{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T20:42:30Z","timestamp":1764103350901,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T00:00:00Z","timestamp":1668988800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Research Foundation of Ukraine","award":["2021.01\/0103"],"award-info":[{"award-number":["2021.01\/0103"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MAKE"],"abstract":"<jats:p>The modern development of the biomedical engineering area is accompanied by the availability of large volumes of data with a non-linear response surface. The effective analysis of such data requires the development of new, more productive machine learning methods. This paper proposes a cascade ensemble that combines the advantages of using a high-order Wiener polynomial and Stochastic Gradient Descent algorithm while eliminating their disadvantages to ensure a high accuracy of the approximation of such data with a satisfactory training time. The work presents flow charts of the learning algorithms and the application of the developed ensemble scheme, and all the steps are described in detail. The simulation was carried out based on a real-world dataset. Procedures for the proposed model tuning have been performed. The high accuracy of the approximation based on the developed ensemble scheme was established experimentally. The possibility of an implicit approximation by high orders of the Wiener polynomial with a slight increase in the number of its members is shown. It ensures a low training time for the proposed method during the analysis of large datasets, which provides the possibility of its practical use in the biomedical engineering area.<\/jats:p>","DOI":"10.3390\/make4040055","type":"journal-article","created":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T05:18:57Z","timestamp":1669094337000},"page":"1088-1106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["SGD-Based Cascade Scheme for Higher Degrees Wiener Polynomial Approximation of Large Biomedical Datasets"],"prefix":"10.3390","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9761-0096","authenticated-orcid":false,"given":"Ivan","family":"Izonin","sequence":"first","affiliation":[{"name":"Department of Artificial Intelligence, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9802-6799","authenticated-orcid":false,"given":"Roman","family":"Tkachenko","sequence":"additional","affiliation":[{"name":"Department of Publishing Information Technologies, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"given":"Rostyslav","family":"Holoven","sequence":"additional","affiliation":[{"name":"Department of System Design, Ivan Franko National University of Lviv, 79005 Lviv, Ukraine"}]},{"given":"Kyrylo","family":"Yemets","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"given":"Myroslav","family":"Havryliuk","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3308-4445","authenticated-orcid":false,"given":"Shishir Kumar","family":"Shandilya","sequence":"additional","affiliation":[{"name":"School of Computing Science and Engineering, VIT Bhopal University, Bhopal 466114, India"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Garza-Ulloa, J. (2022). Applied Biomedical Engineering Using Artificial Intelligence and Cognitive Models, Academic Press.","DOI":"10.1016\/B978-0-12-820718-5.00009-X"},{"key":"ref_2","unstructured":"Tsmots, I., and Skorokhoda, O. (2010, January 20\u201323). Methods and VLSI-Structures for Neural Element Implementation. Proceedings of the 2010 VIth International Conference on Perspective Technologies and Methods in MEMS Design, Lviv, Ukraine."},{"key":"ref_3","first-page":"1","article-title":"Development and Implementation of the Technical Accident Prevention Subsystem for the Smart Home System","volume":"10","author":"Teslyuk","year":"2018","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Radutniy, R., Nechyporenko, A., Alekseeva, V., Titova, G., Bibik, D., and Gargin, V.V. (2020, January 21\u201325). Automated Measurement of Bone Thickness on SCT Sections and Other Images. Proceedings of the 2020 IEEE Third International Conference on Data Stream Mining & Processing (DSMP), Lviv, Ukraine.","DOI":"10.1109\/DSMP47368.2020.9204289"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"130","DOI":"10.2174\/18750362021140100130","article-title":"Complex Automatic Determination of Morphological Parameters for Bone Tissue in Human Paranasal Sinuses","volume":"14","author":"Nechyporenko","year":"2021","journal-title":"Open Bioinform. J."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Babichev, S., and \u0160kvor, J. (2020). Technique of Gene Expression Profiles Extraction Based on the Complex Use of Clustering and Classification Methods. Diagnostics, 10.","DOI":"10.20944\/preprints202008.0241.v1"},{"key":"ref_7","unstructured":"Mochurad, L., and Yatskiv, M. (2020, January 19\u201321). Simulation of a Human Operator\u2019s Response to Stressors under Production Conditions. Proceedings of the 3rd International Conference on Informatics and Data-Driven Medicine, V\u00e4xj\u00f6, Sweden. CEUR-WS 2753."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chumachenko, D., Chumachenko, T., Meniailov, I., Pyrohov, P., Kuzin, I., and Rodyna, R. (2020, January 21\u201325). On-Line Data Processing, Simulation and Forecasting of the Coronavirus Disease (COVID-19) Propagation in Ukraine Based on Machine Learning Approach. Proceedings of the Data Stream Mining and Processing, Lviv, Ukraine.","DOI":"10.1007\/978-3-030-61656-4_25"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"921","DOI":"10.1111\/coin.12289","article-title":"Using Visual Analytics to Develop Human and Machine-centric Models: A Review of Approaches and Proposed Information Technology","volume":"38","author":"Krak","year":"2020","journal-title":"Comput. Intell."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bisikalo, O., Chernenko, D., Danylchuk, O., Kovtun, V., and Romanenko, V. (2020, January 6\u20139). Information Technology for TTF Optimization of an Information System for Critical Use That Operates in Aggressive Cyber-Physical Space. Proceedings of the 2020 IEEE International Conference on Problems of Infocommunications. Science and Technology (PIC S&T), Kharkiv, Ukraine.","DOI":"10.1109\/PICST51311.2020.9467997"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bisikalo, O.V., Kovtun, V.V., Kovtun, O.V., and Romanenko, V.B. (2020, January 14\u201318). Research of Safety and Survivability Models of the Information System for Critical Use. Proceedings of the 2020 IEEE 11th International Conference on Dependable Systems, Services and Technologies (DESSERT), Kyiv, Ukraine.","DOI":"10.1109\/DESSERT50317.2020.9125061"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s13534-018-0058-3","article-title":"Machine Learning in Biomedical Engineering","volume":"8","author":"Park","year":"2018","journal-title":"Biomed. Eng. Lett."},{"key":"ref_13","first-page":"11","article-title":"A Novel Hybrid Approach for Detection of Type-2 Diabetes in Women Using Lasso Regression and Artificial Neural Network","volume":"14","author":"Singh","year":"2022","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_14","first-page":"1","article-title":"Investigation of the Effect of Normalization Methods on ANFIS Success: Forestfire and Diabets Datasets","volume":"14","author":"Polatgil","year":"2022","journal-title":"Int. J. Inf. Technol. Comput. Sci."},{"key":"ref_15","first-page":"1","article-title":"Risk Forecasting of Data Confidentiality Breach Using Linear Regression Algorithm","volume":"14","author":"Korystin","year":"2022","journal-title":"Int. J. Comput. Netw. Inf. Secur."},{"key":"ref_16","unstructured":"Tepla, T. (2019). Biocompatible Materials Selection via New Supervised Learning Methods, LAP LAMBERT Academic Publishing."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"13","DOI":"10.5815\/ijmecs.2021.03.02","article-title":"Artificial Neural Network Training Criterion Formulation Using Error Continuous Domain","volume":"13","author":"Hu","year":"2021","journal-title":"Int. J. Mod. Educ. Comput. Sci."},{"key":"ref_18","first-page":"29","article-title":"A Multidimensional Extended Neo-Fuzzy Neuron for Facial Expression Recognition","volume":"9","author":"Hu","year":"2017","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_19","first-page":"57","article-title":"Determination of Structural Parameters of Multilayer Perceptron Designed to Estimate Parameters of Technical Systems","volume":"9","author":"Hu","year":"2017","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"209","DOI":"10.37394\/23207.2021.18.22","article-title":"Classical Machine Learning Methods in Economics Research: Macro and Micro Level Examples","volume":"18","author":"Babenko","year":"2021","journal-title":"WSEAS Trans. Bus. Econ."},{"key":"ref_21","first-page":"40","article-title":"The Combined Use of the Wiener Polynomial and SVM for Material Classification Task in Medical Implants Production","volume":"10","author":"Izonin","year":"2018","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_22","first-page":"81","article-title":"Ensem_SLDR: Classification of Cybercrime Using Ensemble Learning Technique","volume":"14","author":"Pandey","year":"2021","journal-title":"Int. J. Comput. Netw. Inf. Secur."},{"key":"ref_23","first-page":"18","article-title":"TreeLoc: An Ensemble Learning-Based Approach for Range Based Indoor Localization","volume":"11","author":"Maduranga","year":"2021","journal-title":"Int. J. Wirel. Microw. Technol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.5815\/ijmecs.2020.01.01","article-title":"Hybrid Ensemble Learning Technique for Software Defect Prediction","volume":"12","author":"Khan","year":"2020","journal-title":"IJMECS"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Kotsovsky, V., Geche, F., and Batyuk, A. (2019, January 21\u201325). On the Computational Complexity of Learning Bithreshold Neural Units and Networks. Proceedings of the Lecture Notes in Computational Intelligence and Decision Making, Salisnyj Port, Ukraine.","DOI":"10.1007\/978-3-030-26474-1_14"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Garza-Ulloa, J. (2022). Machine Learning Models Applied to Biomedical Engineering. Applied Biomedical Engineering Using Artificial Intelligence and Cognitive Models, Elsevier.","DOI":"10.1016\/B978-0-12-820718-5.00002-7"},{"key":"ref_27","first-page":"1","article-title":"Construction of High-Accuracy Ensemble of Classifiers","volume":"6","author":"Sajedi","year":"2014","journal-title":"Int. J. Inf. Technol. Comput. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wu, J., Chen, S., Zhou, W., Wang, N., and Fan, Z. (2020, January 15). Evaluation of Feature Selection Methods Using Bagging and Boosting Ensemble Techniques on High Throughput Biological Data. Proceedings of the 2020 10th International Conference on Biomedical Engineering and Technology, Tokyo, Japan.","DOI":"10.1145\/3397391.3397403"},{"key":"ref_29","first-page":"51","article-title":"Boosting Afaan Oromo Named Entity Recognition with Multiple Methods","volume":"13","year":"2021","journal-title":"Int. J. Inf. Eng. Electron. Bus."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1016\/j.bbe.2021.04.015","article-title":"Extreme Gradient Boosting Machine Learning Method for Predicting Medical Treatment in Patients with Acute Bronchiolitis","volume":"41","author":"Mateo","year":"2021","journal-title":"Biocybern. Biomed. Eng."},{"key":"ref_31","first-page":"39","article-title":"Combining Different Approaches to Improve Arabic Text Documents Classification","volume":"9","author":"Abuhaiba","year":"2017","journal-title":"Int. J. Intell. Syst. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Rahman, T., Chowdhury, M., Khandakar, A., Mahbub, Z.B., Hossain, M.S.A., Alhatou, A., Abdalla, E., Muthiyal, S., Islam, K.F., and Kashem, S.B.A. (2022). BIO-CXRNET: A Robust Multimodal Stacking Machine Learning Technique for Mortality Risk Prediction of COVID-19 Patients Using Chest X-Ray Images and Clinical Data. arXiv.","DOI":"10.1007\/s00521-023-08606-w"},{"key":"ref_33","unstructured":"Rojas, I., Joya, G., and Catala, A. (2019, January 12\u201314). SGD-Based Wiener Polynomial Approximation for Missing Data Recovery in Air Pollution Monitoring Dataset. Proceedings of the Advances in Computational Intelligence, Gran Canaria, Spain."},{"key":"ref_34","unstructured":"(2022, October 11). Group Method of Data Handling (GMDH) for Deep Learning, Data Mining Algorithms Optimization, Fuzzy Models Analysis, Forecasting Neural Networks and Modeling Software Systems. Available online: http:\/\/www.gmdh.net\/."},{"key":"ref_35","first-page":"513","article-title":"Hybrid Methods of GMDH-Neural Networks Synthesis and Training for Solving Problems of Time Series Forecasting","volume":"Volume 1020","author":"Lytvynenko","year":"2020","journal-title":"Lecture Notes in Computational Intelligence and Decision Making"},{"key":"ref_36","first-page":"90","article-title":"The Problem Solution of the Surface-to-Air Missile Systems Electronic Equipment Durability Prediction When Implementing the Strategy of Condition-Based Maintenance and Repair Using the Group Method of Data Handling","volume":"11","author":"Kobzev","year":"2021","journal-title":"Sci. Pap. Social Dev. Secur."},{"key":"ref_37","unstructured":"Ivakhnenko, A.G., Ivakhnenko, G.A., Savchenko, E., and Wunsch, D. (2002). Problems of Further Development of GMDH Algorithms: Part 2. Mathematical Theory of Pattern Recognition, MAIK \u201cNauka \/Interperiodica\u201d."},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Salamh, M., and Wang, L. (2021). Second-Order Least Squares Method for Dynamic Panel Data Models with Application. J. Risk Financ. Manag., 14.","DOI":"10.3390\/jrfm14090410"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Lake, R.W., Shaeri, S., and Senevirathna, S. (2022). Limitations of Parametric Group Method of Data Handling and Empirical Improvements for the Application of Rainfall Modelling, Research Square.","DOI":"10.21203\/rs.3.rs-1495426\/v1"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Gatto, M., and Marcuzzi, F. (2020). Unbiased Least-Squares Modelling. Mathematics, 8.","DOI":"10.3390\/math8060982"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"1286","DOI":"10.1002\/bbb.2140","article-title":"Application of Linear Regression Algorithm and Stochastic Gradient Descent in a Machine-Learning Environment for Predicting Biomass Higher Heating Value","volume":"14","author":"Ighalo","year":"2020","journal-title":"Biofuels Bioprod. Biorefin."},{"key":"ref_42","first-page":"17","article-title":"GDO Artificial Intelligence-Based Switching PID Baseline Feedback Linearization Method: Controlled PUMA Workspace","volume":"4","author":"Piltan","year":"2012","journal-title":"Int. J. Inf. Eng. Electron. Bus."},{"key":"ref_43","first-page":"19","article-title":"Statistical Techniques for Detecting Cyberattacks on Computer Networks Based on an Analysis of Abnormal Traffic Behavior","volume":"12","author":"Hu","year":"2021","journal-title":"Int. J. Comput. Netw. Inf. Secur."},{"key":"ref_44","unstructured":"(2022, June 19). Heart Rate Prediction to Monitor Stress Level. Available online: https:\/\/www.kaggle.com\/vinayakshanawad\/heart-rate-prediction-to-monitor-stress-level."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1016\/j.procs.2021.12.313","article-title":"An Approach towards the Response Surface Linearization via ANN-Based Cascade Scheme for Regression Modeling in Healthcare","volume":"198","author":"Izonin","year":"2022","journal-title":"Procedia Comput. Sci."},{"key":"ref_46","first-page":"200121","article-title":"Predictive Analysis of Cardiovascular Disease Using Gradient Boosting Based Learning and Recursive Feature Elimination Technique","volume":"16","author":"Theerthagiri","year":"2022","journal-title":"Intell. Syst. Appl."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"68","DOI":"10.5815\/ijmecs.2021.04.06","article-title":"An Optimized Machine Learning Approach for Predicting Parkinson\u2019s Disease","volume":"13","author":"Kundu","year":"2021","journal-title":"Int. J. Mod. Educ. Comput. Sci."}],"container-title":["Machine Learning and Knowledge Extraction"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2504-4990\/4\/4\/55\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:22:54Z","timestamp":1760145774000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2504-4990\/4\/4\/55"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,21]]},"references-count":47,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,12]]}},"alternative-id":["make4040055"],"URL":"https:\/\/doi.org\/10.3390\/make4040055","relation":{},"ISSN":["2504-4990"],"issn-type":[{"type":"electronic","value":"2504-4990"}],"subject":[],"published":{"date-parts":[[2022,11,21]]}}}