{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T06:32:19Z","timestamp":1780468339104,"version":"3.54.1"},"reference-count":41,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2020,4,28]],"date-time":"2020-04-28T00:00:00Z","timestamp":1588032000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>In this paper, we briefly present several modifications and generalizations of the concept of self-organizing neural networks\u2014usually referred to as self-organizing maps (SOMs)\u2014to illustrate their advantages in applications that range from high-dimensional data visualization to complex data clustering. Starting from conventional SOMs, Growing SOMs (GSOMs), Growing Grid Networks (GGNs), Incremental Grid Growing (IGG) approach, Growing Neural Gas (GNG) method as well as our two original solutions, i.e., Generalized SOMs with 1-Dimensional Neighborhood (GeSOMs with 1DN also referred to as Dynamic SOMs (DSOMs)) and Generalized SOMs with Tree-Like Structures (GeSOMs with T-LSs) are discussed. They are characterized in terms of (i) the modification mechanisms used, (ii) the range of network modifications introduced, (iii) the structure regularity, and (iv) the data-visualization\/data-clustering effectiveness. The performance of particular solutions is illustrated and compared by means of selected data sets. We also show that the proposed original solutions, i.e., GeSOMs with 1DN (DSOMs) and GeSOMS with T-LSs outperform alternative approaches in various complex clustering tasks by providing up to     20 %     increase in the clustering accuracy. The contribution of this work is threefold. First, algorithm-oriented original computer-implementations of particular SOM\u2019s generalizations are developed. Second, their detailed simulation results are presented and discussed. Third, the advantages of our earlier-mentioned original solutions are demonstrated.<\/jats:p>","DOI":"10.3390\/a13050109","type":"journal-article","created":{"date-parts":[[2020,4,28]],"date-time":"2020-04-28T09:57:21Z","timestamp":1588067841000},"page":"109","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Evolution of SOMs\u2019 Structure and Learning Algorithm: From Visualization of High-Dimensional Data to Clustering of Complex Data"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1174-3953","authenticated-orcid":false,"given":"Marian B.","family":"Gorza\u0142czany","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, Kielce University of Technology, 25-314 Kielce, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3719-6572","authenticated-orcid":false,"given":"Filip","family":"Rudzi\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, Kielce University of Technology, 25-314 Kielce, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kohonen, T. (2001). Self-Organizing Maps, Springer. [3rd ed.].","DOI":"10.1007\/978-3-642-56927-2"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1007\/BF00337288","article-title":"Self-organized formation of topologically correct feature maps","volume":"43","author":"Kohonen","year":"1982","journal-title":"Biol. Cybern."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Gorricha, J., and Lobo, V. (2011). On the Use of Three-Dimensional Self-Organizing Maps for Visualizing Clusters in Georeferenced Data. Lecture Notes in Geoinformation and Cartography, Spring.","DOI":"10.1007\/978-3-642-19766-6_6"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1109\/72.238310","article-title":"Generalized clustering networks and Kohonen\u2019s self-organizing scheme","volume":"4","author":"Pal","year":"1993","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_5","unstructured":"Ultsch, A. (2005, January 5\u20138). Clustering with SOM: U*C. Proceedings of the Workshop on Self-Organizing Maps, Paris, France."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Vellido, A., Gibert, K., Angulo, C., and Guerrero, M.J.D. (2019, January 26\u201328). Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization. Proceedings of the 13th International Workshop, WSOM+ 2019, Barcelona, Spain.","DOI":"10.1007\/978-3-030-19642-4"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Rodrigues, J.S., and Almeida, L.B. (1990). Improving the learning speed in topological maps of patterns. The International Neural Network Society (INNS), the IEEE Neural Network Council Cooperating Societies, International Neural Network Conference (INNC), Springer.","DOI":"10.1007\/978-94-009-0643-3_96"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1007\/BF02332159","article-title":"Growing grid\u2014A self-organizing network with constant neighborhood range and adaptation strength","volume":"2","author":"Fritzke","year":"1995","journal-title":"Neural Process. Lett."},{"key":"ref_9","unstructured":"Blackmore, J., and Miikkulainen, R. (April, January 28). Incremental grid growing: Encoding high-dimensional structure into a two-dimensional feature map. Proceedings of the IEEE International Conference on Neural Networks, San Francisco, CA, USA."},{"key":"ref_10","first-page":"625","article-title":"A growing neural gas network learns topologies","volume":"Volume 7","author":"Fritzke","year":"1995","journal-title":"Advances in Neural Information Processing Systems"},{"key":"ref_11","first-page":"2833","article-title":"Generalized Self-Organizing Maps for Automatic Determination of the Number of Clusters and Their Multiprototypes in Cluster Analysis","volume":"29","year":"2018","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1007\/11785231_62","article-title":"Cluster analysis via dynamic self-organizing neural networks","volume":"Volume 4029","author":"Rutkowski","year":"2006","journal-title":"Artificial Intelligence and Soft Computing\u2014ICAISC 2006"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"40","DOI":"10.1007\/978-3-540-69731-2_5","article-title":"WWW-newsgroup-document clustering by means of dynamic self-organizing neural networks","volume":"Volume 5097","author":"Rutkowski","year":"2008","journal-title":"Artificial Intelligence and Soft Computing\u2014ICAISC 2008"},{"key":"ref_14","first-page":"725","article-title":"Generalized tree-like self-organizing neural networks with dynamically defined neighborhood for cluster analysis","volume":"Volume 8468","author":"Rutkowski","year":"2014","journal-title":"Artificial Intelligence and Soft Computing\u2014ICAISC 2014"},{"key":"ref_15","first-page":"15","article-title":"Microarray leukemia gene data clustering by means of generalized self-organizing neural networks with evolving tree-like structures","volume":"Volume 9119","author":"Rutkowski","year":"2015","journal-title":"Artificial Intelligence and Soft Computing\u2014ICAISC 2015"},{"key":"ref_16","first-page":"186","article-title":"Generalized SOMs with splitting-merging tree-like structures for WWW-document clustering","volume":"Volume 89","author":"Alonso","year":"2015","journal-title":"Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology (IFSA-EUSFLAT-15)"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Gorza\u0142czany, M.B., Rudzi\u0144ski, F., and Piekoszewski, J. (2016, January 24\u201329). Gene expression data clustering using tree-like SOMs with evolving splitting-merging structures. Proceedings of the IEEE World Congress on Computational Intelligence (IEEE WCCI 2016), International Joint Conference on Neural Networks (IJCNN), Vancouver, BC, Canada.","DOI":"10.1109\/IJCNN.2016.7727671"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Gorza\u0142czany, M.B., Piekoszewski, J., and Rudzi\u0144ski, F. (2019, January 6\u20139). Uncovering informative genes from colon cancer gene expression data via multi-step clustering based on generalized SOMs with splitting-merging structures. Proceedings of the 2019 IEEE Symposium Series on Computational Intelligence (SSCI), Xiamen, China.","DOI":"10.1109\/SSCI44817.2019.9002933"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gorza\u0142czany, M.B., Piekoszewski, J., and Rudzi\u0144ski, F. (2018, January 13\u201315). Electricity Consumption Data Clustering for Load Profiling Using Generalized Self-Organizing Neural Networks with Evolving Splitting-Merging Structures. Proceedings of the 2018 IEEE 27th International Symposium on Industrial Electronics (ISIE), Cairns, Australia.","DOI":"10.1109\/ISIE.2018.8433664"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1016\/S0925-2312(98)00034-4","article-title":"Theoretical aspects of the SOM algorithm","volume":"21","author":"Cottrell","year":"1998","journal-title":"Neurocomputing"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1441","DOI":"10.1016\/0893-6080(94)90091-4","article-title":"Growing cell structures\u2014A self-organizing network for unsupervised and supervised learning","volume":"7","author":"Fritzke","year":"1994","journal-title":"Neural Netw."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Gielen, S., and Kappen, B. (1993, January 13\u201316). Competitive Hebbian learning rule forms perfectly topology preserving maps. Proceedings of the ICANN \u201993, Amsterdam, The Netherlands.","DOI":"10.1007\/978-1-4471-2063-6"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"507","DOI":"10.1016\/0893-6080(94)90109-0","article-title":"Topology representing networks","volume":"7","author":"Martinetz","year":"1994","journal-title":"Neural Netw."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Ultsch, A., and Thrun, M.C. (2017, January 28\u201330). Credible visualizations for planar projections. Proceedings of the 2017 12th International Workshop on Self-Organizing Maps and Learning Vector Quantization, Clustering and Data Visualization (WSOM), Nancy, France.","DOI":"10.1109\/WSOM.2017.8020010"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Thrun, M. (2018). Projection-Based Clustering through Self-Organization and Swarm Intelligence, Springer Vieweg.","DOI":"10.1007\/978-3-658-20540-9"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.neucom.2019.12.125","article-title":"Landmark map: An extension of the self-organizing map for a user-intended nonlinear projection","volume":"388","author":"Onishi","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/j.neucom.2019.06.093","article-title":"ELM-SOM+: A continuous mapping for visualization","volume":"365","author":"Hu","year":"2019","journal-title":"Neurocomputing"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2512","DOI":"10.1177\/1077546316688991","article-title":"A novel gearbox fault feature extraction and classification using Hilbert empirical wavelet transform, singular value decomposition, and SOM neural network","volume":"24","author":"Boualem","year":"2018","journal-title":"J. Vib. Control"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1941","DOI":"10.1007\/s00477-016-1334-3","article-title":"SOM-DRASTIC: Using self-organizing map for evaluating groundwater potential to pollution","volume":"31","author":"Rezaei","year":"2017","journal-title":"Stoch. Environ. Res. Risk Assess."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1016\/j.measurement.2019.01.013","article-title":"Application of improved SOM network in gene data cluster analysis","volume":"145","author":"Feng","year":"2019","journal-title":"Measurement"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.eswa.2017.06.022","article-title":"A SOM prototype-based cluster analysis methodology","volume":"88","author":"Delgado","year":"2017","journal-title":"Expert Syst. Appl."},{"key":"ref_32","first-page":"150","article-title":"Mixed data clustering using dynamic growing hierarchical self-organizing map with improved LM learning","volume":"3","author":"Prasad","year":"2016","journal-title":"Int. Res. J. Eng. Technol."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Hung, W.L., Yang, J.H., Song, I.W., and Chang, Y.C. (2019). A modified self-updating clustering algorithm for application to dengue gene expression data. Commun. Stat. Simul. Comput.","DOI":"10.1080\/03610918.2018.1563149"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"31","DOI":"10.17977\/um018v2i12019p31-40","article-title":"High Dimensional Data Clustering using Self-Organized Map","volume":"2","author":"Febrita","year":"2019","journal-title":"Knowl. Eng. Data Sci."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/72.846731","article-title":"Clustering of the self-organizing map","volume":"11","author":"Vesanto","year":"2000","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1109\/TNN.2007.909556","article-title":"Automatic cluster detection in Kohonen\u2019s SOM","volume":"19","author":"Brugger","year":"2008","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1109\/TNN.2008.2005409","article-title":"Exploiting data topology in visualization and clustering of self-organizing maps","volume":"20","author":"Tasdemir","year":"2009","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1109\/TNN.2011.2107527","article-title":"Topology-based hierarchical clustering of self-organizing maps","volume":"22","author":"Tasdemir","year":"2011","journal-title":"IEEE Trans. Neural Netw."},{"key":"ref_39","unstructured":"Matsopoulos, G.K. (2010). Learning the number of clusters in self organizing map. Self-Organizing Map, Intech."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1023\/A:1026083612746","article-title":"Self-organizing-map based clustering using a local clustering validity index","volume":"17","author":"Wu","year":"2003","journal-title":"Neural Process. Lett."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/5326.661091","article-title":"Multiple-prototype classifier design","volume":"28","author":"Bezdek","year":"1998","journal-title":"IEEE Trans. Syst. Man Cybern. 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