{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:16:41Z","timestamp":1760235401104,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T00:00:00Z","timestamp":1629244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62066017"],"award-info":[{"award-number":["62066017"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Time series analysis has been an important branch of information processing, and the conversion of time series into complex networks provides a new means to understand and analyze time series. In this work, using Variational Auto-Encode (VAE), we explored the construction of latent networks for univariate time series. We first trained the VAE to obtain the space of latent probability distributions of the time series and then decomposed the multivariate Gaussian distribution into multiple univariate Gaussian distributions. By measuring the distance between univariate Gaussian distributions on a statistical manifold, the latent network construction was finally achieved. The experimental results show that the latent network can effectively retain the original information of the time series and provide a new data structure for the downstream tasks.<\/jats:p>","DOI":"10.3390\/e23081071","type":"journal-article","created":{"date-parts":[[2021,8,18]],"date-time":"2021-08-18T22:51:00Z","timestamp":1629327060000},"page":"1071","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Latent Network Construction for Univariate Time Series Based on Variational Auto-Encode"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9375-8918","authenticated-orcid":false,"given":"Jiancheng","family":"Sun","sequence":"first","affiliation":[{"name":"School of Software and Internet of Things Engineering, Jiangxi University of Finance and Economics, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhinan","family":"Wu","sequence":"additional","affiliation":[{"name":"School of Information Management, Jiangxi University of Finance and Economics, Nanchang 330013, China"},{"name":"School of Mathematics and Computer Science, Yichun University, Yichun 336000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Si","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Software and Internet of Things Engineering, Jiangxi University of Finance and Economics, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huimin","family":"Niu","sequence":"additional","affiliation":[{"name":"School of Software and Internet of Things Engineering, Jiangxi University of Finance and Economics, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zongqing","family":"Tu","sequence":"additional","affiliation":[{"name":"School of Software and Internet of Things Engineering, Jiangxi University of Finance and Economics, Nanchang 330013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6936","DOI":"10.1038\/s41598-021-86432-7","article-title":"Time\u2013frequency time\u2013space LSTM for robust classification of physiological signals","volume":"11","author":"Pham","year":"2021","journal-title":"Sci. Rep."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1016\/j.patcog.2019.05.040","article-title":"Univariate time series classification using information geometry","volume":"95","author":"Sun","year":"2019","journal-title":"Pattern Recognit."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.physrep.2006.11.001","article-title":"Recurrence plots for the analysis of complex systems","volume":"438","author":"Marwan","year":"2007","journal-title":"Phys. Rep."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"177","DOI":"10.37394\/23206.2020.19.17","article-title":"Time series analysis for assessing and forecasting of road traffic accidents\u2014case studies","volume":"19","author":"Popescu","year":"2020","journal-title":"WSEAS Trans. Math."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Tsay, R.S., and Chen, R. (2018). Nonlinear Time Series Analysis, Wiley.","DOI":"10.32614\/CRAN.package.NTS"},{"key":"ref_6","first-page":"6845","article-title":"TapNet: Multivariate time series classification with attentional prototypical network","volume":"34","author":"Zhang","year":"2020","journal-title":"Proc. AAAI Conf. Artif. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.future.2019.12.013","article-title":"IoT type-of-traffic forecasting method based on gradient boosting neural networks","volume":"105","author":"Carro","year":"2020","journal-title":"Futur. Gener. Comput. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lopez-Martin, M., Sanchez-Esguevillas, A., Hernandez-Callejo, L., Arribas, J.I., and Carro, B. (2021). Additive ensemble neural network with constrained weighted quantile loss for probabilistic electric-load forecasting. Sensors, 21.","DOI":"10.3390\/s21092979"},{"key":"ref_9","unstructured":"Mitchell, M. (2011). Complexity: A Guided Tour, Oxford University Press."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"238701","DOI":"10.1103\/PhysRevLett.96.238701","article-title":"Complex network from pseudoperiodic time series: Topology versus dynamics","volume":"96","author":"Zhang","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"033025","DOI":"10.1088\/1367-2630\/12\/3\/033025","article-title":"Recurrence networks\u2014A novel paradigm for nonlinear time series analysis","volume":"12","author":"Donner","year":"2010","journal-title":"New J. Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4972","DOI":"10.1073\/pnas.0709247105","article-title":"From time series to complex networks: The visibility graph","volume":"105","author":"Lacasa","year":"2008","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"073114","DOI":"10.1063\/1.4959537","article-title":"Using ordinal partition transition networks to analyze ECG data","volume":"26","author":"Kulp","year":"2016","journal-title":"Chaos An Interdiscip. J. Nonlinear Sci."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"10486","DOI":"10.1038\/s41598-017-10759-3","article-title":"Reconstructing complex network for characterizing the time-varying causality evolution behavior of multivariate time series","volume":"7","author":"Jiang","year":"2017","journal-title":"Sci. Rep."},{"key":"ref_15","unstructured":"Amari, S.-I., and Nagaoka, H. (2000). Methods of Information Geometry, American Mathematical Society."},{"key":"ref_16","first-page":"55","article-title":"Integrating the Gaussian through differentiable topological manifolds","volume":"18","author":"Manale","year":"2019","journal-title":"WSEAS Trans. Math."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1109\/TSMC.2017.2751504","article-title":"Complex network construction of multivariate time series using information geometry","volume":"49","author":"Sun","year":"2019","journal-title":"IEEE Trans. Syst. Man Cybern. Syst."},{"key":"ref_18","unstructured":"Kingma, D.P., and Welling, M. (2014, January 14\u201316). Auto-encoding variational bayes. Proceedings of the 2nd International Conference on Learning Representations, ICLR 2014\u2014Conference Track Proceedings, Banff, AB, Canada."},{"key":"ref_19","unstructured":"Fabius, O., and van Amersfoort, J.R. (2015, January 7\u20139). Variational recurrent auto-encoders. Proceedings of the 3rd International Conference on Learning Representations, ICLR 2015\u2014Workshop Track Proceedings, San Diego, CA, USA."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Comput."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Nagino, G., and Shozakai, M. (2006, January 17\u201321). Distance measure between Gaussian distributions for discriminating speaking styles. Proceedings of the INTERSPEECH 2006\u2014ICSLP, Ninth International Conference on Spoken Language Processing, Pittsburgh, PA, USA.","DOI":"10.21437\/Interspeech.2006-233"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1713","DOI":"10.1109\/TPAMI.2008.75","article-title":"Pedestrian detection via classification on Riemannian manifolds","volume":"30","author":"Tuzel","year":"2008","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1006\/jmva.1999.1853","article-title":"Multivariate normal distributions parametrized as a Riemannian symmetric space","volume":"74","author":"Ruh","year":"2000","journal-title":"J. Multivar. Anal."},{"key":"ref_24","unstructured":"Chen, Y., Keogh, E., Hu, B., Begum, N., Bagnall, A., and Abdullah Mueen, G.B. (2021, August 17). The UCR Time Series Classification Archive. Available online: www.cs.ucr.edu\/~eamonn\/time_series_data\/."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1813","DOI":"10.1109\/JBHI.2014.2303991","article-title":"Analysis and classification of sleep stages based on difference visibility graphs from a single-channel EEG signal","volume":"18","author":"Zhu","year":"2014","journal-title":"IEEE J. Biomed. Health Inform."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"50002","DOI":"10.1209\/0295-5075\/97\/50002","article-title":"Analysis of seismic sequences by using the method of visibility graph","volume":"97","author":"Telesca","year":"2012","journal-title":"Europhys. Lett."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/j.aiopen.2021.01.001","article-title":"Graph neural networks: A review of methods and applications","volume":"1","author":"Zhou","year":"2020","journal-title":"AI Open"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1071\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:46:54Z","timestamp":1760165214000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/23\/8\/1071"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,18]]},"references-count":27,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2021,8]]}},"alternative-id":["e23081071"],"URL":"https:\/\/doi.org\/10.3390\/e23081071","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2021,8,18]]}}}