{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,11]],"date-time":"2026-05-11T12:41:13Z","timestamp":1778503273056,"version":"3.51.4"},"reference-count":26,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T00:00:00Z","timestamp":1742169600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62371246"],"award-info":[{"award-number":["62371246"]}]},{"name":"National Natural Science Foundation of China","award":["62271266"],"award-info":[{"award-number":["62271266"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Self-Organizing Map (SOM) neural networks can project complex, high-dimensional data onto a two-dimensional plane for data visualization, enabling an intuitive understanding of the distribution and symmetric structures of such data, thereby facilitating the clustering and anomaly detection of complex high-dimensional data. However, this algorithm is sensitive to the initial weight matrix and suffers from insufficient feature extraction. To address these issues, this paper proposes an improved SOM based on virtual winning neurons (virtual-winner SOMs, vwSOMs). In this method, the principal component analysis (PCA) is utilized to generate the initial weight matrix, allowing the weights to better capture the main features of the data and thereby enhance clustering performance. Subsequently, when new input sample data are mapped to the output layer, multiple neurons with a high similarity in the weight matrix are selected to calculate a virtual winning neuron, which is then used to update the weight matrix to comprehensively represent the input data features within a minimal error range, thus improving the algorithm\u2019s robustness. Multiple datasets were used to analyze the clustering performance of vwSOM. On the Iris dataset, the S is 0.5262, the F1 value is 0.93, the ACC value is 0.9412, and the VA is 0.0012, and the experimental result with the Wine dataset shows that the S is 0.5255, the F1 value is 0.93, the ACC value is 0.9401, and the VA is 0.0014. Finally, to further demonstrate the performance of the algorithm, we use the more complex Waveform dataset; the S is 0.5101, the F1 value is 0.88, the ACC value is 0.8931, and the VA is 0.0033. All the experimental results show that the proposed algorithm can significantly improve clustering accuracy and have better stability, and its algorithm complexity can meet the requirements for real-time data processing.<\/jats:p>","DOI":"10.3390\/sym17030449","type":"journal-article","created":{"date-parts":[[2025,3,17]],"date-time":"2025-03-17T11:04:22Z","timestamp":1742209462000},"page":"449","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["An Improved Self-Organizing Map (SOM) Based on Virtual Winning Neurons"],"prefix":"10.3390","volume":"17","author":[{"given":"Xiaoliang","family":"Fan","sequence":"first","affiliation":[{"name":"SDIC Gansu Xiaosanxia Power Co., Ltd., Lanzhou 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaodong","family":"Zhang","sequence":"additional","affiliation":[{"name":"SDIC Gansu Xiaosanxia Power Co., Ltd., Lanzhou 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xuefeng","family":"Xue","sequence":"additional","affiliation":[{"name":"SDIC Gansu Xiaosanxia Power Co., Ltd., Lanzhou 730050, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Communications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuwen","family":"Fan","sequence":"additional","affiliation":[{"name":"School of Communications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hanliang","family":"Kou","sequence":"additional","affiliation":[{"name":"School of Communications and Information Engineering, Nanjing University of Posts and Telecommunications, Nanjing 210003, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,17]]},"reference":[{"key":"ref_1","unstructured":"Zhou, Z. (2016). Machine Learning, Tsinghua University Press."},{"key":"ref_2","first-page":"5","article-title":"A review and analysis of outlier detection algorithms","volume":"28","author":"Li","year":"2002","journal-title":"Comput. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2019\/2686378","article-title":"Recent Progress of Anomaly Detection","volume":"2019","author":"Xu","year":"2019","journal-title":"Complexity"},{"key":"ref_4","first-page":"3","article-title":"Machine Learning Techniques for Anomaly Detection: An Overview","volume":"79","author":"Omar","year":"2013","journal-title":"Int. J. Comput. Appl."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"78658","DOI":"10.1109\/ACCESS.2021.3083060","article-title":"Machine Learning for Anomaly Detection: A Systematic Review","volume":"9","author":"Nassif","year":"2021","journal-title":"IEEE Access"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1038\/nmeth.4551","article-title":"Machine learning: Supervised methods","volume":"15","author":"Bzdok","year":"2018","journal-title":"Nat. Methods"},{"key":"ref_7","unstructured":"Ester, M., Kriegel, H.P., Sander, J., and Xu, X. (1996, January 2\u20134). A density-based algorithm for discovering clusters in large spatial databases with noise. Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD\u201996), Portland, OR, USA."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1371\/journal.pone.0152173","article-title":"A comparative evaluation of unsupervised anomaly detection algorithms for multivariate data","volume":"11","author":"Goldstein","year":"2016","journal-title":"PLoS ONE"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Gadal, S., Mokhtar, R., Abdelhaq, M., Alsaqour, R., Ali, E.S., and Saeed, R. (2022). Machine Learning-Based Anomaly Detection Using K-Mean Array and Sequential Minimal Optimization. Electronics, 11.","DOI":"10.3390\/electronics11142158"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"116510","DOI":"10.1016\/j.eswa.2022.116510","article-title":"A K-Means clustering and SVM based hybrid concept drift detection technique for network anomaly detection","volume":"193","author":"Jain","year":"2022","journal-title":"Expert Syst. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"012025","DOI":"10.1088\/1742-6596\/2351\/1\/012025","article-title":"Improved DBSCAN-based Data Anomaly Detection Approach for Battery Energy Storage Stations","volume":"2351","author":"Dai","year":"2022","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Zhang, L., and Liu, L. (2022, January 27\u201329). Data anomaly detection based on isolation forest algorithm. Proceedings of the 2022 International Conference on Computation, Big-Data and Engineering (ICCBE), Yunlin, Taiwan.","DOI":"10.1109\/ICCBE56101.2022.9888169"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1464","DOI":"10.1109\/5.58325","article-title":"The Self-Organizing Map","volume":"78","author":"Kohonen","year":"1990","journal-title":"Proc. IEEE"},{"key":"ref_14","unstructured":"Kohonen, T. (April, January 28). Things you haven\u2019t heard about the Self-Organizing Map. Proceedings of the IEEE international Conference on Neural Networks, San Francisco, CA, USA."},{"key":"ref_15","unstructured":"Kohonen, T. (1997, January 12). Exploration of very large databases by Self-Organizing Maps. In Proceedings of International Conference on Neural Networks (icnn\u201997), Houston, TX, USA."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1016\/j.neunet.2012.09.018","article-title":"Essentials of the Self-Organizing Map","volume":"37","author":"Kohonen","year":"2013","journal-title":"Neural Netw."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Sandoval-Lara, Z., G\u00f3mez-Gil, P., Moreno-Rodr\u00edguez, J.C., and Ram\u00edrez-Cort\u00e9s, M. (2023, January 21\u201322). Self-Organizing Clustering by Growing-SOM for EEG-Based Biometrics. Proceedings of the 2023 International Conference on Artificial Intelligence and Applications (ICAIA) Alliance Technology Conference (ATCON-1), Bangalore, India.","DOI":"10.1109\/ICAIA57370.2023.10169253"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Cui, W., Xue, W., Li, L., and Shi, J. (2020, January 5\u20137). A Method for Intermittent Fault Diagnosis of Electronic Equipment Based on Labeled SOM. In Proceedings of the 2020 International Conference on Sensing, Diagnostics, Prognostics, and Control (SDPC), Beijing, China.","DOI":"10.1109\/SDPC49476.2020.9353111"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Zhang, X., Xu, J., and Zhang, H. (2023, January 20\u201322). Fault Diagnosis of Levitation Controller of Medium-Speed Maglev Train Based on SOM-BP Neural Network. Proceedings of the 2023 35th Chinese Control and Decision Conference (CCDC), Yichang, China.","DOI":"10.1109\/CCDC58219.2023.10326703"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/LGRS.2023.3330882","article-title":"Seismic Facies Visualization Analysis Method of SOM Corrected by Uniform Manifold Approximation and Projection","volume":"20","author":"Chen","year":"2023","journal-title":"IEEE Geosci. Remote. Sens. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1109\/TNNLS.2013.2248094","article-title":"PCA Feature Extraction for Change Detection in Multidimensional Unlabeled Data","volume":"25","author":"Kuncheva","year":"2014","journal-title":"IEEE Trans. Neural Networks Learn. Syst."},{"key":"ref_22","first-page":"2","article-title":"The Irises of the Gaspe Peninsula","volume":"59","author":"Anderson","year":"1935","journal-title":"Bull. Am. Iris Soc."},{"key":"ref_23","unstructured":"Aeberhard, S., Coomans, D., and de Vel, O. (1992). Comparison of Classifiers in High Dimensional Settings, Department of Mathematics and Statistics, James Cook University."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/BF00153759","article-title":"Instance-based learning algorithms","volume":"6","author":"Aha","year":"1991","journal-title":"Mach. Learn."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"104753","DOI":"10.1016\/j.micpro.2022.104753","article-title":"Discover botnets in IoT sensor networks: A lightweight deep learning framework with hybrid Self-Organizing Maps","volume":"97","author":"Khan","year":"2023","journal-title":"Microprocess. Microsystems"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Manikant, M.N. (2024, January 6\u20137). Improved Classification of Cyber-Bullying Tweets in Social Media Using SVM-MaxEnt Based Dynamic Programming Based Self Organizing Maps. Proceedings of the 2024 13th International Conference on System Modeling & Advancement\n          in Research Trends (SMART), Moradabad, India.","DOI":"10.1109\/SMART63812.2024.10882541"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/449\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T16:55:08Z","timestamp":1760028908000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/17\/3\/449"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,17]]},"references-count":26,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,3]]}},"alternative-id":["sym17030449"],"URL":"https:\/\/doi.org\/10.3390\/sym17030449","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,17]]}}}