{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T02:14:03Z","timestamp":1772504043727,"version":"3.50.1"},"reference-count":50,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T00:00:00Z","timestamp":1623628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007446","name":"King Khalid University","doi-asserted-by":"publisher","award":["RGP.2\/1\/42"],"award-info":[{"award-number":["RGP.2\/1\/42"]}],"id":[{"id":"10.13039\/501100007446","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A k-means algorithm is a method for clustering that has already gained a wide range of acceptability. However, its performance extremely depends on the opening cluster centers. Besides, due to weak exploration capability, it is easily stuck at local optima. Recently, a new metaheuristic called Moth Flame Optimizer (MFO) is proposed to handle complex problems. MFO simulates the moths intelligence, known as transverse orientation, used to navigate in nature. In various research work, the performance of MFO is found quite satisfactory. This paper suggests a novel heuristic approach based on the MFO to solve data clustering problems. To validate the competitiveness of the proposed approach, various experiments have been conducted using Shape and UCI benchmark datasets. The proposed approach is compared with five state-of-art algorithms over twelve datasets. The mean performance of the proposed algorithm is superior on 10 datasets and comparable in remaining two datasets. The analysis of experimental results confirms the efficacy of the suggested approach.<\/jats:p>","DOI":"10.3390\/s21124086","type":"journal-article","created":{"date-parts":[[2021,6,14]],"date-time":"2021-06-14T22:25:46Z","timestamp":1623709546000},"page":"4086","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":40,"title":["Data Clustering Using Moth-Flame Optimization Algorithm"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0872-6987","authenticated-orcid":false,"given":"Tribhuvan","family":"Singh","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, Siksha \u2018O\u2019 Anusandhan (Deemed to be University), Bhubaneswar, Odisha 751030, India"}]},{"given":"Nitin","family":"Saxena","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4929-409X","authenticated-orcid":false,"given":"Manju","family":"Khurana","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Thapar Institute of Engineering and Technology, Patiala, Punjab 147004, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6475-4491","authenticated-orcid":false,"given":"Dilbag","family":"Singh","sequence":"additional","affiliation":[{"name":"School of Engineering and Applied Sciences, Bennett University, Greater Noida 201310, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0165-4992","authenticated-orcid":false,"given":"Mohamed","family":"Abdalla","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, King Khalid University, Abha 62529, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9942-8642","authenticated-orcid":false,"given":"Hammam","family":"Alshazly","sequence":"additional","affiliation":[{"name":"Faculty of Computers and Information, South Valley University, Qena 83523, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,14]]},"reference":[{"key":"ref_1","unstructured":"Tan, P.N. (2018). Introduction to Data Mining, Pearson Education India."},{"key":"ref_2","unstructured":"Alpaydin, E. (2014). Introduction to Machine Learning, MIT Press."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1397","DOI":"10.1016\/j.ipm.2008.03.001","article-title":"Towards effective document clustering: A constrained K-means based approach","volume":"44","author":"Hu","year":"2008","journal-title":"Inf. Process. Manag."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1016\/j.datak.2007.08.001","article-title":"Text document clustering based on frequent word meaning sequences","volume":"64","author":"Li","year":"2008","journal-title":"Data Knowl. Eng."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/j.compbiomed.2007.09.002","article-title":"Fuzzy clustering to detect tuberculous meningitis-associated hyperdensity in CT images","volume":"38","author":"Halberstadt","year":"2008","journal-title":"Comput. Biol. Med."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Webb, A.R. (2003). Statistical Pattern Recognition, John Wiley & Sons.","DOI":"10.1002\/0470854774"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1016\/j.patcog.2007.06.006","article-title":"Accurate integration of multi-view range images using k-means clustering","volume":"41","author":"Zhou","year":"2008","journal-title":"Pattern Recognit."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1626","DOI":"10.1109\/TIFS.2018.2796999","article-title":"Face clustering: Representation and pairwise constraints","volume":"13","author":"Shi","year":"2018","journal-title":"IEEE Trans. Inf. Forensics Secur."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Adjabi, I., Ouahabi, A., Benzaoui, A., and Taleb-Ahmed, A. (2020). Past, present, and future of face recognition: A review. Electronics, 9.","DOI":"10.20944\/preprints202007.0479.v1"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Adjabi, I., Ouahabi, A., Benzaoui, A., and Jacques, S. (2021). Multi-Block Color-Binarized Statistical Images for Single-Sample Face Recognition. Sensors, 21.","DOI":"10.3390\/s21030728"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"10245","DOI":"10.1007\/s13369-020-04616-1","article-title":"EELTM: An Energy Efficient LifeTime Maximization Approach for WSN by PSO and Fuzzy-Based Unequal Clustering","volume":"45","author":"Arikumar","year":"2020","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.swevo.2013.11.003","article-title":"A survey on nature inspired metaheuristic algorithms for partitional clustering","volume":"16","author":"Nanda","year":"2014","journal-title":"Swarm Evol. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1007\/s10115-019-01358-x","article-title":"Clustering analysis using a novel locality-informed grey wolf-inspired clustering approach","volume":"62","author":"Aljarah","year":"2020","journal-title":"Knowl. Inf. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.patrec.2017.10.031","article-title":"Magnetic optimization algorithm for data clustering","volume":"115","author":"Kushwaha","year":"2018","journal-title":"Pattern Recognit. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Singh, T., and Mishra, K.K. (2019). Data Clustering Using Environmental Adaptation Method. International Conference on Hybrid Intelligent Systems, Springer.","DOI":"10.1007\/978-3-030-49336-3_16"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1002\/sam.11380","article-title":"An evaluation of data stream clustering algorithms","volume":"11","author":"Mansalis","year":"2018","journal-title":"Stat. Anal. Data Min. ASA Data Sci. J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"10067","DOI":"10.1007\/s13369-020-04578-4","article-title":"Clustering-Based EMT Model for Predicting Student Performance","volume":"45","author":"Almasri","year":"2020","journal-title":"Arab. J. Sci. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"102","DOI":"10.1504\/IJBIC.2020.109713","article-title":"A variant of EAM to uncover community structure in complex networks","volume":"16","author":"Singh","year":"2020","journal-title":"Int. J. Bio-Inspired Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.ins.2012.08.023","article-title":"Black hole: A new heuristic optimization approach for data clustering","volume":"222","author":"Hatamlou","year":"2013","journal-title":"Inf. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Saida, I.B., Nadjet, K., and Omar, B. (2014). A new algorithm for data clustering based on cuckoo search optimization. Genetic and Evolutionary Computing, Springer.","DOI":"10.1007\/978-3-319-01796-9_6"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/s10462-013-9400-4","article-title":"A review on particle swarm optimization algorithm and its variants to clustering high-dimensional data","volume":"44","author":"Esmin","year":"2015","journal-title":"Artif. Intell. Rev."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.engappai.2016.11.003","article-title":"A novel data clustering algorithm based on modified gravitational search algorithm","volume":"61","author":"Han","year":"2017","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1366","DOI":"10.1016\/j.chaos.2006.04.057","article-title":"On the efficiency of chaos optimization algorithms for global optimization","volume":"34","author":"Yang","year":"2007","journal-title":"Chaos Solitons Fractals"},{"key":"ref_24","first-page":"1076","article-title":"Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms","volume":"187","author":"Tavazoei","year":"2007","journal-title":"Appl. Math. Comput."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"14555","DOI":"10.1016\/j.eswa.2011.05.027","article-title":"Chaotic particle swarm optimization for data clustering","volume":"38","author":"Chuang","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2387","DOI":"10.1016\/j.asoc.2012.03.037","article-title":"Chaotic ant swarm approach for data clustering","volume":"12","author":"Wan","year":"2012","journal-title":"Appl. Soft Comput."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"17789","DOI":"10.1007\/s00521-020-04951-2","article-title":"A chaotic sequence-guided Harris hawks optimizer for data clustering","volume":"32","author":"Singh","year":"2020","journal-title":"Neural Comput. Appl."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Singh, T., and Saxena, N. (2021). Chaotic sequence and opposition learning guided approach for data clustering. Pattern Anal. Appl., 1\u201315.","DOI":"10.1007\/s10044-021-00964-2"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Senthilnath, J., Das, V., Omkar, S., and Mani, V. (2013). Clustering using levy flight cuckoo search. Proceedings of Seventh International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2012), Springer.","DOI":"10.1007\/978-81-322-1041-2_6"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"142085","DOI":"10.1109\/ACCESS.2019.2937021","article-title":"An Enhanced Version of Black Hole Algorithm via Levy Flight for Optimization and Data Clustering Problems","volume":"7","author":"Abdulwahab","year":"2019","journal-title":"IEEE Access"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1016\/j.cie.2017.06.028","article-title":"A survey and classification of opposition-based metaheuristics","volume":"110","author":"Rojas","year":"2017","journal-title":"Comput. Ind. Eng."},{"key":"ref_32","first-page":"1000","article-title":"An Improved Cat Swarm Optimization Algorithm Based on Opposition-Based Learning and Cauchy Operator for Clustering","volume":"13","author":"Kumar","year":"2017","journal-title":"J. Inf. Process. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Sun, L., Chen, S., Xu, J., and Tian, Y. (2019). Improved monarch butterfly optimization algorithm based on opposition-based learning and random local perturbation. Complexity, 2019.","DOI":"10.1155\/2019\/4182148"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1483565","DOI":"10.1080\/25742558.2018.1483565","article-title":"A whale optimization algorithm (WOA) approach for clustering","volume":"5","author":"Nasiri","year":"2018","journal-title":"Cogent Math. Stat."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1569","DOI":"10.1016\/j.aej.2017.04.013","article-title":"WGC: Hybridization of exponential grey wolf optimizer with whale optimization for data clustering","volume":"57","author":"Jadhav","year":"2018","journal-title":"Alex. Eng. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.asoc.2019.03.013","article-title":"Variance-based differential evolution algorithm with an optional crossover for data clustering","volume":"80","author":"Alswaitti","year":"2019","journal-title":"Appl. Soft Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"546","DOI":"10.1016\/j.knosys.2018.09.013","article-title":"Automatic data clustering using nature-inspired symbiotic organism search algorithm","volume":"163","author":"Zhou","year":"2019","journal-title":"Knowl. Based Syst."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"e12478","DOI":"10.1111\/exsy.12478","article-title":"A new clustering method based on the bio-inspired cuttlefish optimization algorithm","volume":"37","author":"Eesa","year":"2019","journal-title":"Expert Syst."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1332","DOI":"10.1109\/JAS.2019.1911744","article-title":"Clustering Structure Analysis in Time Series Data with Density-Based Clusterability","volume":"6","author":"Juho","year":"2019","journal-title":"IEEE\/CAA J. Autom. Sinica"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"e12657","DOI":"10.1111\/exsy.12657","article-title":"A novel data clustering approach based on whale optimization algorithm","volume":"38","author":"Singh","year":"2020","journal-title":"Expert Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","article-title":"No free lunch theorems for optimization","volume":"1","author":"Wolpert","year":"1997","journal-title":"IEEE Trans. Evol. Comput."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.knosys.2015.07.006","article-title":"Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm","volume":"89","author":"Mirjalili","year":"2015","journal-title":"Knowl. Based Syst."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Barbakh, W.A., Wu, Y., and Fyfe, C. (2009). Review of clustering algorithms. Non-Standard Parameter Adaptation for Exploratory Data Analysis, Springer.","DOI":"10.1007\/978-3-642-04005-4"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"651","DOI":"10.1016\/j.patrec.2009.09.011","article-title":"Data clustering: 50 years beyond K-means","volume":"31","author":"Jain","year":"2010","journal-title":"Pattern Recognit. Lett."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"495","DOI":"10.1007\/s00521-015-1870-7","article-title":"Multi-verse optimizer: A nature-inspired algorithm for global optimization","volume":"27","author":"Mirjalili","year":"2016","journal-title":"Neural Comput. Appl."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"849","DOI":"10.1016\/j.future.2019.02.028","article-title":"Harris Hawks optimization: Algorithm and applications","volume":"97","author":"Heidari","year":"2019","journal-title":"Future Gener. Comput. Syst."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"46","DOI":"10.1016\/j.advengsoft.2013.12.007","article-title":"Grey wolf optimizer","volume":"69","author":"Mirjalili","year":"2014","journal-title":"Adv. Eng. Softw."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1080\/03610928008827904","article-title":"Approximations of the critical region of the Friedman statistic","volume":"9","author":"Inman","year":"1980","journal-title":"Commun. Stat. Theory Methods A"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Sheskin, D.J. (2003). Handbook of Parametric and Nonparametric Statistical Procedures, Chapman and Hall\/CRC.","DOI":"10.1201\/9781420036268"},{"key":"ref_50","first-page":"65","article-title":"A simple sequentially rejective multiple test procedure","volume":"6","author":"Holm","year":"1979","journal-title":"Scand. J. Stat."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4086\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:14:01Z","timestamp":1760163241000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4086"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,14]]},"references-count":50,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["s21124086"],"URL":"https:\/\/doi.org\/10.3390\/s21124086","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,14]]}}}