{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T20:37:57Z","timestamp":1763152677818,"version":"3.45.0"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"16","license":[{"start":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T00:00:00Z","timestamp":1763078400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T00:00:00Z","timestamp":1763078400000},"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":["J Supercomput"],"DOI":"10.1007\/s11227-025-08053-5","type":"journal-article","created":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T20:34:55Z","timestamp":1763152495000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["QTL-Net: an advanced quartet PCA-driven temporal learning model with logistic\u2013sigmoid normalization for accurate multivariate forecasting"],"prefix":"10.1007","volume":"81","author":[{"given":"Yuvaraja","family":"Boddu","sequence":"first","affiliation":[]},{"given":"A","family":"Manimaran","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,11,14]]},"reference":[{"key":"8053_CR1","doi-asserted-by":"publisher","first-page":"54776","DOI":"10.1109\/ACCESS.2020.2980942","volume":"8","author":"GT Reddy","year":"2020","unstructured":"Reddy GT et al (2020) Analysis of dimensionality reduction techniques on big data. IEEE Access 8:54776\u201354788","journal-title":"IEEE Access"},{"issue":"5","key":"8053_CR2","first-page":"2028","volume":"8","author":"JP Bharadiya","year":"2023","unstructured":"Bharadiya JP (2023) A tutorial on principal component analysis for dimensionality reduction in machine learning. Int Jo Innov Sci Res Technol 8(5):2028\u20132032","journal-title":"Int Jo Innov Sci Res Technol"},{"key":"8053_CR3","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1016\/j.neucom.2015.07.010","volume":"171","author":"H Li","year":"2016","unstructured":"Li H (2016) Accurate and efficient classification based on common principal components analysis for multivariate time series. Neurocomputing 171:744\u2013753","journal-title":"Neurocomputing"},{"issue":"6","key":"8053_CR4","doi-asserted-by":"publisher","first-page":"2842","DOI":"10.1016\/j.eswa.2013.10.019","volume":"41","author":"H Li","year":"2014","unstructured":"Li H (2014) Asynchronism-based principal component analysis for time series data mining. Expert Syst Appl 41(6):2842\u20132850","journal-title":"Expert Syst Appl"},{"issue":"7","key":"8053_CR5","doi-asserted-by":"publisher","first-page":"9862","DOI":"10.1007\/s11227-021-04303-4","volume":"78","author":"X Wan","year":"2022","unstructured":"Wan X et al (2022) Dimensionality reduction for multivariate time-series data mining. J Supercomput 78(7):9862\u20139878","journal-title":"J Supercomput"},{"key":"8053_CR6","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1016\/j.conengprac.2018.07.012","volume":"80","author":"Q Jiang","year":"2018","unstructured":"Jiang Q, Yan X (2018) Parallel PCA\u2013KPCA for nonlinear process monitoring. Control Eng Pract 80:17\u201325","journal-title":"Control Eng Pract"},{"key":"8053_CR7","doi-asserted-by":"publisher","first-page":"239","DOI":"10.1016\/j.neucom.2019.03.060","volume":"349","author":"H Li","year":"2019","unstructured":"Li H (2019) Multivariate time series clustering based on common principal component analysis. Neurocomputing 349:239\u2013247","journal-title":"Neurocomputing"},{"issue":"7","key":"8053_CR8","doi-asserted-by":"publisher","first-page":"535","DOI":"10.1016\/j.knosys.2008.03.014","volume":"21","author":"X Weng","year":"2008","unstructured":"Weng X, Shen J (2008) Classification of multivariate time series using two-dimensional singular value decomposition. Knowl Based Syst 21(7):535\u2013539","journal-title":"Knowl Based Syst"},{"key":"8053_CR9","doi-asserted-by":"publisher","first-page":"114571","DOI":"10.1016\/j.eswa.2021.114571","volume":"171","author":"B Du","year":"2021","unstructured":"Du B et al (2021) Deep learning with long short-term memory neural networks combining wavelet transform and principal component analysis for daily urban water demand forecasting. Expert Syst Appl 171:114571","journal-title":"Expert Syst Appl"},{"unstructured":"Gao T et al (2016) Deep learning with stock indicators and two-dimensional principal component analysis for closing price prediction system. In: 2016 7th IEEE International Conference On Software Engineering and Service Science (ICSESS). IEEE","key":"8053_CR10"},{"key":"8053_CR11","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2024.3454540","author":"Y Boddu","year":"2024","unstructured":"Boddu Y et al (2024) Design of an iterative dual metaheuristic VARMAx model enhancing efficiency of time series predictions. IEEE Access. https:\/\/doi.org\/10.1109\/ACCESS.2024.3454540","journal-title":"IEEE Access"},{"key":"8053_CR12","doi-asserted-by":"publisher","first-page":"76690","DOI":"10.1109\/ACCESS.2019.2921578","volume":"7","author":"Q Tao","year":"2019","unstructured":"Tao Q et al (2019) Air pollution forecasting using a deep learning model based on 1D convnets and bidirectional GRU. IEEE Access 7:76690\u201376698","journal-title":"IEEE Access"},{"key":"8053_CR13","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2024.3515095","author":"Y Boddu","year":"2024","unstructured":"Boddu Y et al (2024) Advanced air quality forecasting using an enhanced temporal attention-driven graph convolutional long short-term memory model with seasonal-trend decomposition. IEEE Access. https:\/\/doi.org\/10.1109\/ACCESS.2024.3515095","journal-title":"IEEE Access"},{"key":"8053_CR14","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10614-023-10424-0","volume":"64","author":"Y Boddu","year":"2024","unstructured":"Boddu Y, Manimaran A (2024) Maximizing forecasting precision: empowering multivariate time series prediction with QPCA-LSTM. Comput Econ 64:1\u201336","journal-title":"Comput Econ"},{"issue":"2","key":"8053_CR15","doi-asserted-by":"publisher","first-page":"317","DOI":"10.37934\/araset.54.2.317343","volume":"54","author":"IR Salman","year":"2025","unstructured":"Salman IR et al (2025) Efficient human activity recognition using PCA dimensionality reduction and GWO-enhanced LSTM. J Adv Res Appl Sci Eng Technol 54(2):317\u2013343","journal-title":"J Adv Res Appl Sci Eng Technol"},{"key":"8053_CR16","doi-asserted-by":"publisher","first-page":"109309","DOI":"10.1016\/j.petrol.2021.109309","volume":"208","author":"X Li","year":"2022","unstructured":"Li X et al (2022) Time-series production forecasting method based on the integration of Bidirectional Gated Recurrent Unit (Bi-GRU) network and Sparrow Search Algorithm (SSA). J Pet Sci Eng 208:109309","journal-title":"J Pet Sci Eng"},{"issue":"1","key":"8053_CR17","doi-asserted-by":"publisher","first-page":"19038","DOI":"10.1038\/s41598-019-55320-6","volume":"9","author":"A Sagheer","year":"2019","unstructured":"Sagheer A, Kotb M (2019) Unsupervised pre-training of a deep LSTM-based stacked autoencoder for multivariate time series forecasting problems. Sci Rep 9(1):19038","journal-title":"Sci Rep"},{"key":"8053_CR18","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2024.3435683","author":"T Jayanth","year":"2024","unstructured":"Jayanth T, Manimaran A (2024) Developing a novel hybrid model double exponential smoothing and dual attention encoder-decoder based bi-directional gated recurrent unit enhanced with Bayesian optimization to forecast stock price. IEEE Access. https:\/\/doi.org\/10.1109\/ACCESS.2024.3435683","journal-title":"IEEE Access"},{"issue":"8","key":"8053_CR19","doi-asserted-by":"publisher","first-page":"1046","DOI":"10.1007\/s42979-024-03355-6","volume":"5","author":"T Jayanth","year":"2024","unstructured":"Jayanth T, Manimaran A (2024) Unlocking stock price prognostication dual attention-infused bi-directional LSTM empowered by Bayesian optimization DA-Bi-LSTM-BO. SN Comput Sci 5(8):1046","journal-title":"SN Comput Sci"},{"key":"8053_CR20","doi-asserted-by":"publisher","DOI":"10.1109\/ACCESS.2024.3502175","author":"T Jayanth","year":"2024","unstructured":"Jayanth T, Manimaran A, Siva G (2024) Enhancing stock price forecasting with a hybrid SES-DA-Bi-LSTM-BO model: superior accuracy in high-frequency financial data analysis. IEEE Access. https:\/\/doi.org\/10.1109\/ACCESS.2024.3502175","journal-title":"IEEE Access"},{"key":"8053_CR21","doi-asserted-by":"publisher","first-page":"105189","DOI":"10.1016\/j.eneco.2021.105189","volume":"97","author":"M He","year":"2021","unstructured":"He M et al (2021) Forecasting crude oil prices: a scaled PCA approach. Energy Econ 97:105189","journal-title":"Energy Econ"},{"key":"8053_CR22","doi-asserted-by":"publisher","first-page":"31443","DOI":"10.1109\/ACCESS.2024.3369891","volume":"12","author":"K Tzoumpas","year":"2024","unstructured":"Tzoumpas K et al (2024) A data filling methodology for time series based on CNN and (Bi) LSTM neural networks. IEEE Access 12:31443\u201331460","journal-title":"IEEE Access"},{"issue":"5","key":"8053_CR23","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1007\/s11063-024-11656-3","volume":"56","author":"A Mahmoud","year":"2024","unstructured":"Mahmoud A, Mohammed A (2024) Leveraging hybrid deep learning models for enhanced multivariate time series forecasting. Neural Process Lett 56(5):223","journal-title":"Neural Process Lett"},{"issue":"3","key":"8053_CR24","first-page":"393","volume":"12","author":"F Moodi","year":"2024","unstructured":"Moodi F et al (2024) Advanced stock price forecasting using a 1D-CNN-GRU-LSTM model. J AI Data Min 12(3):393\u2013408","journal-title":"J AI Data Min"},{"key":"8053_CR25","doi-asserted-by":"publisher","DOI":"10.1007\/s41060-024-00640-8","author":"N Khodadadi","year":"2024","unstructured":"Khodadadi N et al (2024) Predicting normalized difference vegetation index using a deep attention network with bidirectional GRU: a hybrid parametric optimization approach. Int J Data Sci Anal. https:\/\/doi.org\/10.1007\/s41060-024-00640-8","journal-title":"Int J Data Sci Anal"},{"doi-asserted-by":"crossref","unstructured":"Yu C et al (2023) Dsformer: a double sampling transformer for multivariate time series long-term prediction. In: Proceedings of the 32nd ACM International Conference on Information and Knowledge Management","key":"8053_CR26","DOI":"10.1145\/3583780.3614851"},{"key":"8053_CR27","doi-asserted-by":"publisher","first-page":"102607","DOI":"10.1016\/j.inffus.2024.102607","volume":"113","author":"C Yu","year":"2025","unstructured":"Yu C et al (2025) Mgsfformer: a multi-granularity spatiotemporal fusion transformer for air quality prediction. Inf Fusion 113:102607","journal-title":"Inf Fusion"},{"issue":"3","key":"8053_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s12145-025-01987-7","volume":"18","author":"Y Boddu","year":"2025","unstructured":"Boddu Y, Talabathula J (2025) Enhanced environmental time-series forecasting using ICA-LSD Bayesian LSTM: a robust approach for accurate and uncertainty-aware predictions. Earth Sci Inform 18(3):1\u201323","journal-title":"Earth Sci Inform"},{"key":"8053_CR29","first-page":"4383","volume":"32","author":"J Xu","year":"2019","unstructured":"Xu J et al (2019) Understanding and improving layer normalization. Adv Neural Inf Process Syst 32:4383\u20134393","journal-title":"Adv Neural Inf Process Syst"},{"key":"8053_CR30","doi-asserted-by":"publisher","first-page":"280","DOI":"10.1016\/j.proeng.2015.12.390","volume":"131","author":"D Kucharavy","year":"2015","unstructured":"Kucharavy D, De Guio R (2015) Application of logistic growth curve. Procedia Eng 131:280\u2013290","journal-title":"Procedia Eng"},{"issue":"3","key":"8053_CR31","doi-asserted-by":"publisher","first-page":"18","DOI":"10.5755\/j01.eie.25.3.23671","volume":"25","author":"Y Liu","year":"2019","unstructured":"Liu Y, Cheng Hu, Hong Yi (2019) Electric energy substitution potential prediction based on logistic curve fitting and improved BP neural network algorithm. Elektron Elektrotech 25(3):18\u201324","journal-title":"Elektron Elektrotech"},{"doi-asserted-by":"crossref","unstructured":"Wang B, Wang X, Ma X (2020) Study on optimal combination settlement prediction model based on logistic curve and Gompertz curve. Stavebn\u00ed obzor Civ Eng J 29(3)","key":"8053_CR32","DOI":"10.14311\/CEJ.2020.03.0031"},{"unstructured":"Ba JL (2016) Layer normalization. arXiv:1607.06450","key":"8053_CR33"},{"unstructured":"Zhang B, Sennrich R (2019) Root mean square layer normalization. Adv Neural Inf Process Syst 32","key":"8053_CR34"},{"unstructured":"Riechers PM (2024) Geometry and dynamics of LayerNorm. arXiv:2405.04134","key":"8053_CR35"},{"doi-asserted-by":"crossref","unstructured":"Liu X et al (2021) Neighborhood normalization for robust geometric feature learning. In: Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition","key":"8053_CR36","DOI":"10.1109\/CVPR46437.2021.01285"},{"unstructured":"Aalto MS, Lubana ES, Tanaka H (2022) Geometric considerations for normalization layers in equivariant neural networks. AI for Accelerated Materials Design NeurIPS 2022 Workshop","key":"8053_CR37"}],"container-title":["The Journal of Supercomputing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-08053-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11227-025-08053-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11227-025-08053-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,14]],"date-time":"2025-11-14T20:34:59Z","timestamp":1763152499000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11227-025-08053-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,14]]},"references-count":37,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["8053"],"URL":"https:\/\/doi.org\/10.1007\/s11227-025-08053-5","relation":{},"ISSN":["1573-0484"],"issn-type":[{"type":"electronic","value":"1573-0484"}],"subject":[],"published":{"date-parts":[[2025,11,14]]},"assertion":[{"value":"17 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 November 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 November 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":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"Not applicable.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Research involving human and\/or animal"}},{"value":"Not applicable.","order":4,"name":"Ethics","group":{"name":"EthicsHeading","label":"Informed consent"}}],"article-number":"1566"}}