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However, missing data can degrade processing and lead to bias and misunderstandings or even wrong decision-making. In this paper, a recurrent neural network-based denoising autoencoder is proposed for gap imputation in related multivariate time series, i.e., series that exhibit spatio-temporal correlations. The denoising autoencoder (DAE) is able to reproduce input missing data by learning to remove intentionally added gaps, while the recurrent neural network (RNN) captures temporal patterns and relationships among variables. For that reason, different unidirectional (simple RNN, GRU, LSTM) and bidirectional (BiSRNN, BiGRU, BiLSTM) architectures are compared with each other and to state-of-the-art methods using three different datasets in the experiments. The implementation with BiGRU layers outperforms the others, effectively filling gaps with a low reconstruction error. The use of this approach is appropriate for complex scenarios where several variables contain long gaps. However, extreme scenarios with very short gaps in one variable or no available data should be avoided.<\/jats:p>","DOI":"10.3233\/ica-230728","type":"journal-article","created":{"date-parts":[[2023,12,29]],"date-time":"2023-12-29T11:53:51Z","timestamp":1703850831000},"page":"157-172","source":"Crossref","is-referenced-by-count":14,"title":["Gap imputation in related multivariate time series through recurrent neural network-based denoising autoencoder"],"prefix":"10.1177","volume":"31","author":[{"given":"Seraf\u00edn","family":"Alonso","sequence":"first","affiliation":[]},{"given":"Antonio","family":"Mor\u00e1n","sequence":"additional","affiliation":[]},{"given":"Daniel","family":"P\u00e9rez","sequence":"additional","affiliation":[]},{"given":"Miguel A.","family":"Prada","sequence":"additional","affiliation":[]},{"given":"Juan J.","family":"Fuertes","sequence":"additional","affiliation":[]},{"given":"Manuel","family":"Dom\u00ednguez","sequence":"additional","affiliation":[]}],"member":"179","reference":[{"issue":"3","key":"10.3233\/ICA-230728_ref1","doi-asserted-by":"publisher","first-page":"570","DOI":"10.1108\/JMTM-09-2018-0325","article-title":"Industry 4.0 as a data-driven paradigm: A systematic literature review on technologies","volume":"32","author":"Klingenberg","year":"2021","journal-title":"Journal of Manufacturing Technology Management"},{"key":"10.3233\/ICA-230728_ref2","doi-asserted-by":"publisher","first-page":"23484","DOI":"10.1109\/ACCESS.2017.2765544","article-title":"Industrial Big Data in an Industry 4.0 Environment: Challenges, schemes, and applications for predictive maintenance","volume":"5","author":"Yan","year":"2017","journal-title":"IEEE Access"},{"key":"10.3233\/ICA-230728_ref3","doi-asserted-by":"publisher","DOI":"10.1186\/s40537-020-0285-1"},{"key":"10.3233\/ICA-230728_ref4","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1016\/j.rser.2017.01.100","article-title":"Non-technical loss analysis and prevention using smart meters","volume":"72","author":"Ahmad","year":"2017","journal-title":"Renewable and Sustainable Energy Reviews"},{"key":"10.3233\/ICA-230728_ref5","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1016\/j.rser.2017.02.085","article-title":"A review on time series forecasting techniques for building energy consumption","volume":"74","author":"Deb","year":"2017","journal-title":"Renewable and Sustainable Energy Reviews"},{"key":"10.3233\/ICA-230728_ref6","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/j.neucom.2020.05.033","article-title":"Smoothed LSTM-AE: A spatio-temporal deep model for multiple time-series missing imputation","volume":"411","author":"Li","year":"2020","journal-title":"Neurocomputing"},{"key":"10.3233\/ICA-230728_ref8","doi-asserted-by":"publisher","first-page":"103826","DOI":"10.1016\/j.trc.2022.103826","article-title":"Memory-augmented dynamic graph convolution networks for traffic data imputation with diverse missing patterns","volume":"143","author":"Liang","year":"2022","journal-title":"Transportation Research Part C: Emerging Technologies"},{"issue":"2","key":"10.3233\/ICA-230728_ref9","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1007\/s10260-018-00435-9","article-title":"Reconstructing missing data sequences in multivariate time series: An application to environmental data","volume":"28","author":"Parrella","year":"2019","journal-title":"Statistical Methods & Applications"},{"key":"10.3233\/ICA-230728_ref10","doi-asserted-by":"crossref","first-page":"333","DOI":"10.1016\/j.apenergy.2016.06.046","article-title":"K-means based load estimation of domestic smart meter measurements","volume":"194","author":"Al-Wakeel","year":"2017","journal-title":"Applied Energy"},{"issue":"19","key":"10.3233\/ICA-230728_ref11","doi-asserted-by":"crossref","first-page":"10321","DOI":"10.3390\/ijerph181910321","article-title":"BiLSTM-I: A deep learning-based long interval gap-filling method for meteorological observation data","volume":"18","author":"Xie","year":"2021","journal-title":"International Journal of Environmental Research and Public Health"},{"key":"10.3233\/ICA-230728_ref12","unstructured":"Cao W, Wang D, Li J, Zhou H, Li L, Li Y. 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