{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T16:42:09Z","timestamp":1778172129995,"version":"3.51.4"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T00:00:00Z","timestamp":1718928000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["JSAN"],"abstract":"<jats:p>In the rapidly advancing landscape of digital technologies, clustering plays a critical role in the domains of artificial intelligence and big data. Clustering is essential for extracting meaningful insights and patterns from large, intricate datasets. Despite the efficacy of traditional clustering techniques in handling diverse data types and sizes, they encounter challenges posed by the increasing volume and dimensionality of data, as well as the complex structures inherent in high-dimensional spaces. This research recognizes the constraints of conventional clustering methods, including sensitivity to initial centroids, dependence on prior knowledge of cluster counts, and scalability issues, particularly in large datasets and Internet of Things implementations. In response to these challenges, we propose a K-level clustering algorithm inspired by the collective behavior of fish locomotion. K-level introduces a novel clustering approach based on greedy merging driven by distances in stages. This iterative process efficiently establishes hierarchical structures without the need for exhaustive computations. K-level gives users enhanced control over computational complexity, enabling them to specify the number of clusters merged simultaneously. This flexibility ensures accurate and efficient hierarchical clustering across diverse data types, offering a scalable solution for processing extensive datasets within a reasonable timeframe. The internal validation metrics, including the Silhouette Score, Davies\u2013Bouldin Index, and Calinski\u2013Harabasz Index, are utilized to evaluate the K-level algorithm across various types of datasets. Additionally, comparisons are made with rivals in the literature, including UPGMA, CLINK, UPGMC, SLINK, and K-means. The experiments and analyses show that the proposed algorithm overcomes many of the limitations of existing clustering methods, presenting scalable and adaptable clustering in the dynamic landscape of evolving data challenges.<\/jats:p>","DOI":"10.3390\/jsan13040036","type":"journal-article","created":{"date-parts":[[2024,6,21]],"date-time":"2024-06-21T11:10:28Z","timestamp":1718968228000},"page":"36","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Nature-Inspired Partial Distance-Based Clustering Algorithm"],"prefix":"10.3390","volume":"13","author":[{"given":"Mohammed","family":"El Habib Kahla","sequence":"first","affiliation":[{"name":"LIAP Laboratory, University of El Oued, P.O. Box 789, El Oued 39000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mounir","family":"Beggas","sequence":"additional","affiliation":[{"name":"LIAP Laboratory, University of El Oued, P.O. Box 789, El Oued 39000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8175-8467","authenticated-orcid":false,"given":"Abdelkader","family":"Laouid","sequence":"additional","affiliation":[{"name":"LIAP Laboratory, University of El Oued, P.O. Box 789, El Oued 39000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1058-0996","authenticated-orcid":false,"given":"Mohammad","family":"Hammoudeh","sequence":"additional","affiliation":[{"name":"Information & Computer Science Department, King Fahd University of Petroleum & Minerals, Academic Belt Road, Dhahran 31261, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,6,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"e1682","DOI":"10.7717\/peerj-cs.1682","article-title":"A P2P multi-path routing algorithm based on Skyline operator for data aggregation in IoMT environments","volume":"9","author":"Kertiou","year":"2023","journal-title":"PeerJ Comput. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1016\/S0306-4379(00)00022-3","article-title":"ROCK: A robust clustering algorithm for categorical attributes","volume":"25","author":"Guha","year":"2000","journal-title":"Inf. Syst."},{"key":"ref_3","first-page":"230","article-title":"Unweighted pair group method with arithmetic mean","volume":"10","author":"Sneath","year":"1973","journal-title":"Numer. Taxon."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1007\/s00453-017-0284-6","article-title":"Improved analysis of complete-linkage clustering","volume":"78","author":"Grosswendt","year":"2017","journal-title":"Algorithmica"},{"key":"ref_5","unstructured":"MacQueen, J. (July, January 21). Some methods for classification and analysis of multivariate observations. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Oakland, CA, USA."},{"key":"ref_6","first-page":"1193","article-title":"Implementasi Algoritma K-Means dalam Klasterisasi Kasus Stunting pada Balita di Desa Randudongkal","volume":"5","author":"Pratistha","year":"2024","journal-title":"J. Indones. Manaj. Inform."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1002\/9780470316801.ch2","article-title":"Partitioning around medoids (program pam)","volume":"344","author":"Kaufman","year":"1990","journal-title":"Find. Groups Data"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1016\/j.comcom.2021.11.010","article-title":"Deep reinforcement learning based transmission policy enforcement and multi-hop routing in QoS aware LoRa IoT networks","volume":"183","author":"Muthanna","year":"2022","journal-title":"Comput. Commun."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"18495","DOI":"10.1109\/JIOT.2023.3271831","article-title":"Pelican Gorilla Troop Optimization Based on Deep Feed Forward Neural Network for Human Activity Abnormality Detection in Smart Spaces","volume":"10","author":"Berdjouh","year":"2023","journal-title":"IEEE Internet Things J."},{"key":"ref_10","unstructured":"Abuarqoub, A., Al-Fayez, F., Alsboui, T., Hammoudeh, M., and Nisbet, A. (2012, January 19\u201324). Simulation issues in wireless sensor networks: A survey. Proceedings of the Sixth International Conference on Sensor Technologies and Applications (SENSORCOMM 2012), Rome, Italy."},{"key":"ref_11","first-page":"5594","article-title":"Nc-link: A new linkage method for efficient hierarchical clustering of large-scale data","volume":"5","author":"Jeon","year":"2017","journal-title":"IEEE Access"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"3958","DOI":"10.1016\/j.patcog.2010.06.021","article-title":"Fast agglomerative clustering using information of k-nearest neighbors","volume":"43","author":"Chang","year":"2010","journal-title":"Pattern Recognit."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1007\/s00357-014-9161-z","article-title":"Ward\u2019s hierarchical agglomerative clustering method: Which algorithms implement Ward\u2019s criterion?","volume":"31","author":"Murtagh","year":"2014","journal-title":"J. Classif."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.18576\/amis\/100332","article-title":"An improved agglomerative clustering algorithm for outlier detection","volume":"10","author":"Krishnamoorthy","year":"2016","journal-title":"Appl. Math. Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"3336","DOI":"10.1016\/j.eswa.2008.01.039","article-title":"A simple and fast algorithm for K-medoids clustering","volume":"36","author":"Park","year":"2009","journal-title":"Expert Syst. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"012128","DOI":"10.1088\/1757-899X\/725\/1\/012128","article-title":"Analysis of determining centroid clustering x-means algorithm with davies-bouldin index evaluation","volume":"Volume 725","author":"Mughnyanti","year":"2020","journal-title":"IOP Conference Series: Materials Science and Engineering"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/S0167-8655(97)00168-2","article-title":"A new cluster validity index for the fuzzy c-mean","volume":"19","author":"Rezaee","year":"1998","journal-title":"Pattern Recognit. Lett."},{"key":"ref_18","unstructured":"Leonard, K., and Peter, J.R. (2009). Finding Groups in Data: An Introduction to Cluster Analysis, John Wiley & Sons."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1003","DOI":"10.1109\/TKDE.2002.1033770","article-title":"CLARANS: A method for clustering objects for spatial data mining","volume":"14","author":"Ng","year":"2002","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1109\/TKDE.2005.21","article-title":"Combining partitional and hierarchical algorithms for robust and efficient data clustering with cohesion self-merging","volume":"17","author":"Lin","year":"2005","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Thang, V.V., Pantiukhin, D., and Galushkin, A. (2015, January 18\u201319). A hybrid clustering algorithm: The fastDBSCAN. Proceedings of the 2015 International Conference on Engineering and Telecommunication (EnT), Moscow, Russia.","DOI":"10.1109\/EnT.2015.31"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1049\/cje.2015.10.006","article-title":"A Novel Hybrid Data Clustering Algorithm Based on Artificial Bee Colony Algorithm and K-Means","volume":"24","author":"Tran","year":"2015","journal-title":"Chin. J. Electron."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"751","DOI":"10.3233\/AIC-150677","article-title":"A hybrid data clustering approach based on improved cat swarm optimization and K-harmonic mean algorithm","volume":"28","author":"Kumar","year":"2015","journal-title":"AI Commun."},{"key":"ref_24","unstructured":"Elhabib, M. (2024, May 28). K-Level Clustering Algorithm. Available online: https:\/\/github.com\/mohammed-elhabib\/k-level."},{"key":"ref_25","unstructured":"Jain, A.K., and Dubes, R.C. (1988). Algorithms for Clustering Data, Prentice-Hall, Inc."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"411","DOI":"10.1111\/1467-9868.00293","article-title":"Estimating the number of clusters in a data set via the gap statistic","volume":"63","author":"Tibshirani","year":"2001","journal-title":"J. R. Stat. Soc. Ser. B (Stat. Methodol)"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1109\/TPAMI.1979.4766909","article-title":"A cluster separation measure","volume":"PAMI-1","author":"Davies","year":"1979","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/03610927408827101","article-title":"A dendrite method for cluster analysis","volume":"3","author":"Harabasz","year":"1974","journal-title":"Commun. Stat.-Theory Methods"}],"container-title":["Journal of Sensor and Actuator Networks"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2224-2708\/13\/4\/36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:02:34Z","timestamp":1760108554000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2224-2708\/13\/4\/36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,21]]},"references-count":28,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["jsan13040036"],"URL":"https:\/\/doi.org\/10.3390\/jsan13040036","relation":{},"ISSN":["2224-2708"],"issn-type":[{"value":"2224-2708","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,6,21]]}}}