{"id":4919,"date":"2025-11-16T14:06:55","date_gmt":"2025-11-16T14:06:55","guid":{"rendered":"https:\/\/izvestiyakbncran.ru\/?page_id=4919"},"modified":"2026-06-02T13:50:20","modified_gmt":"2026-06-02T12:50:20","slug":"27-5-3-en","status":"publish","type":"page","link":"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-5-3-en\/","title":{"rendered":"27.5.3 En"},"content":{"rendered":"\n

Sigma-pi neural network model for data clustering<\/strong><\/h1>\n\n\n\n

R.A. Zhilov<\/strong><\/p>\n\n\n\n

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Abstract<\/strong><\/strong>: <\/em>Mudflows are some of the most destructive geological phenomena, and their prediction is challenging due to their complexity and the strong nonlinear relationships between the various factors that contribute to their formation. Traditional modeling methods have limitations in their ability to interpret and account for the complex interactions between different factors, and this lead to the need for the development of more advanced approaches.
Aim.<\/strong> The study aims to develop and test a sigma-pi neural network architecture for mudflow clustering based on morphometric and genetic characteristics as well as to identify the key factors and their combinations that contribute to the formation of different mudflow types.
Materials and methods<\/strong>. Cadastral data on mudflows in the southern European part of Russia is used as the initial data. A sigma-pi neural network capable of accounting for both linear features and their second-order interactions is employed for analysis. A silhouette coefficient is used to determine the number of clusters. The results are compared with those obtained using Kohonen’s self-organizing maps (SOM).
Results<\/strong>. The model identified three stable clusters corresponding to mud, rock, and mud-rock types of mudflows. Analysis of the significance of features has revealed that the basin area, channel slope, and maximum sediment volume make the greatest contributions to cluster formation, as well as their various pairwise combinations. Comparison with the SOM (self-organizing map) confirmed the improved interpretability of the proposed model and its ability to identify hidden, nonlinear relationships.
Conclusions<\/strong>. The use of sigma-pi neural networks not only improves the accuracy of mudflow clustering, but also ensures the interpretability of the results by analyzing the ignificance of features and their combinations. This approach is promising for engineering geology and can be used in geoecological monitoring systems and forecasting of hazardous processes.<\/p>\n\n\n\n

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Keywords<\/strong><\/em><\/strong>:<\/em> mudflows, clustering, sigma-pi neural network, machine learning, interpretability, nonlinear dependencies, engineering geology, geo-environmental monitoring<\/p>\n\n\n\n

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For citation<\/strong>.<\/strong> Zhilov R.A. Sigma-pi neural network model for data clustering. News of the Kabardino-Balkarian Scientific Center of RAS<\/em>. 2025. Vol. 27. No. 5. Pp. 34\u201342. DOI: 10.35330\/1991-6639-2025-27-5-34-42<\/p>\n\n\n\n

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R<\/strong>eferences<\/summary>\n
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  1. Tatarenko N.V., Shagin S.I., Mashukov Kh.V. Geographical features of the distribution of mudflow phenomena in the Kabardino-Balkarian Republic. Scientific News. 2019. No. 17. Pp. 26\u201330. EDN: ZJPAGU. (In Russian)<\/li>\n\n\n\n
  2. Zhilov R.A. Construction of a Kohonen self-organizing map (SOM) for predicting types of mudflows. News of the Kabardino-Balkarian Scientific Center of the RAS.<\/em> 2024. No. 5.
    Pp. 129\u2013137. DOI: 10.35330\/1991-6639-2024-26-5-129-137. (In Russian)<\/li>\n\n\n\n
  3. Lyutikova L.A. Analysis of mudflow characteristics with limited data using machine learning models. Modeling, Optimization and Information Technology. 2024. Vol. 12. No. 4. ID: 36. DOI: 10.26102\/2310-6018\/2024.47.4.029. (In Russian)<\/li>\n\n\n\n
  4. Sleiman A., Kozlov D.V. Using artificial neural networks to assess surface runoff in water management balance calculations of the upper Orontes River Basin. Water Sector of Russia: problems, Technologies, Management. 2024. No. 3. Pp. 92\u2013107. DOI: 10.35567\/19994508-2024-3-21-37. (In Russian)<\/li>\n\n\n\n
  5. Bodianskii E.V., Kulishova N.E. Multidimensional artificial neural sigma-pi network and its training algorithm. Radioelectronics and Informatics. 2005. No. 4. Pp. 122\u2013125. (In Russian)<\/li>\n\n\n\n
  6. Jiao J., Su K. A new Sigma-Pi-Sigma neural network based on L1 and L2 regularization and applications. AIMS Mathematics. 2024. Vol. 9. No. 3. Pp. 5995\u20136012. DOI:
    10.3934\/math.2024293<\/li>\n\n\n\n
  7. Deng F., Liang S., Qian K. et al. A recurrent sigma pi sigma neural network. PMC \/ NCBI, DOI: 10.1038\/s41598-024-84299-y<\/li>\n\n\n\n
  8. Zhilov R.A. Intelligent methods for data clustering. News of the Kabardino-Balkarian Scientific Center of the RAS<\/em>. 2023. No. 6(116). Pp. 152\u2013159. DOI: 10.35330\/1991-6639-2023-6-116-152-159. (In Russian)<\/li>\n<\/ol>\n<\/details>\n\n\n\n
    Information about the author<\/strong><\/summary>\n
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    Ruslan A. Zhilov<\/strong>, Junior Researcher, Neuroinformatics and Machine Learning Department, Institute of Applied Mathematics and Automation \u2013 branch of Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences;
    89 A Shortanov street, Nalchik, 360000, Russia;
    zhilov91@gmail.com, ORCID: https:\/\/orcid.org\/0000-0002-3552-4854, SPIN-code: 9389-6188<\/p>\n\n\n\n

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    Sigma-pi neural network model for data clustering R.A. Zhilov Abstract: Mudflows are some of the most destructive geological phenomena, and their prediction is challenging due to their complexity and the strong nonlinear relationships between the various factors that contribute to their formation. Traditional modeling methods have limitations in their ability to interpret and account for […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"wp-custom-template-home","meta":{"footnotes":""},"class_list":["post-4919","page","type-page","status-publish","hentry"],"yoast_head":"\n27.5.3 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/izvestiyakbncran.ru\/index.php\/en\/27-5-3-en\/\" \/>\n<meta property=\"og:locale\" content=\"ru_RU\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"27.5.3 En - \u0418\u0417\u0412\u0415\u0421\u0422\u0418\u042f \u041a\u0410\u0411\u0410\u0420\u0414\u0418\u041d\u041e-\u0411\u0410\u041b\u041a\u0410\u0420\u0421\u041a\u041e\u0413\u041e \u041d\u0410\u0423\u0427\u041d\u041e\u0413\u041e \u0426\u0415\u041d\u0422\u0420\u0410 \u0420\u0410\u041d\u00bb\" \/>\n<meta property=\"og:description\" content=\"Sigma-pi neural network model for data clustering R.A. 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