{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:29:32Z","timestamp":1760146172236,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T00:00:00Z","timestamp":1728604800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union","award":["871072"],"award-info":[{"award-number":["871072"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Currently, the tasks of intelligent data analysis in medicine are becoming increasingly common. Existing artificial intelligence tools provide high effectiveness in solving these tasks when analyzing sufficiently large datasets. However, when there is very little training data available, current machine learning methods do not ensure adequate classification accuracy or may even produce inadequate results. This paper presents an enhanced input-doubling method for classification tasks in the case of limited data analysis, achieved via expanding the number of independent attributes in the augmented dataset with probabilities of belonging to each class of the task. The authors have developed an algorithmic implementation of the improved method using two Na\u00efve Bayes classifiers. The method was modeled on a small dataset for cardiovascular risk assessment. The authors explored two options for the combined use of Na\u00efve Bayes classifiers at both stages of the method. It was found that using different methods at both stages potentially enhances the accuracy of the classification task. The results of the improved method were compared with a range of existing methods used for solving the task. It was demonstrated that the improved input-doubling method achieved the highest classification accuracy based on various performance indicators.<\/jats:p>","DOI":"10.3390\/computation12100203","type":"journal-article","created":{"date-parts":[[2024,10,11]],"date-time":"2024-10-11T03:53:47Z","timestamp":1728618827000},"page":"203","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Enhanced Input-Doubling Method Leveraging Response Surface Linearization to Improve Classification Accuracy in Small Medical Data Processing"],"prefix":"10.3390","volume":"12","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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0008-2039-3055","authenticated-orcid":false,"given":"Pavlo","family":"Yendyk","sequence":"additional","affiliation":[{"name":"Department of Artificial Intelligence, Lviv Polytechnic National University, 79013 Lviv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Iryna","family":"Pliss","sequence":"additional","affiliation":[{"name":"Control Systems Research Laboratory, Kharkiv National University of Radio Electronics, Nauky Ave. 14, 61166 Kharkiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yevgeniy","family":"Bodyanskiy","sequence":"additional","affiliation":[{"name":"Control Systems Research Laboratory, Kharkiv National University of Radio Electronics, Nauky Ave. 14, 61166 Kharkiv, Ukraine"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8156-8962","authenticated-orcid":false,"given":"Michal","family":"Gregus","sequence":"additional","affiliation":[{"name":"Faculty of Management, Comenius University Bratislava, Odboj\u00e1rov 10, 820 05 Bratislava, Slovakia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,10,11]]},"reference":[{"key":"ref_1","unstructured":"(2024, September 18). Overview of Lifestyle Medicine\u2014StatPearls\u2014NCBI Bookshelf, Available online: https:\/\/www.ncbi.nlm.nih.gov\/books\/NBK589672\/."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Rubi\u015b, P.P. (2022). Cardiac Disease: Diagnosis, Treatment, and Outcomes. JPM, 12.","DOI":"10.3390\/jpm12081212"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Subramani, S., Varshney, N., Anand, M.V., Soudagar, M.E.M., Al-keridis, L.A., Upadhyay, T.K., Alshammari, N., Saeed, M., Subramanian, K., and Anbarasu, K. (2023). Cardiovascular Diseases Prediction by Machine Learning Incorporation with Deep Learning. Front. Med., 10.","DOI":"10.3389\/fmed.2023.1150933"},{"key":"ref_4","first-page":"47","article-title":"ECG Arrhythmia Classification and Interpretation Using Convolutional Networks for Intelligent IoT Healthcare System","volume":"3736","author":"Kovalchuk","year":"2024","journal-title":"CEUR Workshop Proc."},{"key":"ref_5","first-page":"1","article-title":"Robust R-Peak Detection Using Deep Learning Based on Integrating Domain Knowledge","volume":"3609","author":"Kovalchuk","year":"2023","journal-title":"CEUR Workshop Proc."},{"key":"ref_6","first-page":"77","article-title":"Myocardium Segmentation Using Two-Step Deep Learning with Smoothed Masks by Gaussian Blur","volume":"3609","author":"Slobodzian","year":"2023","journal-title":"CEUR Workshop Proc."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ferrara, E. (2023). Fairness and Bias in Artificial Intelligence: A Brief Survey of Sources, Impacts, and Mitigation Strategies. Sci, 6.","DOI":"10.2196\/preprints.48399"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tolstyak, Y., Zhuk, R., Yakovlev, I., Shakhovska, N., Gregus Ml, M., Chopyak, V., and Melnykova, N. (2021). The Ensembles of Machine Learning Methods for Survival Predicting after Kidney Transplantation. Appl. Sci., 11.","DOI":"10.3390\/app112110380"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Hekler, E.B., Klasnja, P., Chevance, G., Golaszewski, N.M., Lewis, D., and Sim, I. (2019). Why We Need a Small Data Paradigm. BMC Med, 17.","DOI":"10.1186\/s12916-019-1366-x"},{"key":"ref_10","first-page":"35","article-title":"Modeling of Small Data with Unsupervised Generative Ensemble Learning","volume":"3302","author":"Dolgikh","year":"2022","journal-title":"CEUR-WS.org"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zhang, Y., Deng, L., and Wei, B. (2024). Imbalanced Data Classification Based on Improved Random-SMOTE and Feature Standard Deviation. Mathematics, 12.","DOI":"10.3390\/math12111709"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"827","DOI":"10.3390\/make6020039","article-title":"Impact of Nature of Medical Data on Machine and Deep Learning for Imbalanced Datasets: Clinical Validity of SMOTE Is Questionable","volume":"6","author":"Gholampour","year":"2024","journal-title":"MAKE"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Althnian, A., AlSaeed, D., Al-Baity, H., Samha, A., Dris, A.B., Alzakari, N., Abou Elwafa, A., and Kurdi, H. (2021). Impact of Dataset Size on Classification Performance: An Empirical Evaluation in the Medical Domain. Appl. Sci., 11.","DOI":"10.3390\/app11020796"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1556\/1647.2023.00109","article-title":"A Machine Learning Framework for Performing Binary Classification on Tabular Biomedical Data","volume":"15","author":"Lakatos","year":"2023","journal-title":"Imaging"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Kumar, V., Lalotra, G.S., Sasikala, P., Rajput, D.S., Kaluri, R., Lakshmanna, K., Shorfuzzaman, M., Alsufyani, A., and Uddin, M. (2022). Addressing Binary Classification over Class Imbalanced Clinical Datasets Using Computationally Intelligent Techniques. Healthcare, 10.","DOI":"10.3390\/healthcare10071293"},{"key":"ref_16","unstructured":"Izonin, I., Tkachenko, R., Pidkostelnyi, R., Pavliuk, O., Khavalko, V., and Batyuk, A. (2021, January 19\u201321). Experimental Evaluation of the Effectiveness of ANN-Based Numerical Data Augmentation Methods for Diagnostics Tasks. Proceedings of the 4th International Conference on Informatics&Data-Driven Medicine, Valencia, Spain."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/j.procs.2024.08.024","article-title":"An Adaptation of the Input Doubling Method for Solving Classification Tasks in Case of Small Data Processing","volume":"241","author":"Izonin","year":"2024","journal-title":"Procedia Comput. Sci."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Izonin, I., and Tkachenko, R. (2022). Universal Intraensemble Method Using Nonlinear AI Techniques for Regression Modeling of Small Medical Data Sets. Cognitive and Soft Computing Techniques for the Analysis of Healthcare Data, Elsevier.","DOI":"10.1016\/B978-0-323-85751-2.00002-5"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1007\/978-3-030-80475-6_3","article-title":"RBF-Based Input Doubling Method for Small Medical Data Processing","volume":"Volume 82","author":"Hu","year":"2021","journal-title":"Advances in Artificial Systems for Logistics Engineering"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Shahadat, N., and Pal, B. (2015, January 26\u201327). An Empirical Analysis of Attribute Skewness over Class Imbalance on Probabilistic Neural Network and Na\u00efve Bayes Classifier. Proceedings of the 2015 International Conference on Computer and Information Engineering (ICCIE), Rajshahi, Bangladesh.","DOI":"10.1109\/CCIE.2015.7399301"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Zub, K., Zhezhnych, P., and Strauss, C. (2023). Two-Stage PNN\u2013SVM Ensemble for Higher Education Admission Prediction. BDCC, 7.","DOI":"10.3390\/bdcc7020083"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Changpetch, P., Pitpeng, A., Hiriote, S., and Yuangyai, C. (2021). Integrating Data Mining Techniques for Na\u00efve Bayes Classification: Applications to Medical Datasets. Computation, 9.","DOI":"10.3390\/computation9090099"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Sugahara, S., and Ueno, M. (2021). Exact Learning Augmented Naive Bayes Classifier. Entropy, 23.","DOI":"10.3390\/e23121703"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kaushik, K., Bhardwaj, A., Dahiya, S., Maashi, M.S., Al Moteri, M., Aljebreen, M., and Bharany, S. (2022). Multinomial Naive Bayesian Classifier Framework for Systematic Analysis of Smart IoT Devices. Sensors, 22.","DOI":"10.3390\/s22197318"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Alenazi, F.S., El Hindi, K., and AsSadhan, B. (2023). Complement-Class Harmonized Na\u00efve Bayes Classifier. Appl. Sci., 13.","DOI":"10.3390\/app13084852"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ou, G., He, Y., Fournier-Viger, P., and Huang, J.Z. (2022). A Novel Mixed-Attribute Fusion-Based Naive Bayesian Classifier. Appl. Sci., 12.","DOI":"10.3390\/app122010443"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Yang, Z., Ren, J., Zhang, Z., Sun, Y., Zhang, C., Wang, M., and Wang, L. (2023). A New Three-Way Incremental Naive Bayes Classifier. Electronics, 12.","DOI":"10.3390\/electronics12071730"},{"key":"ref_28","unstructured":"(2024, September 07). Heart Attack Analysis & Prediction Dataset (A Dataset for Heart Attack Classification). Available online: https:\/\/www.kaggle.com\/datasets\/rashikrahmanpritom\/heart-attack-analysis-prediction-dataset."},{"key":"ref_29","unstructured":"(2023, August 21). Sklearn.Preprocessing.MaxAbsScaler. Available online: https:\/\/scikit-learn.org\/stable\/modules\/generated\/sklearn.preprocessing.MaxAbsScaler.html."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Manna, S. (2022, January 24). Small Sample Estimation of Classification Metrics. Proceedings of the 2022 Interdisciplinary Research in Technology and Management (IRTM), Kolkata, India.","DOI":"10.1109\/IRTM54583.2022.9791645"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Orozco-Arias, S., Pi\u00f1a, J.S., Tabares-Soto, R., Castillo-Ossa, L.F., Guyot, R., and Isaza, G. (2020). Measuring Performance Metrics of Machine Learning Algorithms for Detecting and Classifying Transposable Elements. Processes, 8.","DOI":"10.3390\/pr8060638"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Kozak, J., Probierz, B., Kania, K., and Juszczuk, P. (2022). Preference-Driven Classification Measure. Entropy, 24.","DOI":"10.3390\/e24040531"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Kenyeres, \u00c9., Kummer, A., and Abonyi, J. (2024). Machine Learning Classifier-Based Metrics Can Evaluate the Efficiency of Separation Systems. Entropy, 26.","DOI":"10.3390\/e26070571"},{"key":"ref_34","unstructured":"(2024, September 07). Heart Attack\u2014From EDA to Prediction (Notebook). Available online: https:\/\/kaggle.com\/code\/dreygaen\/heart-attack-from-eda-to-prediction."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"7","DOI":"10.3103\/S1060992X20010051","article-title":"Radial-Basis Function Neural Network Synthesis on the Basis of Decision Tree","volume":"29","author":"Subbotin","year":"2020","journal-title":"Opt. Mem. Neural Netw."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Chumachenko, D., Butkevych, M., Lode, D., Frohme, M., Schmailzl, K.J.G., and Nechyporenko, A. (2022). Machine Learning Methods in Predicting Patients with Suspected Myocardial Infarction Based on Short-Time HRV Data. Sensors, 22.","DOI":"10.3390\/s22187033"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1007\/978-3-030-33585-4_28","article-title":"Data Classification Based on the Features Reduction and Piecewise Linear Separation","volume":"Volume 1072","author":"Vasant","year":"2020","journal-title":"Intelligent Computing and Optimization"}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/10\/203\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:10:59Z","timestamp":1760112659000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/10\/203"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,11]]},"references-count":37,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2024,10]]}},"alternative-id":["computation12100203"],"URL":"https:\/\/doi.org\/10.3390\/computation12100203","relation":{},"ISSN":["2079-3197"],"issn-type":[{"type":"electronic","value":"2079-3197"}],"subject":[],"published":{"date-parts":[[2024,10,11]]}}}