{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T09:57:09Z","timestamp":1773482229030,"version":"3.50.1"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T00:00:00Z","timestamp":1765238400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T00:00:00Z","timestamp":1765238400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Int J Data Sci Anal"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1007\/s41060-025-00982-x","type":"journal-article","created":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T06:34:13Z","timestamp":1765262053000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A continuous, bounded and uniformly converging hypertan-normalization approach for improved classification accuracy and feature entropy"],"prefix":"10.1007","volume":"21","author":[{"given":"Mannat","family":"Mand","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Birmohan","family":"Singh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vijay Kumar","family":"Kukreja","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,12,9]]},"reference":[{"key":"982_CR1","doi-asserted-by":"publisher","DOI":"10.1016\/j.ijar.2025.109440","volume":"183","author":"P Adjei","year":"2025","unstructured":"Adjei, P., Gomez-Rosero, S., Capretz, M.A.: Prospect utility with hyperbolic tangent function. Int. J. Approximate Reasoning 183, 109440 (2025)","journal-title":"Int. J. Approximate Reasoning"},{"key":"982_CR2","doi-asserted-by":"publisher","DOI":"10.1016\/j.padiff.2023.100523","volume":"7","author":"KT Akinfe","year":"2023","unstructured":"Akinfe, K.T.: A reliable analytic technique for the modified prototypical kelvin-voigt viscoelastic fluid model by means of the hyperbolic tangent function. Partial Differential Equations in Applied Mathematics 7, 100523 (2023)","journal-title":"Partial Differential Equations in Applied Mathematics"},{"key":"982_CR3","doi-asserted-by":"crossref","unstructured":"Ali, H.: On general form of tanh method and its application to medical problems. In: J.\u00a0Xu, A.\u00a0Hajiyev, S.\u00a0Nickel, M.\u00a0Gen (eds.) Proceedings of the Tenth International Conference on Management Science and Engineering Management, pp. 269\u2013278. Springer Singapore, Singapore (2017)","DOI":"10.1007\/978-981-10-1837-4_23"},{"key":"982_CR4","unstructured":"Becker, G.F., Van\u00a0Orstrand, C.E.: Hyperbolic functions. 1871. Smithsonian Institution (1909)"},{"issue":"3","key":"982_CR5","doi-asserted-by":"publisher","first-page":"474","DOI":"10.1080\/0020739X.2015.1078003","volume":"47","author":"L Bourchtein","year":"2016","unstructured":"Bourchtein, L., Bourchtein, A.: Comparison of some tests for convergence of positive series. Int. J. Math. Educ. Sci. Technol. 47(3), 474\u2013489 (2016)","journal-title":"Int. J. Math. Educ. Sci. Technol."},{"issue":"1","key":"982_CR6","doi-asserted-by":"publisher","first-page":"27","DOI":"10.1093\/bjps\/22.1.27","volume":"22","author":"JP Cleave","year":"1971","unstructured":"Cleave, J.P.: Cauchy, convergence and continuity. Br. J. Philos. Sci. 22(1), 27\u201337 (1971)","journal-title":"Br. J. Philos. Sci."},{"key":"982_CR7","doi-asserted-by":"publisher","unstructured":"Dash, M., Liu, H.: Feature selection for classification. Intelligent Data Analysis 1(1), 131\u2013156 (1997). https:\/\/doi.org\/10.1016\/S1088-467X(97)00008-5. https:\/\/www.sciencedirect.com\/science\/article\/pii\/S1088467X97000085","DOI":"10.1016\/S1088-467X(97)00008-5"},{"key":"982_CR8","doi-asserted-by":"publisher","unstructured":"Dhieb, M., Lahiani, M., Ghariani, H.: Mathematical approximation of the hyperbolic tangent. In: 2009 6th International Multi-Conference on Systems, Signals and Devices, pp. 1\u20136 (2009). https:\/\/doi.org\/10.1109\/SSD.2009.4956699","DOI":"10.1109\/SSD.2009.4956699"},{"key":"982_CR9","doi-asserted-by":"crossref","unstructured":"Drachen, A., Thurau, C., Togelius, J., Yannakakis, G.N., Bauckhage, C.: Game data mining. Game analytics: Maximizing the value of player data pp. 205\u2013253 (2013)","DOI":"10.1007\/978-1-4471-4769-5_12"},{"key":"982_CR10","volume-title":"Fundamentals of data normalization","author":"AF Dutka","year":"1991","unstructured":"Dutka, A.F., Hansen, H.H.: Fundamentals of data normalization. Addison-Wesley Longman Publishing Co., Inc, USA (1991)"},{"issue":"1","key":"982_CR11","first-page":"230","volume":"11","author":"H Gadde","year":"2020","unstructured":"Gadde, H.: Ai-assisted decision-making in database normalization and optimization. International Journal of Machine Learning Research in Cybersecurity and Artificial Intelligence 11(1), 230\u2013259 (2020)","journal-title":"International Journal of Machine Learning Research in Cybersecurity and Artificial Intelligence"},{"key":"982_CR12","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/978-3-540-31865-1_25","volume-title":"Advances in Information Retrieval","author":"C Goutte","year":"2005","unstructured":"Goutte, C., Gaussier, E.: A probabilistic interpretation of precision, recall and f-score, with implication for evaluation. In: Losada, D.E., Fern\u00e1ndez-Luna, J.M. (eds.) Advances in Information Retrieval, pp. 345\u2013359. Springer, Berlin Heidelberg, Berlin, Heidelberg (2005)"},{"issue":"11","key":"982_CR13","doi-asserted-by":"publisher","first-page":"1942","DOI":"10.3390\/math10111942","volume":"10","author":"I Izonin","year":"2022","unstructured":"Izonin, I., Tkachenko, R., Shakhovska, N., Ilchyshyn, B., Singh, K.K.: A two-step data normalization approach for improving classification accuracy in the medical diagnosis domain. Mathematics 10(11), 1942 (2022)","journal-title":"Mathematics"},{"issue":"1","key":"982_CR14","first-page":"1793","volume":"3","author":"T Jayalakshmi","year":"2011","unstructured":"Jayalakshmi, T., Santhakumaran, A.: Statistical normalization and back propagation for classification. International Journal of Computer Theory and Engineering 3(1), 1793\u20138201 (2011)","journal-title":"International Journal of Computer Theory and Engineering"},{"key":"982_CR15","doi-asserted-by":"crossref","unstructured":"Kang, M., Tian, J.: Machine learning: Data pre-processing. Prognostics and health management of electronics: fundamentals, machine learning, and the internet of things pp. 111\u2013130 (2018)","DOI":"10.1002\/9781119515326.ch5"},{"key":"982_CR16","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-7-134","volume":"7","author":"SY Kim","year":"2006","unstructured":"Kim, S.Y., Lee, J.W., Bae, J.S.: Effect of data normalization on fuzzy clustering of dna microarray data. BMC Bioinformatics 7, 1\u201314 (2006)","journal-title":"BMC Bioinformatics"},{"key":"982_CR17","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s13312-011-0055-4","volume":"48","author":"R Kumar","year":"2011","unstructured":"Kumar, R., Indrayan, A.: Receiver operating characteristic (roc) curve for medical researchers. Indian Pediatr. 48, 277\u2013287 (2011)","journal-title":"Indian Pediatr."},{"key":"982_CR18","doi-asserted-by":"publisher","DOI":"10.1016\/j.eswa.2022.118994","volume":"213","author":"R Laishram","year":"2023","unstructured":"Laishram, R., Rabidas, R.: Optimized hyperbolic tangent function-based contrast-enhanced mammograms for breast mass detection. Expert Syst. Appl. 213, 118994 (2023)","journal-title":"Expert Syst. Appl."},{"issue":"6","key":"982_CR19","first-page":"1","volume":"33","author":"L Li","year":"2021","unstructured":"Li, L., Zhang, J.: Research and analysis of an enterprise e-commerce marketing system under the big data environment. Journal of Organizational and End User Computing (JOEUC) 33(6), 1\u201319 (2021)","journal-title":"Journal of Organizational and End User Computing (JOEUC)"},{"key":"982_CR20","doi-asserted-by":"publisher","unstructured":"Lin, C.W., Wang, J.S.: A digital circuit design of hyperbolic tangent sigmoid function for neural networks. In: 2008 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 856\u2013859 (2008). https:\/\/doi.org\/10.1109\/ISCAS.2008.4541553","DOI":"10.1109\/ISCAS.2008.4541553"},{"key":"982_CR21","doi-asserted-by":"publisher","DOI":"10.1016\/j.engappai.2025.110659","volume":"152","author":"S Liu","year":"2025","unstructured":"Liu, S., Zheng, Y., Zeng, X., Yuan, J., Li, J., Chen, R.: Hierarchical cascaded networks with multi-task balanced loss for fine-grained hashing. Eng. Appl. Artif. Intell. 152, 110659 (2025)","journal-title":"Eng. Appl. Artif. Intell."},{"issue":"1","key":"982_CR22","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s10203-020-00305-8","volume":"44","author":"M Mininni","year":"2021","unstructured":"Mininni, M., Orlando, G., Taglialatela, G.: Challenges in approximating the black and scholes call formula with hyperbolic tangents. Decisions Econ. Finan. 44(1), 73\u2013100 (2021)","journal-title":"Decisions Econ. Finan."},{"issue":"3","key":"982_CR23","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1177\/1469066720918446","volume":"26","author":"BB Misra","year":"2020","unstructured":"Misra, B.B.: Data normalization strategies in metabolomics: Current challenges, approaches, and tools. Eur. J. Mass Spectrom. 26(3), 165\u2013174 (2020)","journal-title":"Eur. J. Mass Spectrom."},{"key":"982_CR24","first-page":"13","volume":"6","author":"S Nayak","year":"2014","unstructured":"Nayak, S., Misra, B.B., Behera, H.S.: Impact of data normalization on stock index forecasting. International Journal of Computer Information Systems and Industrial Management Applications 6, 13\u201313 (2014)","journal-title":"International Journal of Computer Information Systems and Industrial Management Applications"},{"key":"982_CR25","doi-asserted-by":"crossref","unstructured":"Noordin, A., Basri, M.A.M., Mohamed, Z.: Sliding mode control with tanh function for quadrotor uav altitude and attitude stabilization. In: Intelligent Manufacturing and Mechatronics: Proceedings of SympoSIMM 2020, pp. 471\u2013491. Springer (2021)","DOI":"10.1007\/978-981-16-0866-7_41"},{"key":"982_CR26","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/1471-2105-6-120","volume":"6","author":"X Qiu","year":"2005","unstructured":"Qiu, X., Brooks, A.I., Klebanov, L., Yakovlev, A.: The effects of normalization on the correlation structure of microarray data. BMC Bioinformatics 6, 1\u201311 (2005)","journal-title":"BMC Bioinformatics"},{"issue":"3","key":"982_CR27","first-page":"561","volume":"55","author":"F Reyes-Cortes","year":"2019","unstructured":"Reyes-Cortes, F., Felix-Beltran, O., Cid-Monjaraz, J., Alonso-Aruffo, G.: A family of hyperbolic-type control schemes for robot manipulators. Kybernetika 55(3), 561\u2013585 (2019)","journal-title":"Kybernetika"},{"issue":"3","key":"982_CR28","doi-asserted-by":"publisher","first-page":"1464","DOI":"10.1109\/23.589532","volume":"44","author":"J Sola","year":"1997","unstructured":"Sola, J., Sevilla, J.: Importance of input data normalization for the application of neural networks to complex industrial problems. IEEE Trans. Nucl. Sci. 44(3), 1464\u20131468 (1997)","journal-title":"IEEE Trans. Nucl. Sci."},{"issue":"4","key":"982_CR29","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1080\/10095020.2018.1489576","volume":"21","author":"M Song","year":"2018","unstructured":"Song, M., Chen, D.: An improved knowledge-informed nsga-ii for multi-objective land allocation (mola). Geo-spatial Information Science 21(4), 273\u2013287 (2018)","journal-title":"Geo-spatial Information Science"},{"key":"982_CR30","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1007\/11573067_20","volume-title":"Biological and Medical Data Analysis","author":"M Sordo","year":"2005","unstructured":"Sordo, M., Zeng, Q.: On sample size and classification accuracy: A performance comparison. In: Oliveira, J.L., Maojo, V., Mart\u00edn-S\u00e1nchez, F., Pereira, A.S. (eds.) Biological and Medical Data Analysis, pp. 193\u2013201. Springer, Berlin Heidelberg, Berlin, Heidelberg (2005)"},{"key":"982_CR31","doi-asserted-by":"publisher","unstructured":"Souayeh, B., Sabir, Z.: Designing hyperbolic tangent sigmoid function for solving the williamson nanofluid model. Fractal and Fractional 7(5) (2023). https:\/\/doi.org\/10.3390\/fractalfract7050350. https:\/\/www.mdpi.com\/2504-3110\/7\/5\/350","DOI":"10.3390\/fractalfract7050350"},{"issue":"2","key":"982_CR32","doi-asserted-by":"publisher","first-page":"506","DOI":"10.1111\/coin.12476","volume":"38","author":"A Thapa","year":"2022","unstructured":"Thapa, A., Alsadoon, A., Prasad, P., Bajaj, S., Alsadoon, O.H., Rashid, T.A., Ali, R.S., Jerew, O.D.: Deep learning for breast cancer classification: Enhanced tangent function. Comput. Intell. 38(2), 506\u2013529 (2022)","journal-title":"Comput. Intell."},{"key":"982_CR33","unstructured":"Totter, S.R.: A study on infinite series and the development of convergence tests. Texas Woman\u2019s University (1997)"},{"issue":"4","key":"982_CR34","doi-asserted-by":"publisher","first-page":"64","DOI":"10.34021\/ve.2024.07.04(4)","volume":"7","author":"L Vancsura","year":"2024","unstructured":"Vancsura, L., Tatay, T., Bareith, T.: Investigating the role of activation functions in predicting the price of cryptocurrencies during critical economic periods. Virtual Economics 7(4), 64\u201391 (2024)","journal-title":"Virtual Economics"},{"key":"982_CR35","doi-asserted-by":"publisher","unstructured":"Vieira, S.M., Kaymak, U., Sousa, J.M.C.: Cohen\u2019s kappa coefficient as a performance measure for feature selection. In: International Conference on Fuzzy Systems, pp. 1\u20138 (2010). https:\/\/doi.org\/10.1109\/FUZZY.2010.5584447","DOI":"10.1109\/FUZZY.2010.5584447"},{"issue":"5","key":"982_CR36","doi-asserted-by":"publisher","DOI":"10.1049\/tje2.12275","volume":"2023","author":"Y Wang","year":"2023","unstructured":"Wang, Y., Huang, S., Zhou, S., Liu, Y.: A novel hyperbolic tangent sliding mode observation of vehicle lateral force fed back by longitudinal force error. The Journal of Engineering 2023(5), e12275 (2023)","journal-title":"The Journal of Engineering"},{"key":"982_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.neunet.2022.05.022","volume":"153","author":"H Wen","year":"2022","unstructured":"Wen, H., He, X., Huang, T.: Sparse signal reconstruction via recurrent neural networks with hyperbolic tangent function. Neural Netw. 153, 1\u201312 (2022)","journal-title":"Neural Netw."},{"key":"982_CR38","doi-asserted-by":"publisher","first-page":"323","DOI":"10.1016\/j.ins.2012.07.049","volume":"222","author":"Y Wu","year":"2013","unstructured":"Wu, Y., Zhou, Y., Saveriades, G., Agaian, S., Noonan, J.P., Natarajan, P.: Local shannon entropy measure with statistical tests for image randomness. Inf. Sci. 222, 323\u2013342 (2013)","journal-title":"Inf. Sci."},{"issue":"9","key":"982_CR39","doi-asserted-by":"publisher","first-page":"1023","DOI":"10.1002\/fld.975","volume":"48","author":"F Xiao","year":"2005","unstructured":"Xiao, F., Honma, Y., Kono, T.: A simple algebraic interface capturing scheme using hyperbolic tangent function. Int. J. Numer. Meth. Fluids 48(9), 1023\u20131040 (2005)","journal-title":"Int. J. Numer. Meth. Fluids"},{"key":"982_CR40","doi-asserted-by":"crossref","unstructured":"Zeng, X., Zhou, J., Liu, D., Yuan, J., Yin, M., Xu, W., Liu, S.: Large-scale fine-grained image retrieval via proxy mask pooling and multilateral semantic relations. Knowledge-Based Systems p. 114018 (2025)","DOI":"10.1016\/j.knosys.2025.114018"},{"key":"982_CR41","doi-asserted-by":"crossref","unstructured":"Zeng, X., Zhou, J., Ye, C., Yuan, J., Li, J., Jiang, J., Chen, R., Liu, S.: Stacked and decorrelated hashing with adaptanh for large-scale fine-grained image retrieval. Signal Processing: Image Communication p. 117374 (2025)","DOI":"10.1016\/j.image.2025.117374"},{"issue":"6","key":"982_CR42","doi-asserted-by":"publisher","first-page":"1381","DOI":"10.1109\/JAS.2024.124485","volume":"11","author":"Z Zuo","year":"2024","unstructured":"Zuo, Z., Tang, J., Ke, R., Han, Q.L.: Hyperbolic tangent function-based protocols for global\/semi-global finite-time consensus of multi-agent systems. IEEE\/CAA Journal of Automatica Sinica 11(6), 1381\u20131397 (2024)","journal-title":"IEEE\/CAA Journal of Automatica Sinica"}],"container-title":["International Journal of Data Science and Analytics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41060-025-00982-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s41060-025-00982-x","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s41060-025-00982-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,14]],"date-time":"2026-03-14T09:36:30Z","timestamp":1773480990000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s41060-025-00982-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,9]]},"references-count":42,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,6]]}},"alternative-id":["982"],"URL":"https:\/\/doi.org\/10.1007\/s41060-025-00982-x","relation":{},"ISSN":["2364-415X","2364-4168"],"issn-type":[{"value":"2364-415X","type":"print"},{"value":"2364-4168","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,9]]},"assertion":[{"value":"12 June 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 December 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"No author associated with this paper has disclosed any potential or pertinent conflicts which may be perceived to have impending conflict with this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"There is no ethical problem in this paper.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Ethical approval"}},{"value":"The authors declare no conflict of interest.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"70"}}