| With the economy’s growth in recent years,the environment significantly influences people’s lives,behaviors,and enterprise production and operation.Management scientists are payer closer attention to environmental factors in their studies.Therefore,there is a growing need for acquiring large-volume and high-quality data on environmental factors.It vastly increases the cost of accessing and pre-processing environmental data collected by the ground station.Moreover,ground stations’ distribution density might be thin in some regions,which leads to partial space coverage and low data granularity.Thus,the use of traditional ground-station-collected environmental data is limited in some intensive studies.Remote sensing imagery is a good measure of environmental factors,capturing their spatial-temporal distributions.It takes advantage of the high sampling frequency,the broad spatial coverage,the fine data granularity,and the low cost.Hence,validating remote sensing imagery in a forecasting model may increase its accuracy and timeliness.However,there are still challenges in modeling remote sensing imagery.In many cases,the forecasting model includes both image data and structured data from multiple sources.Thus,data sampling frequencies may be different,resulting in a mixed-frequency phenomenon.The quantitative relationship between model variables can be non-linear,and the sample size is often limited.This paper aims to solve the challenges above and build a forecast model based on the remote sensing imagery mixed-frequency data and remote sensing imagery co-frequency data with soft set theory and deep learning methods.Specifically,it contains three major parts: the algebraic representation of remote sensing imagery,the hybrid modeling of remote sensing image data and structured panel data,and the forecasting model based on remote sensing imagery mixed frequency data.They are carried out in the following order:First,the algebraic representation method for remote sensing imagery and spatial-temporal variables is proposed.The soft set theory focuses on the algebraic representation and operation of parameterized sets of a universe.It is widely applied in forecasting model based on heterogeneous data.This paper regards remote sensing images as observations of spatial-temporal variables,structured data as observations of numeric variables,and spatial regions as subsets of the spatial domain.Therefore,the paper defines the spatial-temporal soft set and the spatial-temporal fuzzy soft set,the algebraic representation of spatial regions based on them,and studies their mathematical properties.Afterward,their mathematical operations are defined,and the algebraic representation of remote sensing images and spatial-temporal variables is proposed.This part is the foundation of the following paper.Second,the study on the soft set forecasting model based on co-frequency data is conducted.Co-frequency data can be regarded as a special case of the mixed-frequency data when the sampling ratios of different variables equal to 1.The forecasting model based on co-frequency data is the foundation of the forecasting model based on mix-frequency data.Thus,it is a major part of this paper.This part aims to solve the data heterogeneity problem in the forecasting model.The soft set forecasting model based on co-frequency data is proposed on the basis of the results in the first part.Then,the model is proved to be consistent under certain premises.The model is implemented with the soft tensor and the convolutional neural network.This part ends with two experiments of predicting the cancer mortality rate and the health expenditure based on heterogeneous co-frequency data.The experimental results show that the proposed model is valid in forecasting with relatively small samples.Third,the study on the soft set forecasting model based on mixed-frequency data is conducted.This part studies the imagery and structured data’s mixed-frequency phenomenon based on current studies in mixed-frequency data and the above research results.The soft set forecasting model based on mixed-frequency data is proposed in this part,and its statistical properties are studied.Then,the model is implemented based on dynamic image processing methods.A hybrid feature selection algorithm for the model is proposed based on the feature information fuzzy soft set.The proposed model is verified to be effective in forecasting cancer mortality rate and residential health expenditure with mixed-frequency heterogeneous data.In conclusion,the soft set forecasting models proposed in the paper are robust enough to validate remote sensing imagery data with small sample data.The study contributes to the soft set theory,image processing theory,and mixed-frequency data forecasting methods.The proposed models can be implemented for real-time forecasting in practical.The examples of predicting cancer mortality rate and health expenditure can be useful in health information system management,medical insurance pricing,and government budget decisions.The proposed models are also useful in other fields. |
