Diversity Constraint and Adaptive Graph Multi-View Functional Matrix Completion

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.