{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T01:49:40Z","timestamp":1767923380136,"version":"3.49.0"},"reference-count":49,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T00:00:00Z","timestamp":1654041600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012190","name":"Ministry of Science and Higher Education of the Russian Federation","doi-asserted-by":"publisher","award":["FEFE-2020-0013"],"award-info":[{"award-number":["FEFE-2020-0013"]}],"id":[{"id":"10.13039\/501100012190","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>Automatic grouping (clustering) involves dividing a set of objects into subsets (groups) so that the objects from one subset are more similar to each other than to the objects from other subsets according to some criterion. Kohonen neural networks are a class of artificial neural networks, the main element of which is a layer of adaptive linear adders, operating on the principle of \u201cwinner takes all\u201d. One of the advantages of Kohonen networks is their ability of online clustering. Greedy agglomerative procedures in clustering consistently improve the result in some neighborhood of a known solution, choosing as the next solution the option that provides the least increase in the objective function. Algorithms using the agglomerative greedy heuristics demonstrate precise and stable results for a k-means model. In our study, we propose a greedy agglomerative heuristic algorithm based on a Kohonen neural network with distance measure variations to cluster industrial products. Computational experiments demonstrate the comparative efficiency and accuracy of using the greedy agglomerative heuristic in the problem of grouping of industrial products into homogeneous production batches.<\/jats:p>","DOI":"10.3390\/a15060191","type":"journal-article","created":{"date-parts":[[2022,6,1]],"date-time":"2022-06-01T12:48:31Z","timestamp":1654087711000},"page":"191","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Clustering Algorithm with a Greedy Agglomerative Heuristic and Special Distance Measures"],"prefix":"10.3390","volume":"15","author":[{"given":"Guzel","family":"Shkaberina","sequence":"first","affiliation":[{"name":"Institute of Informatics and Telecommunications, Reshetnev Siberian State University of Science and Technology, 31 Krasnoyarsky Rabochy Av., 660037 Krasnoyarsk, Russia"}]},{"given":"Leonid","family":"Verenev","sequence":"additional","affiliation":[{"name":"Institute of Informatics and Telecommunications, Reshetnev Siberian State University of Science and Technology, 31 Krasnoyarsky Rabochy Av., 660037 Krasnoyarsk, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8500-2050","authenticated-orcid":false,"given":"Elena","family":"Tovbis","sequence":"additional","affiliation":[{"name":"Institute of Informatics and Telecommunications, Reshetnev Siberian State University of Science and Technology, 31 Krasnoyarsky Rabochy Av., 660037 Krasnoyarsk, Russia"}]},{"given":"Natalia","family":"Rezova","sequence":"additional","affiliation":[{"name":"Institute of Informatics and Telecommunications, Reshetnev Siberian State University of Science and Technology, 31 Krasnoyarsky Rabochy Av., 660037 Krasnoyarsk, Russia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0667-4001","authenticated-orcid":false,"given":"Lev","family":"Kazakovtsev","sequence":"additional","affiliation":[{"name":"Institute of Informatics and Telecommunications, Reshetnev Siberian State University of Science and Technology, 31 Krasnoyarsky Rabochy Av., 660037 Krasnoyarsk, Russia"},{"name":"Institute of Business Process Management, Siberian Federal University, 79 Svobodny Av., 660041 Krasnoyarsk, Russia"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Shirkhorshidi, A.S., Aghabozorgi, S., and Wah, T. (2015). A comparison study on similarity and dissimilarity measures in clustering continuous data. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0144059"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1104","DOI":"10.1016\/j.phpro.2012.03.206","article-title":"A clustering method based on k-means algorithm","volume":"25","author":"Youguo","year":"2012","journal-title":"Phys. Procedia"},{"key":"ref_3","first-page":"801","article-title":"Sur la divisiondes corps materiels en parties","volume":"4","author":"Steinhaus","year":"1956","journal-title":"Bull. Acad. Polon. Sci."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s10479-008-0352-z","article-title":"On the point for which the sum of the distances to n given points is minimum","volume":"167","author":"Weiszfeld","year":"2009","journal-title":"Ann. Oper. Res."},{"key":"ref_5","first-page":"362","article-title":"A sequential method for discrete optimization problems and its application to the assignment, traveling salesman and tree scheduling problems","volume":"13","author":"Nicholson","year":"1965","journal-title":"J. Inst. Math. Appl."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","article-title":"Least squares quantization in PCM","volume":"28","author":"Lloyd","year":"1982","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_7","unstructured":"Arthur, D., and Vassilvitskii, S. (2007, January 7\u20139). K-means++: The advantages of careful seeding. Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, LA, USA."},{"key":"ref_8","unstructured":"Bradley, P.S., and Fayyad, U.M. (1998, January 24\u201327). Refining initial points for k-means clustering. Proceedings of the Fifteenth International Conference on Machine Learning (ICML 1998), Madison, WI, USA."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/978-981-10-3409-1_7","article-title":"Comparison of k-means clustering initialization approaches with brute-force initialization","volume":"Volume 567","author":"Golasowski","year":"2017","journal-title":"Advanced Computing and Systems for Security. Advances in Intelligent Systems and Computing"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Kalczynski, P., Brimberg, J., and Drezner, Z. (2021). Less is more: Simple algorithms for the minimum sum of squares clustering problem. IMA J. Manag. Math., dpab031.","DOI":"10.1093\/imaman\/dpab031"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"6361","DOI":"10.1007\/s00500-018-3289-4","article-title":"A hybrid approach using genetic algorithm and the differential evolution heuristic for enhanced initialization of the k-means algorithm with applications in text clustering","volume":"23","author":"Mustafi","year":"2019","journal-title":"Soft Comput."},{"key":"ref_12","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 Recogn. Lett."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Ahmed, M., Seraj, R., and Islam, S.M.S. (2020). The k-means algorithm: A comprehensive survey and performance evaluation. Electronics, 9.","DOI":"10.3390\/electronics9081295"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.eswa.2012.07.021","article-title":"A comparative study of efficient initialization methods for the k-means clustering algorithm","volume":"40","author":"Celebi","year":"2013","journal-title":"Expert Syst. Appl."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kohonen, T. (1995). Self-Organizing Maps, Springer.","DOI":"10.1007\/978-3-642-97610-0"},{"key":"ref_16","unstructured":"Kohonen, T., and Somervuo, P. (1997, January 4\u20136). Self-organizing maps of symbol strings with application to speech recognition. Proceedings of the Workshop on Self-Organizing Maps (WSOM\u201997), Espoo, Finland."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"\u015awietlicka, I., Kuniszyk-J\u00f3\u017akowiak, W., and \u015awietlicki, M. (2022). Artificial neural networks combined with the principal component analysis for non-fluent speech recognition. Sensors, 22.","DOI":"10.3390\/s22010321"},{"key":"ref_18","first-page":"2151","article-title":"Vector quantization by improved Kohonen algorithm","volume":"4","author":"Ettaouil","year":"2012","journal-title":"J. Comput."},{"key":"ref_19","unstructured":"Younis, K.S., Rogers, S.K., and DeSimio, M.P. (1996, January 20\u201323). Vector quantization based on dynamic adjustment of Mahalanobis distance. Proceedings of the IEEE 1996 National Aerospace and Electronics Conference NAECON, Dayton, OH, USA."},{"key":"ref_20","first-page":"2250","article-title":"Image segmentation by self-organizing map with Mahalanobis distance","volume":"3","author":"Paul","year":"2013","journal-title":"Int. J. Emerg. Technol. Adv. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Sun, Y., Liu, H., and Sun, Q. (2014, January 5). Online learning on incremental distance metric for person re-identification. Proceedings of the 2014 IEEE International Conference on Robotics and Biomimetics, Bali, Indonesia.","DOI":"10.1109\/ROBIO.2014.7090533"},{"key":"ref_22","unstructured":"Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., and Zurada, J.M. (29\u20133, January 29). Improving Performance of self-organising maps with distance metric learning method. Proceedings of the International Conference on Artificial Intelligence and Soft Computing, Zakopane, Poland."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1007\/s10015-008-0555-z","article-title":"Face recognition under varying illumination using Mahalanobis self-organizing map","volume":"13","author":"Saleh","year":"2008","journal-title":"Artif. Life Robot."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"61","DOI":"10.7763\/IJMO.2016.V6.504","article-title":"Appropriate learning rate and neighborhood function of self-organizing map (SOM) for specific humidity pattern classification over Southern Thailand","volume":"6","author":"Natita","year":"2016","journal-title":"Int. J. Modeling Optim."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1007\/s12065-020-00518-1","article-title":"SOMDROID: Android malware detection by artificial neural network trained using unsupervised learning","volume":"15","author":"Mahindru","year":"2022","journal-title":"Evol. Intel."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Solovev, D.B., Kyriakopoulos, G.L., and Venelin, T. (2022). Kohonen self-organizing map in seasonal sales planning. SMART Automatics and Energy. Smart Innovation, Systems and Technologies, Springer.","DOI":"10.1007\/978-981-16-8759-4"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Wang, Y., Wang, H., Li, S., and Wang, L. (2022). Survival risk prediction of esophageal cancer based on the Kohonen network clustering algorithm and kernel extreme learning machine. Mathematics, 10.","DOI":"10.3390\/math10091367"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Radionov, A.A., and Gasiyarov, V.R. (2022). Intelligent support for medical decision making. Advances in Automation III. RusAutoCon 2021. Lecture Notes in Electrical Engineering, Springer.","DOI":"10.1007\/978-3-030-94202-1"},{"key":"ref_29","first-page":"482","article-title":"A cluster validity for optimal configuration of Kohonen maps in e-learning recommendation","volume":"26","author":"Mawane","year":"2022","journal-title":"Indones. J. Electr. Eng. Comput. Sci."},{"key":"ref_30","first-page":"4729526","article-title":"Application of computer data mining technology based on AKN algorithm in denial of service attack defense detection","volume":"2022","author":"Huang","year":"2022","journal-title":"Wirel. Commun. Mob. Comput."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"127082","DOI":"10.1016\/j.jhydrol.2021.127082","article-title":"Using a linear discriminant analysis (LDA)-based nomenclature system and self-organizing maps (SOM) for spatiotemporal assessment of groundwater quality in a coastal aquifer","volume":"603","author":"Amiri","year":"2021","journal-title":"J. Hydrol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1186\/s40537-021-00529-4","article-title":"Exploration of the investment patterns of potential retail banking customers using two-stage cluster analysis","volume":"8","author":"Ko","year":"2021","journal-title":"J. Big Data"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1287\/mnsc.9.4.643","article-title":"A heuristic program for locating warehouses","volume":"9","author":"Kuehn","year":"1963","journal-title":"Manag. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1023\/A:1026130003508","article-title":"An efficient genetic algorithm for the p-median problem","volume":"122","author":"Alp","year":"2003","journal-title":"Ann. Oper. Res."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1287\/opre.45.2.226","article-title":"Optimized crossover for the independent set problem","volume":"45","author":"Agarwal","year":"1997","journal-title":"Oper. Res."},{"key":"ref_36","first-page":"229","article-title":"Genetic algorithm wish fast greedy heuristic for clustering and location problems","volume":"38","author":"Kazakovtsev","year":"2014","journal-title":"Informatica"},{"key":"ref_37","unstructured":"Andras, P., and Idowu, O. (2005, January 5\u20138). Kohonen networks with graph-based augmented metrics. Proceedings of the Workshop on Self-Organizing Maps (WSOM 2005), Paris, France."},{"key":"ref_38","unstructured":"Horio, K., Koga, T., and Yamakawa, T. (October, January 28). Self-organizing map with distance measure defined by data distribution. Proceedings of the 2008 World Automation Congress, Waikoloa, HI, USA."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1321","DOI":"10.1162\/neco.1997.9.6.1321","article-title":"Self-organized formation of various invariant-feature filters in the adaptive-subspace SOM","volume":"9","author":"Kohonen","year":"1997","journal-title":"Neural Comput."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1016\/j.neunet.2009.01.012","article-title":"SOM of SOMs","volume":"22","author":"Furukawa","year":"2009","journal-title":"Neural Netw."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1016\/j.neucom.2010.08.016","article-title":"Local matrix adaptation in topographic neural maps","volume":"74","author":"Arnonkijpanich","year":"2011","journal-title":"Neurocomputing"},{"key":"ref_42","first-page":"2343","article-title":"Distance metric learning for the self-organizing map using a co-training approach","volume":"14","author":"Yoneda","year":"2018","journal-title":"Int. J. Innov. Comput. Inf. Control"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1089\/big.2018.0175","article-title":"Effects of distance measure choice on K-Nearest Neighbor classifier performance: A review","volume":"7","author":"Alfeilat","year":"2019","journal-title":"Big Data"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/COMST.2014.2336610","article-title":"A Survey of Distance and similarity measures used within network intrusion anomaly detection","volume":"17","author":"Borghetti","year":"2015","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1007\/BF02834632","article-title":"Mahalanobis distance","volume":"4","author":"McLachlan","year":"1999","journal-title":"Resonance"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1016\/j.neucom.2003.09.009","article-title":"On the use of self-organizing maps to accelerate vector quantization","volume":"56","author":"Cottrell","year":"2004","journal-title":"Neurocomputing"},{"key":"ref_47","unstructured":"Haykin, S. (2009). Neural Networks and Learning Machines, Pearson Education."},{"key":"ref_48","unstructured":"Fausett, L. (1994). Fundamental of Neural Networks: Architectures, Algorithms, and Applications, Prentice Hall International."},{"key":"ref_49","first-page":"421","article-title":"On the optimization models for automatic grouping of industrial products by homogeneous production batches","volume":"Volume 1275","author":"Kochetov","year":"2020","journal-title":"Mathematical Optimization Theory and Operations Research 2020, Communications in Computer and Information Science"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/6\/191\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T23:23:27Z","timestamp":1760138607000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/15\/6\/191"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,6,1]]},"references-count":49,"journal-issue":{"issue":"6","published-online":{"date-parts":[[2022,6]]}},"alternative-id":["a15060191"],"URL":"https:\/\/doi.org\/10.3390\/a15060191","relation":{},"ISSN":["1999-4893"],"issn-type":[{"value":"1999-4893","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,6,1]]}}}