{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T05:18:56Z","timestamp":1761801536136,"version":"build-2065373602"},"reference-count":47,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T00:00:00Z","timestamp":1761609600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Social Science Fund of China","award":["21BTJ042"],"award-info":[{"award-number":["21BTJ042"]}]},{"name":"National Key Statistical Science Research Project","award":["2025LZ007"],"award-info":[{"award-number":["2025LZ007"]}]},{"DOI":"10.13039\/501100004775","name":"Gansu Provincial Natural Science Foundation","doi-asserted-by":"crossref","award":["23JRRA1186"],"award-info":[{"award-number":["23JRRA1186"]}],"id":[{"id":"10.13039\/501100004775","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Gansu Provincial Universities\u2019 Young Doctor Support Program","award":["2025QB-058"],"award-info":[{"award-number":["2025QB-058"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The integrity of real-time monitoring data is paramount to the accuracy of scientific research and the reliability of decision-making. However, data incompleteness arising from transmission interruptions or extreme weather disrupting equipment operations severely compromises the validity of statistical analyses and the stability of modelling. From a mathematical view, real-time monitoring data may be regarded as continuous functions, exhibiting intricate correlations and mutual influences between different indicators. Leveraging their inherent smoothness and interdependencies enables high-precision data imputation. Within the functional data analysis framework, this paper proposes a Diversity Constraint and Adaptive Graph Multi-View Functional Matrix Completion (DCAGMFMC) method. Integrating multi-view learning with an adaptive graph strategy, this approach comprehensively accounts for complex correlations between data from different views while extracting differential information across views, thereby enhancing information utilization and imputation accuracy. Random simulation experiments demonstrate that the DCAGMFMC method exhibits significant imputation advantages over classical methods such as KNN, HFI, SFI, MVNFMC, and GRMFMC. Furthermore, practical applications on meteorological datasets reveal that, compared to these imputation methods, the root mean square error (RMSE), mean absolute error (MAE), and normalized root mean square error (NRMSE) of the DCAGMVNFMC method decreased by an average of 39.11% to 59.15%, 54.50% to 71.97%, and 43.96% to 63.70%, respectively. It also demonstrated stable imputation performance across various meteorological indicators and missing data rates, exhibiting good adaptability and practical value.<\/jats:p>","DOI":"10.3390\/axioms14110793","type":"journal-article","created":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T03:44:39Z","timestamp":1761795879000},"page":"793","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Diversity Constraint and Adaptive Graph Multi-View Functional Matrix Completion"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5736-0600","authenticated-orcid":false,"given":"Haiyan","family":"Gao","sequence":"first","affiliation":[{"name":"Key Laboratory of Digital Economy and Social Computing Science of Gansu, Lanzhou 730020, China"},{"name":"School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youdi","family":"Bian","sequence":"additional","affiliation":[{"name":"School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,28]]},"reference":[{"key":"ref_1","first-page":"6630","article-title":"An experimental survey of missing data Imputation algorithms","volume":"35","author":"Miao","year":"2022","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"110188","DOI":"10.1016\/j.knosys.2022.110188","article-title":"Dynamic graph convolutional recurrent imputation network for spatiotemporal traffic missing data","volume":"261","author":"Kong","year":"2023","journal-title":"Knowl.-Based Syst."},{"key":"ref_3","first-page":"37","article-title":"Function-based multiple imputation method based on cross-sectional and longitudinal information","volume":"41","author":"Gao","year":"2025","journal-title":"Tongji Yu Juece\/Stat. Decis."},{"key":"ref_4","first-page":"1","article-title":"From predictive methods to missing data imputation: An optimization approach","volume":"18","author":"Bertsimas","year":"2018","journal-title":"J. Mach. Learn. Res."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1198\/016214504000001745","article-title":"Functional data analysis for sparse longitudinal data","volume":"100","author":"Yao","year":"2005","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.18637\/jss.v045.i04","article-title":"Multiple Imputation by Chained Equations (MICE): Implementation in Stata","volume":"45","author":"Royston","year":"2011","journal-title":"J. Stat. Softw."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1137","DOI":"10.1002\/sim.4201","article-title":"A functional multiple imputation approach to incomplete longitudinal Data","volume":"30","author":"He","year":"2011","journal-title":"Stat. Med."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1080\/01621459.2021.1942011","article-title":"Elucidating age and sex-dependent association between frontal EEG asymmetry and depression: An application of multiple imputation in functional regression","volume":"117","author":"Ciarleglio","year":"2022","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"e331","DOI":"10.1002\/sta4.331","article-title":"Modern multiple imputation with functional data","volume":"10","author":"Rao","year":"2021","journal-title":"Stat"},{"key":"ref_10","first-page":"133","article-title":"Ultra-short-term load forecasting considering missing data in abnormal situations","volume":"49","author":"Li","year":"2025","journal-title":"Autom. Electr. Power Syst."},{"key":"ref_11","first-page":"388","article-title":"Research progress on abnormal and missing data processing methods in marine environmental monitoring","volume":"44","author":"Liu","year":"2025","journal-title":"J. Appl. Oceanogr."},{"key":"ref_12","first-page":"80","article-title":"Research on intelligent prediction of gas concentration in working face based on CS-LSTM","volume":"49","author":"Liang","year":"2022","journal-title":"J. Mine Saf. Environ. Prot."},{"key":"ref_13","first-page":"2653","article-title":"Review on wind power output prediction technology","volume":"16","author":"Wu","year":"2022","journal-title":"Comput. Sci. Explor."},{"key":"ref_14","first-page":"24","article-title":"Longitudinal data analysis using matrix completion","volume":"1050","author":"Kidzinski","year":"2018","journal-title":"Stat"},{"key":"ref_15","first-page":"5","article-title":"A non-negative functional matrix completion algorithm based on multi-view learning","volume":"38","author":"Xue","year":"2022","journal-title":"Stat. Decis."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kramer, O. (2013). K-nearest neighbors. Dimensionality Reduction with Unsupervised Nearest Neighbors, Springer.","DOI":"10.1007\/978-3-642-38652-7"},{"key":"ref_17","first-page":"63","article-title":"Comparison and application of time series data imputation methods for surface water quality monitoring","volume":"44","author":"Gao","year":"2024","journal-title":"Hydrology"},{"key":"ref_18","first-page":"1514","article-title":"Missing data: A comparison of neural network and expectation maximization techniques","volume":"93","author":"Nelwamondo","year":"2007","journal-title":"Curr. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/MC.2009.263","article-title":"Matrix factorization techniques for recommender systems","volume":"42","author":"Koren","year":"2009","journal-title":"Computer"},{"key":"ref_20","unstructured":"Yu, H.F., Rao, N., and Dhillon, I.S. (2016). Temporal regularized matrix factorization for high-dimensional time series prediction. Adv. Neural Inf. Process. Syst., 29, Available online: https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2016\/hash\/85422afb467e9456013a2a51d4dff702-Abstract.html."},{"key":"ref_21","first-page":"598","article-title":"Time series imputation method based on joint tensor completion and recurrent neural network","volume":"39","author":"He","year":"2024","journal-title":"Data Acquis. Process."},{"key":"ref_22","unstructured":"Cao, W., Wang, D., Li, J., Zhou, H., Li, L., and Li, Y. (2018). BRITS: Bidirectional recurrent imputation for time series. Adv. Neural Inf. Process. Syst., 31, Available online: https:\/\/proceedings.neurips.cc\/paper_files\/paper\/2018\/hash\/734e6bfcd358e25ac1db0a4241b95651-Abstract.html."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Carmona, C.U., Aubet, F.X., Flunkert, V., and Gasthaus, J. (2021). Neural contextual anomaly detection for time series. arXiv.","DOI":"10.24963\/ijcai.2022\/394"},{"key":"ref_24","unstructured":"Yoon, J.S., Jordon, J., and Schaar, M. (2018, January 10\u201315). GAIN: Missing data imputation using generative adversarial nets. Proceedings of the International Conference on Machine Learning, Stockholm, Sweden."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1146\/annurev-statistics-041715-033624","article-title":"Functional data analysis","volume":"3","author":"Wang","year":"2016","journal-title":"Annu. Rev. Stat. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Ullah, S., and Finch, C.F. (2013). Applications of functional data analysis: A systematic review. BMC Med. Res. Methodol., 13.","DOI":"10.1186\/1471-2288-13-43"},{"key":"ref_27","unstructured":"Yao, X.H. (2022). Research on Several Multivariate Functional Clustering Methods Based on Multi-View Learning. [Ph.D. Thesis, Lanzhou University of Finance and Economics]. Available online: https:\/\/library.lzufe.edu.cn\/asset\/detail\/0\/20471970033."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1214\/17-AOS1590","article-title":"Functional data analysis by matrix completion","volume":"47","author":"Descary","year":"2019","journal-title":"Ann. Stat."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Kong, S., Wang, X., Wang, D., and Wu, F. (2013, January 22\u201326). Multiple feature fusion for face recognition. Proceedings of the 2013 10th IEEE International Conference and Workshops on Automatic Face and Gesture Recognition (FG), Shanghai, China.","DOI":"10.1109\/FG.2013.6553718"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/j.neunet.2020.08.019","article-title":"Low-rank tensor constrained co-regularized multi-view spectral clustering","volume":"132","author":"Xu","year":"2020","journal-title":"Neural Netw."},{"key":"ref_31","first-page":"1","article-title":"Multi-view semi-supervised marked distribution learning","volume":"42","author":"Wu","year":"2025","journal-title":"Comput. Appl. Res."},{"key":"ref_32","first-page":"5357","article-title":"Air quality data restoration based on graph regularization and multi-view function matrix completion","volume":"44","author":"Gao","year":"2024","journal-title":"China Environ. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1016\/j.ins.2023.03.119","article-title":"Robust multi-view non-negative matrix factorization with adaptive graph and diversity constraints","volume":"634","author":"Li","year":"2023","journal-title":"Inf. Sci."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2620","DOI":"10.1109\/TCYB.2017.2747400","article-title":"Diverse non-negative matrix factorization for multiview data representation","volume":"48","author":"Wang","year":"2017","journal-title":"IEEE Trans. Cybern."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"105582","DOI":"10.1016\/j.knosys.2020.105582","article-title":"Multi-view clustering by non-negative matrix factorization with co-orthogonal constraints","volume":"194","author":"Liang","year":"2020","journal-title":"Knowl.-Based Syst."},{"key":"ref_36","first-page":"1548","article-title":"Graph regularized nonnegative matrix factorization for data representation","volume":"33","author":"Cai","year":"2010","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1016\/j.neucom.2019.12.054","article-title":"Deep graph regularized non-negative matrix factorization for multi-view clustering","volume":"390","author":"Li","year":"2020","journal-title":"Neurocomputing"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"15818","DOI":"10.1007\/s10489-022-04339-w","article-title":"Adaptive graph nonnegative matrix factorization with the self-paced regularization","volume":"53","author":"Yang","year":"2023","journal-title":"Appl. Intell."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.neucom.2017.10.023","article-title":"Dual regularized multi-view non-negative matrix factorization for clustering","volume":"294","author":"Luo","year":"2018","journal-title":"Neurocomputing"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1587","DOI":"10.1109\/TNNLS.2018.2868847","article-title":"Generalized uncorrelated regression with adaptive graph for unsupervised feature selection","volume":"30","author":"Li","year":"2018","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1198\/0003130042836","article-title":"A tutorial on MM algorithms","volume":"58","author":"Hunter","year":"2004","journal-title":"Am. Stat."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1023\/A:1017501703105","article-title":"Convergence of a block coordinate descent method for nondifferentiable minimization","volume":"109","author":"Tseng","year":"2001","journal-title":"J. Optim. Theory Appl."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Mucherino, A., Papajorgji, P.J., and Pardalos, P.M. (2009). K-nearest neighbor classification. Data Mining in Agriculture, Springer.","DOI":"10.1007\/978-0-387-88615-2"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1016\/j.csda.2012.12.004","article-title":"Model-based clustering for multivariate functional data","volume":"71","author":"Jacques","year":"2014","journal-title":"Comput. Stat. Data Anal."},{"key":"ref_45","unstructured":"Boor, C.D. (1978). A Practical Guide to Splines, Springer."},{"key":"ref_46","first-page":"106","article-title":"A functional data approach to missing value imputation and outlier detection for traffic flow data","volume":"2","author":"Chiou","year":"2014","journal-title":"Transp. B Transp. Dyn."},{"key":"ref_47","unstructured":"NOAA National Centers for Environmental Information (2024, October 01). Global Summary of the Day\u2014Weather Data, Available online: https:\/\/www.ncei.noaa.gov\/data\/global-summary-of-the-day\/archive."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/11\/793\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,30]],"date-time":"2025-10-30T05:15:32Z","timestamp":1761801332000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/11\/793"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,28]]},"references-count":47,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2025,11]]}},"alternative-id":["axioms14110793"],"URL":"https:\/\/doi.org\/10.3390\/axioms14110793","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,10,28]]}}}