

    Google Scholar 

  77. He, Zhenfeng, and Chunyan Yu. 2019. Clustering stability-based evolutionary k-means. Soft Computing 23 (1): 305–321.

    Article  MATH  Google Scholar 

  78. Hubert, Lawrence, and Phipps Arabie. 1985. Comparing partitions. Journal of Classification 2 (1): 193–218.

    Article  MATH  Google Scholar 

  79. Hubert, Lawrence, and James Schultz. 1976. Quadratic assignment as a general data analysis strategy. British Journal of Mathematical and Statistical Psychology 29 (2): 190–241.

    Article  MathSciNet  MATH  Google Scholar 

  80. Jaccard, Paul. 1901. Étude comparative de la distribution florale dans une portion des alpes et des jura. Bulletin de la Societe Vaudoise des Sciences Naturelles 37: 547–579.

    Google Scholar 

  81. Jadhav, Amolkumar Narayan, and N. Gomathi. 2018. WGC: Hybridization of exponential grey wolf optimizer with whale optimization for data clustering. Alexandria Engineering Journal 57 (3): 1569–1584.

    Article  Google Scholar 

  82. Jauhiainen, Susanne, and Tommi Kärkkäinen. 2017. A simple cluster validation index with maximal coverage. In European symposium on artificial neural networks, computational intelligence and machine learning. ESANN.

    Google Scholar 

  83. Jiang, Lei, and Datong Xie. 2018. An efficient differential memetic algorithm for clustering problem. IAENG International Journal of Computer Science 45 (1).

    Google Scholar 

  84. Jiang, Xiaoping, Chenghua Li, and Jing Sun. 2018. A modified k-means clustering for mining of multimedia databases based on dimensionality reduction and similarity measures. Cluster Computing 21 (1): 797–804.

    Article  Google Scholar 

  85. Joopudi, Sreeram, Suraj S. Rathi, Shankar Narasimhan, and Raghunathan Rengaswamy. 2013. A new cluster validity index for fuzzy clustering. IFAC Proceedings Volumes 46 (32): 325–330.

    Article  Google Scholar 

  86. Kapp, Amy V., and Robert Tibshirani. 2006. Are clusters found in one dataset present in another dataset? Biostatistics 8 (1): 9–31.

    Article  MATH  Google Scholar 

  87. Kendall, Maurice G. 1938. A new measure of rank correlation. Biometrika 30 (1/2): 81–93.

    Article  MATH  Google Scholar 

  88. Khobragade, Sneha, and Preeti Mulay. 2018. Enhance incremental clustering for time series datasets using distance measures. In International conference on intelligent computing and applications, 543–556. Springer.

    Google Scholar 

  89. Kim, Minho, and R.S. Ramakrishna. 2005. Some new indexes of cluster validity. Pattern Recognition Letters 26 (15): 2353–2363.

    Article  Google Scholar 

  90. Kirkland, Oliver, Victor J. Rayward-Smith, and Beatriz de la Iglesia. 2011. A novel multi-objective genetic algorithm for clustering. In International conference on intelligent data engineering and automated learning, 317–326. Springer.

    Google Scholar 

  91. Klamroth, Kathrin. 2002. Measuring distances. In Single-facility location problems with barriers, 3–14. Springer.

    Google Scholar 

  92. Krzanowski, Wojtek J., and Y.T. Lai. 1988. A criterion for determining the number of groups in a data set using sum-of-squares clustering. Biometrics 23–34.

    Google Scholar 

  93. Kumar, Lalit, and Kusum Kumari Bharti. 2019. An improved BPSO algorithm for feature selection. In Recent trends in communication, computing, and electronics, 505–513. Springer.

    Google Scholar 

  94. Kuo, R.J., and L.M. Lin. 2010. Application of a hybrid of genetic algorithm and particle swarm optimization algorithm for order clustering. Decision Support Systems 49: 451–462.

    Article  Google Scholar 

  95. Kurada, Ramachandra Rao, and Karteeka Pavan Kanadam. 2019. A novel evolutionary automatic clustering technique by unifying initial seed selection algorithms into teaching–learning-based optimization. In Soft computing and medical bioinformatics, 1–9. Springer.

    Google Scholar 

  96. Kwedlo, Wojciech. 2011. A clustering method combining differential evolution with the k-means algorithm. Pattern Recognition Letters 32 (12): 1613–1621.

    Article  Google Scholar 

  97. Kwon, Soon H. 1998. Cluster validity index for fuzzy clustering. Electronics Letters 34 (22): 2176–2177.

    Article  Google Scholar 

  98. Lago-Fernández, Luis F., and Fernando Corbacho. 2010. Normality-based validation for crisp clustering. Pattern Recognition 43 (3): 782–795.

    Article  MATH  Google Scholar 

  99. Li, Chaoshun, Jianzhong Zhou, Pangao Kou, and Jian Xiao. 2012. A novel chaotic particle swarm optimization based fuzzy clustering algorithm. Neurocomputing 83: 98–109.

    Article  Google Scholar 

  100. Li, Yanyan, Qing Wang, Jianping Chen, Liming Xu, and Shengyuan Song. 2015. K-means algorithm based on particle swarm optimization for the identification of rock discontinuity sets. Rock Mechanics and Rock Engineering 48 (1): 375–385.

    Article  Google Scholar 

  101. Liao, Erchong, and Changan Liu. 2018. A hierarchical algorithm based on density peaks clustering and ant colony optimization for traveling salesman problem. IEEE Access 6: 38921–38933.

    Article  Google Scholar 

  102. Liu, Chao, Yuanrui Li, Qi Zhao, and Chenqi Liu. 2019. Reference vector-based multi-objective clustering for high-dimensional data. Applied Soft Computing 78: 614–629.

    Article  Google Scholar 

  103. Liu, Chao, Jing Xie, Qi Zhao, Qiwei Xie, and Chenqi Liu. 2019. Novel evolutionary multi-objective soft subspace clustering algorithm for credit risk assessment. Expert Systems with Applications 138: 112827.

    Article  Google Scholar 

  104. Liu, Chuanren, Tianming Hu, Yong Ge, and Hui Xiong. 2012. Which distance metric is right: An evolutionary k-means view. In Proceedings of the 2012 SIAM international conference on data mining, 907–918. SIAM.

    Google Scholar 

  105. Liu, Yimin, Tansel Özyer, Reda Alhajj, and Ken Barker. 2005. Integrating multi-objective genetic algorithm and validity analysis for locating and ranking alternative clustering. Informatica 29 (1).

    Google Scholar 

  106. Łukasik, Szymon, Piotr A. Kowalski, Małgorzata Charytanowicz, and Piotr Kulczycki. 2016. Clustering using flower pollination algorithm and Calinski-Harabasz index. In 2016 IEEE congress on evolutionary computation (CEC), 2724–2728. IEEE.

    Google Scholar 

  107. Luna-Romera, José María, Jorge García-Gutiérrez, María Martínez-Ballesteros, and José C. Riquelme Santos. 2018. An approach to validity indices for clustering techniques in big data. Progress in Artificial Intelligence 7 (2): 81–94.

    Article  Google Scholar 

  108. Mageshkumar, C., S. Karthik, and V.P. Arunachalam. 2019. Hybrid metaheuristic algorithm for improving the efficiency of data clustering. Cluster Computing 22 (1): 435–442.

    Article  Google Scholar 

  109. Marriott, F.H.C. 1971. Practical problems in a method of cluster analysis. Biometrics 501–514.

    Google Scholar 

  110. Martarelli, Nádia Junqueira, and Marcelo Seido Nagano. 2018. A constructive evolutionary approach for feature selection in unsupervised learning. Swarm and Evolutionary Computation 42: 125–137.

    Article  Google Scholar 

  111. Martínez-Peñaloza, María-Guadalupe, Efrén Mezura-Montes, Nicandro Cruz-Ramírez, Héctor-Gabriel Acosta-Mesa, and Homero-Vladimir Ríos-Figueroa. 2017. Improved multi-objective clustering with automatic determination of the number of clusters. Neural Computing and Applications 28 (8): 2255–2275.

    Article  Google Scholar 

  112. Matake, Nobukazu, Tomoyuki Hiroyasu, Mitsunori Miki, and Tomoharu Senda. 2007. Multiobjective clustering with automatic k-determination for large-scale data. In Proceedings of the 9th annual conference on genetic and evolutionary computation, 861–868. ACM.

    Google Scholar 

  113. Maulik, Ujjwal, and Sanghamitra Bandyopadhyay. 2000. Genetic algorithm-based clustering technique. Pattern Recognition 33 (9): 1455–1465.

    Article  Google Scholar 

  114. Maulik, Ujjwal, and Sanghamitra Bandyopadhyay. 2002. Performance evaluation of some clustering algorithms and validity indices. IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (12): 1650–1654.

    Article  Google Scholar 

  115. Maulik, Ujjwal, and Indrajit Saha. 2009. Modified differential evolution based fuzzy clustering for pixel classification in remote sensing imagery. Pattern Recognition 42 (9): 2135–2149.

    Article  MATH  Google Scholar 

  116. McClain, John O., and Vithala R. Rao. 1975. CLUSTISZ: A program to test for the quality of clustering of a set of objects. JMR, Journal of Marketing Research (pre-1986) 12 (000004): 456.

    Google Scholar 

  117. Milligan, Glenn W. 1980. An examination of the effect of six types of error perturbation on fifteen clustering algorithms. Psychometrika 45 (3): 325–342.

    Article  Google Scholar 

  118. Milligan, Glenn W., and Martha C. Cooper. 1985. An examination of procedures for determining the number of clusters in a data set. Psychometrika 50 (2): 159–179.

    Article  Google Scholar 

  119. Milligan, Glenn W., and Martha C. Cooper. 1986. A study of the comparability of external criteria for hierarchical cluster analysis. Multivariate Behavioral Research 21 (4): 441–458.

    Article  Google Scholar 

  120. Mirkin, Boris. 1998. Mathematical classification and clustering: From how to what and why. In Classification, data analysis, and data highways, 172–181. Springer.

    Google Scholar 

  121. Mohapatra, Smruti Sourava, Prasanta Kumar Bhuyan, and K.V. Rao. 2012. Genetic algorithm fuzzy clustering using GPS data for defining level of service criteria of urban streets.

    Google Scholar 

  122. Mukhopadhyay, Anirban, Ujjwal Maulik, and Sanghamitra Bandyopadhyay. 2015. A survey of multiobjective evolutionary clustering. ACM Computing Surveys (CSUR) 47 (4): 61.

    Article  Google Scholar 

  123. Muravyov, Sergey, Denis Antipov, Arina Buzdalova, and Andrey Filchenkov. 2019. Efficient computation of fitness function for evolutionary clustering. MENDEL 25: 87–94.

    Article  Google Scholar 

  124. Murthy, Chivukula A., and Nirmalya Chowdhury. 1996. In search of optimal clusters using genetic algorithms. Pattern Recognition Letters 17: 825–832.

    Article  Google Scholar 

  125. Myers, Leann, and Maria J. Sirois. 2004. Spearman correlation coefficients, differences between. In Encyclopedia of statistical sciences, 12.

    Google Scholar 

  126. Naik, Nitin, Ren Diao, and Qiang Shen. 2015. Choice of effective fitness functions for genetic algorithm-aided dynamic fuzzy rule interpolation. In 2015 IEEE international conference on fuzzy systems (FUZZ-IEEE), 1–8. IEEE.

    Google Scholar 

  127. Nerurkar, Pranav, Aruna Pavate, Mansi Shah, and Samuel Jacob. 2019. Performance of internal cluster validations measures for evolutionary clustering. In Computing, communication and signal processing, 305–312. Springer.

    Google Scholar 

  128. Neumann, Aneta, and Frank Neumann. 2018. On the use of colour-based segmentation in evolutionary image composition. In 2018 IEEE congress on evolutionary computation (CEC), 1–8. IEEE.

    Google Scholar 

  129. Nguyen, Thi Phuong Quyen, and R.J. Kuo. 2019. Partition-and-merge based fuzzy genetic clustering algorithm for categorical data. Applied Soft Computing 75: 254–264.

    Article  Google Scholar 

  130. Oujezsky, Vaclav, and Tomas Horvath. 2018. Traffic similarity observation using a genetic algorithm and clustering. Technologies 6 (4): 103.

    Article  Google Scholar 

  131. Ozyer, Tansel, and Reda Alhajj. 2006. Achieving natural clustering by validating results of iterative evolutionary clustering approach. In 2006 3rd international IEEE conference intelligent systems, 488–493. IEEE.

    Google Scholar 

  132. Özyer, Tansel, Ming Zhang, and Reda Alhajj. 2011. Integrating multi-objective genetic algorithm based clustering and data partitioning for skyline computation. Applied Intelligence 35 (1): 110–122.

    Article  Google Scholar 

  133. Pakhira, Malay K., Sanghamitra Bandyopadhyay, and Ujjwal Maulik. 2004. Validity index for crisp and fuzzy clusters. Pattern Recognition 37 (3): 487–501.

    Article  MATH  Google Scholar 

  134. Pandey, Avinash Chandra, and Dharmveer Singh Rajpoot. 2019. Spam review detection using spiral cuckoo search clustering method. Evolutionary Intelligence 12 (2): 147–164.

    Article  Google Scholar 

  135. Pantula, Priyanka D., Srinivas S. Miriyala, and Kishalay Mitra. 2019. A novel ANN-fuzzy formulation towards evolution of efficient clustering algorithm. In 2019 Fifth Indian control conference (ICC), 254–259. IEEE.

    Google Scholar 

  136. Paterlini, Sandra, and Thiemo Krink. 2006. Differential evolution and particle swarm optimisation in partitional clustering. Computational Statistics & Data Analysis 50 (5): 1220–1247.

    Article  MathSciNet  MATH  Google Scholar 

  137. Patnaik, Ashish Kumar, and Prasanta Kumar Bhuyan. 2016. Application of genetic programming clustering in defining LOS criteria of urban street in Indian context. Travel Behaviour and Society 3: 38–50.

    Article  Google Scholar 

  138. Peng, Hong, Peng Shi, Jun Wang, Agustín Riscos-Núñez, and Mario J. Pérez-Jiménez. 2017. Multiobjective fuzzy clustering approach based on tissue-like membrane systems. Knowledge-Based Systems 125: 74–82.

    Article  Google Scholar 

  139. Pomponi, Eraldo, and Alexei Vinogradov. 2013. A real-time approach to acoustic emission clustering. Mechanical Systems and Signal Processing 40 (2): 791–804.

    Article  Google Scholar 

  140. Qaddoura, Raneem, Hossam Faris, and Ibrahim Aljarah. 2020. An efficient clustering algorithm based on the k-nearest neighbors with an indexing ratio. International Journal of Machine Learning and Cybernetics 11 (3): 675–714.

    Article  Google Scholar 

  141. Qaddoura, Raneem, Hossam Faris, Ibrahim Aljarah, and Pedro A. Castillo. 2020. EvoCluster: An open-source nature-inspired optimization clustering framework in Python. In International conference on the applications of evolutionary computation (part of EvoStar), 20–36. Springer.

    Google Scholar 

  142. Qaddoura, R., H. Faris, and I. Aljarah. 2020. An efficient evolutionary algorithm with a nearest neighbor search technique for clustering analysis. Journal of Ambient Intelligence and Humanized Computing 1–26.

    Google Scholar 

  143. Qaddoura, R., H. Faris, I. Aljarah, J. Merelo, and P. Castillo. 2020. Empirical evaluation of distance measures for nearest point with indexing ratio clustering algorithm. In Proceedings of the 12th international joint conference on computational intelligence, vol. 1, 430–438. NCTA. ISBN 978-989-758-475-6, https://doi.org/10.5220/0010121504300438.

  144. Radhakrishna, Vangipuram, Chintakindi Srinivas, and C.V. GuruRao. 2014. A modified gaussian similarity measure for clustering software components and documents. In Proceedings of the international conference on information systems and design of communication, 99–104. ACM.

    Google Scholar 

  145. Raitoharju, Jenni, Kaveh Samiee, Serkan Kiranyaz, and Moncef Gabbouj. 2017. Particle swarm clustering fitness evaluation with computational centroids. Swarm and Evolutionary Computation 34: 103–118.

    Article  Google Scholar 

  146. Rand, William M. 1971. Objective criteria for the evaluation of clustering methods. Journal of the American Statistical Association 66 (336): 846–850.

    Article  Google Scholar 

  147. Ratkowsky, D.A., and G.N. Lance. 1978. Criterion for determining the number of groups in a classification.

    Google Scholar 

  148. Ray, Siddheswar, and Rose H. Turi. 1999. Determination of number of clusters in k-means clustering and application in colour image segmentation. In Proceedings of the 4th international conference on advances in pattern recognition and digital techniques, 137–143. Calcutta, India.

    Google Scholar 

  149. Rezaee, Babak. 2010. A cluster validity index for fuzzy clustering. Fuzzy Sets and Systems 161 (23): 3014–3025.

    Article  MathSciNet  MATH  Google Scholar 

  150. Ripon, Kazi Shah Nawaz, and Mia Nazmul Haque Siddique. 2009. Evolutionary multi-objective clustering for overlapping clusters detection. In 2009 IEEE congress on evolutionary computation, 976–982. IEEE.

    Google Scholar 

  151. Ripon, K.S. Nawaz, Chi-Ho Tsang, Sam Kwong, and Man-Ki Ip. 2006. Multi-objective evolutionary clustering using variable-length real jumping genes genetic algorithm. In 18th international conference on pattern recognition (ICPR’06), vol. 1, 1200–1203. IEEE.

    Google Scholar 

  152. Ritz, Christian, and Ib Skovgaard. 2005. Module 2: Cluster analysis. Master of Applied Statistics, 1–20. http://www2.imm.dtu.dk/~pbb/MAS/ST116/module02/module.pdf.

  153. Rohlf, F.James. 1974. Methods of comparing classifications. Annual Review of Ecology and Systematics 5 (1): 101–113.

    Article  Google Scholar 

  154. Rosenberg, Andrew, and Julia Hirschberg. 2007. V-measure: A conditional entropy-based external cluster evaluation measure. In Proceedings of the 2007 joint conference on empirical methods in natural language processing and computational natural language learning (EMNLP-CoNLL), 410–420.

    Google Scholar 

  155. Ross, Edith M., and Florian Markowetz. 2016. OncoNEM: Inferring tumor evolution from single-cell sequencing data. Genome Biology 17 (1): 69.

    Article  Google Scholar 

  156. Rousseeuw, Peter J. 1987. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics 20: 53–65.

    Article  MATH  Google Scholar 

  157. Roy, Parthajit, and J.K. Mandal. 2016. An SVD based real coded genetic algorithm for graph clustering.

    Google Scholar 

  158. Runkler, Thomas A., and James C. Bezdek. 2019. Optimizing the c index using a canonical genetic algorithm. In International conference on the applications of evolutionary computation (part of EvoStar), 287–298. Springer.

    Google Scholar 

  159. Saha, Sriparna, and Sanghamitra Bandyopadhyay. 2008. Application of a new symmetry-based cluster validity index for satellite image segmentation. IEEE Geoscience and Remote Sensing Letters 5 (2): 166–170.

    Article  Google Scholar 

  160. Saha, Sriparna, and Ranjita Das. 2018. Exploring differential evolution and particle swarm optimization to develop some symmetry-based automatic clustering techniques: Application to gene clustering. Neural Computing and Applications 30 (3): 735–757.

    Article  Google Scholar 

  161. Saini, Naveen, Sriparna Saha, and Pushpak Bhattacharyya. 2019. Automatic scientific document clustering using self-organized multi-objective differential evolution. Cognitive Computation 11 (2): 271–293.

    Article  Google Scholar 

  162. Saitta, Sandro, Benny Raphael, and Ian F.C. Smith. 2007. A bounded index for cluster validity. In International workshop on machine learning and data mining in pattern recognition, 174–187. Springer.

    Google Scholar 

  163. Saitta, Sandro, Benny Raphael, and Ian F.C. Smith. 2008. A comprehensive validity index for clustering. Intelligent Data Analysis 12 (6): 529–548.

    Article  Google Scholar 

  164. Santos, Adam, Eloi Figueiredo, Moisés Silva, Reginaldo Santos, Claudomiro Sales, and João C.W.A. Costa. 2017. Genetic-based EM algorithm to improve the robustness of gaussian mixture models for damage detection in bridges. Structural Control and Health Monitoring 24 (3): e1886.

    Article  Google Scholar 

  165. Sarle, W.S. 1983. SAS technical report A-108, cubic clustering criterion, 56. Cary, NC: SAS Institute Inc.

    Google Scholar 

  166. Sayed, Gehad Ismail, Ashraf Darwish, and Aboul Ella Hassanien. 2019. Binary whale optimization algorithm and binary moth flame optimization with clustering algorithms for clinical breast cancer diagnoses. Journal of Classification 1–31.

    Google Scholar 

  167. Schwarz, Gideon, et al. 1978. Estimating the dimension of a model. The Annals of Statistics 6 (2): 461–464.

    Article  MathSciNet  MATH  Google Scholar 

  168. Scott, Allen J., and Symons, Michael J. 1971. Clustering methods based on likelihood ratio criteria. Biometrics 387–397.

    Google Scholar 

  169. sheng Li, Chun. 2011. The improved partition coefficient. Procedia Engineering 24: 534–538.

    Article  Google Scholar 

  170. Shirakawa, Shinichi, and Tomoharu Nagao. 2009. Evolutionary image segmentation based on multiobjective clustering. In 2009 IEEE congress on evolutionary computation, 2466–2473. IEEE.

    Google Scholar 

  171. Shtar, Guy, Bracha Shapira, and Lior Rokach. 2019. Clustering Wi-Fi fingerprints for indoor-outdoor detection. Wireless Networks 25 (3): 1341–1359.

    Article  Google Scholar 

  172. Shukri, Sarah, Hossam Faris, Ibrahim Aljarah, Seyedali Mirjalili, and Ajith Abraham. 2018. Evolutionary static and dynamic clustering algorithms based on multi-verse optimizer. Engineering Applications of Artificial Intelligence 72: 54–66.

    Article  Google Scholar 

  173. Silva, Jesús, Omar Bonerge Pineda Lezama, Noel Varela, Jesús García Guiliany, Ernesto Steffens Sanabria, Madelin Sánchez Otero, and Vladimir Álvarez Rojas. 2019. U-control chart based differential evolution clustering for determining the number of cluster in k-means. In International conference on green, pervasive, and cloud computing, 31–41. Springer.

    Google Scholar 

  174. Sinha, Ankita, and Prasanta K. Jana. 2018. A hybrid mapreduce-based k-means clustering using genetic algorithm for distributed datasets. The Journal of Supercomputing 74 (4): 1562–1579.

    Article  Google Scholar 

  175. Song, Wei, Wei Ma, and Yingying Qiao. 2017. Particle swarm optimization algorithm with environmental factors for clustering analysis. Soft Computing 21 (2): 283–293.

    Article  Google Scholar 

  176. Sørensen, Thorvald Julius. 1948. A method of establishing groups of equal amplitude in plant sociology based on similarity of species content and its application to analyses of the vegetation on Danish commons. I kommission hos E. Munksgaard.

    Google Scholar 

  177. Starczewski, Artur. 2017. A new validity index for crisp clusters. Pattern Analysis and Applications 20 (3): 687–700.

    Article  MathSciNet  Google Scholar 

  178. Strauss, Trudie, and Michael Johan von Maltitz. 2017. Generalising ward’s method for use with Manhattan distances. PloS One 12 (1): e0168288.

    Article  Google Scholar 

  179. Strehl, Alexander. 2002. Relationship-based clustering and cluster ensembles for high-dimensional data mining. PhD thesis.

    Google Scholar 

  180. Strehl, Alexander, and Joydeep Ghosh. 2002. Cluster ensembles—a knowledge reuse framework for combining multiple partitions. Journal of Machine Learning Research 3: 583–617.

    MathSciNet  MATH  Google Scholar 

  181. Tan, Teck Yan, Li Zhang, Chee Peng Lim, Ben Fielding, Yu. Yonghong, and Emma Anderson. 2019. Evolving ensemble models for image segmentation using enhanced particle swarm optimization. IEEE Access 7: 34004–34019.

    Article  Google Scholar 

  182. Thomson, Robert, Elie Alhajjar, Joshua Irwin, and Travis Russell. 2018. Predicting bias in machine learned classifiers using clustering. In Annual social computing, behavior prediction, and modeling-behavioral representation in modeling simulation conference.

    Google Scholar 

  183. Tibshirani, Robert, Guenther Walther, and Trevor Hastie. 2001. Estimating the number of clusters in a data set via the gap statistic. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 63 (2): 411–423.

    Article  MathSciNet  MATH  Google Scholar 

  184. Tinós, Renato, Zhao Liang, Francisco Chicano, and Darrell Whitley. 2016. A new evaluation function for clustering: The NK internal validation criterion. In Proceedings of the genetic and evolutionary computation conference 2016, 509–516. ACM.

    Google Scholar 

  185. Trauwaert, E., P. Rousseeuw, and L. Kaufman. 1993. Fuzzy clustering by minimizing the total hypervolume. In Information and classification, 61–71. Springer.

    Google Scholar 

  186. Tripathi, Ashish Kumar, Kapil Sharma, and Manju Bala. 2018. Dynamic frequency based parallel k-bat algorithm for massive data clustering (DFBPKBA). International Journal of System Assurance Engineering and Management 9 (4): 866–874.

    Google Scholar 

  187. van Heerwaarden, Joost, T.L. Odong, and F.A. van Eeuwijk. 2013. Maximizing genetic differentiation in core collections by PCA-based clustering of molecular marker data. Theoretical and Applied Genetics 126 (3): 763–772.

    Article  Google Scholar 

  188. Vazirgiannis, Michalis. 2009. Clustering validity, 388–393. Boston, MA: Springer, US.

    Google Scholar 

  189. Vinh, Nguyen Xuan, Julien Epps, and James Bailey. 2010. Information theoretic measures for clusterings comparison: Variants, properties, normalization and correction for chance. Journal of Machine Learning Research 11: 2837–2854.

    MathSciNet  MATH  Google Scholar 

  190. Von Luxburg, Ulrike. 2007. A tutorial on spectral clustering. Statistics and Computing 17 (4): 395–416.

    Article  MathSciNet  Google Scholar 

  191. Wallace, David L. 1983. A method for comparing two hierarchical clusterings: Comment. Journal of the American Statistical Association 78 (383): 569–576.

    Google Scholar 

  192. Wu, Kuo-Lung, and Miin-Shen Yang. 2005. A cluster validity index for fuzzy clustering. Pattern Recognition Letters 26 (9): 1275–1291.

    Article  MathSciNet  Google Scholar 

  193. Wu, Yi-Leh, Cheng-Yuan Tang, Maw-Kae Hor, and Wu Pei-Fen. 2011. Feature selection using genetic algorithm and cluster validation. Expert Systems with Applications 38 (3): 2727–2732.

    Article  Google Scholar 

  194. Xie, Xuanli Lisa, and Gerardo Beni. 1991. A validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis & Machine Intelligence 8: 841–847.

    Article  Google Scholar 

  195. Xu, Kevin S., Mark Kliger, and Alfred O. Hero. 2010. Evolutionary spectral clustering with adaptive forgetting factor. In 2010 IEEE international conference on acoustics, speech and signal processing, 2174–2177. IEEE.

    Google Scholar 

  196. Xu, Kevin S., Mark Kliger, and Alfred O. Hero III. 2014. Adaptive evolutionary clustering. Data Mining and Knowledge Discovery 28 (2): 304–336.

    Article  MathSciNet  MATH  Google Scholar 

  197. Xu, Rui, Jie Xu, and Donald C. Wunsch. 2012. A comparison study of validity indices on swarm-intelligence-based clustering. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics) 42 (4): 1243–1256.

    Google Scholar 

  198. Yang, Dongdong, Xiaowei Zhang, Lintao Lv, and Wenzhun Huang. 2018. An automatic SAR image segmentation framework by multi-objective clustering and artificial immune learning. In 2018 international conference on mathematics, modelling, simulation and algorithms (MMSA 2018). Atlantis Press.

    Google Scholar 

  199. Yesilbudak, Mehmet. 2018. Implementation of novel hybrid approaches for power curve modeling of wind turbines. Energy Conversion and Management 171: 156–169.

    Article  Google Scholar 

  200. Žalik, Krista Rizman, and Borut Žalik. 2011. Validity index for clusters of different sizes and densities. Pattern Recognition Letters 32 (2): 221–234.

    Article  MATH  Google Scholar 

  201. Zang, Wenke, Zhenni Jiang, and Liyan Ren. 2017. Improved spectral clustering based on density combining DNA genetic algorithm. International Journal of Pattern Recognition and Artificial Intelligence 31 (04): 1750010.

    Article  Google Scholar 

  202. Zhang, Yunjie, Weina Wang, Xiaona Zhang, and Yi Li. 2008. A cluster validity index for fuzzy clustering. Information Sciences 178 (4): 1205–1218.

    Article  MATH  Google Scholar 

  203. Zhao, Qinpei, and Pasi Fränti. 2014. WB-index: A sum-of-squares based index for cluster validity. Data & Knowledge Engineering 92: 77–89.

    Article  Google Scholar 

  204. Zhao, Ying, and George Karypis. 2002. Evaluation of hierarchical clustering algorithms for document datasets. In Proceedings of the eleventh international conference on Information and knowledge management, 515–524. ACM.

    Google Scholar 

  205. Zhou, Shibing, and Xu Zhenyuan. 2018. A novel internal validity index based on the cluster centre and the nearest neighbour cluster. Applied Soft Computing 71: 78–88.

    Article  Google Scholar 

  206. Zhu, Shuwei, Lihong Xu, and Erik D. Goodman. 2019.Evolutionary multi-objective automatic clustering enhanced with quality metrics and ensemble strategy. Knowledge-Based Systems 105018.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. King Abdullah II School for Information Technology, The University of Jordan, Amman, Jordan

    Ibrahim Aljarah, Maria Habib, Razan Nujoom & Hossam Faris

  2. Center for Artificial Intelligence Research and Optimization, Torrens University Australia, Fortitude Valley, Brisbane, Australia

    Seyedali Mirjalili

Authors
  1. Ibrahim Aljarah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Maria Habib
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Razan Nujoom
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Hossam Faris
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Seyedali Mirjalili
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ibrahim Aljarah .

Editor information

Editors and Affiliations

  1. King Abdullah II School for Information Technology, The University of Jordan, Amman, Jordan

    Ibrahim Aljarah

  2. King Abdullah II School for Information Technology, The University of Jordan, Amman, Jordan

    Hossam Faris

  3. Center for Artificial Intelligence Research and Optimization, Torrens University Australia, Brisbane, QLD, Australia

    Seyedali Mirjalili

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Aljarah, I., Habib, M., Nujoom, R., Faris, H., Mirjalili, S. (2021). A Comprehensive Review of Evaluation and Fitness Measures for Evolutionary Data Clustering. In: Aljarah, I., Faris, H., Mirjalili, S. (eds) Evolutionary Data Clustering: Algorithms and Applications. Algorithms for Intelligent Systems. Springer, Singapore. https://doi.org/10.1007/978-981-33-4191-3_2

Download citation

Publish with us

Policies and ethics

Search

Navigation