Tensor-based Feature Analysis Method For Irregular Geographical Spatiotemporal Field Data

The rapid developments of the earth observation system and the global change simulation have accumulated a large amount of spatiotemporal field data,which have multi-dimensions,multi-attributes and irregular structures.Supporting the integrated expression,modeling and analysis of multi-dimensional irregular spatiotemporal data is a hot topic in geoscience analysis and GIS research.However,the corresponding spatiotemporal data representation and analysis methods are still based on traditional matrix theory,which makes it difficult to support the multi-dimensional attribute structure.Besides that,the other tensor-based the multi-dimensional rule cube model is still difficult to effectively deal with the irregular characteristics of spatiotemporal data.Basing on the algebraic expression of irregular spatiotemporal data,introducing the multi-dimensional expression structure and multi-dimensional fusion analysis model of irregular data,innovating the existing spatiotemporal field expression and analysis methods from the fundamental theory,and then designing feature analysis and structure extraction methods,is an effective way to break through the difficult problem of dimension expansion of existing spatiotemporal analysis methods,which can improve the existing spatiotemporal analysis ability of GIS,and promote the development of analytical GIS focused on complex data.This thesis focuses on the typical irregular spatiotemporal field data with the sparseness,dimensional asymmetry and structural heterogeneity,designs the feature detection method system of multi-dimensional irregular spatiotemporal field data from the perspectives of tensor-based irregular data expression,irregular feature measure space construction and the feature extraction.This paper analyzes the mapping mode from irregular spatiotemporal field data to the multidimensional expression structure of tensor,researches the organizational structure of spatiotemporal field data based on irregular tensor,and combs the relationship between tensor measure and geographic data feature representation,constructs the measurement space of irregular spatial-temporal field data based on tensor.On the basis of analyzing the traditional tensor decomposition model,this paper systematically studies the multi-mode decomposition strategy and calculation method of irregular tensor,and establishes the feature analysis and exploratory data analysis method of irregular spatiotemporal data under multi-dimensional fusion framework.On these basis,this paper designs an irregular spatiotemporal field data feature analysis system and conducts case verification with meteorological reanalysis data.The main research achievements are as follows.(1)On the foundation of multidimensional expression characteristics of tensor algebra,this paper constructs the mapping mode from irregular spatiotemporal field data to irregular tensor space,expands existing tensor operators such as dimension splitting,sparse calibration,and data partitioning for irregular tensor analysis and calculation.Utilizing the dimension expansion and dimension oriented calculation characteristics of tensor,irregular tensor expression structures are designed from the perspectives of multi-dimensional sparse tensor structure,tensor feature coefficients and hierarchical dimension tree structure.Additionally,the potential applications of these structures in the aspects of data analysis and data storage are analyzed.Finally,the irregular tensor structures,which can support the expression of irregular spatial temporal field with different types,are achieved.(2)Basing on the tensor expression of irregular spatiotemporal field data,the basic measures of tensor space are summarized,and the multidimensional operator description set composed of data size,order degree,linear characteristic direction and size are constructed.Then,this paper designs the measure methods of irregular characteristics of irregular spatiotemporal field data,and constructs a complete characteristic measure space.With this measure space,this paper studies the analytical framework of irregular spatiotemporal field data,proposes an analytical model of basic measure-data operation-irregular measure-data operation and analysis.The theoretical models of irregular extension of tensor decomposition are studied,and the data operation operators,such as the data index,retrieval and dimension segmentation are constructed to realize the construction of analytical framework based on irregular measure space.(3)With the multi-dimensional revelation characteristics of tensor decomposition,the multi-mode irregular tensor analysis strategies,which are composed of constrained tensor,subspace tensor and block tensor,are proposed for the typical irregular spatiotemporal field data.Utilizing three typical tensor decomposition models(CP?Tucker and hierarchical decomposition),a multi-scales structure analysis method for sparse spatiotemporal data,a multi-perspectives comprehensive analysis method for dimensionally asymmetric data and a local analysis method for structural heterogeneous data are constructed.Besides that,a sparse tensor solution algorithm independent with sparseness and missing data distribution is designed.And a feature aggregation operator,which is based on the asymmetric dimension of information entropy distribution,is constructed.Additionally,a local analysis method based on heterogeneity measure is proposed.Basing on the simplicity of the parameters and the clarity of the physical meaning of tensor decomposition models,the rules and strategies for parameter selection of the irregular tensor analysis model under the constraints of solving accuracy and running time are designed,and realizes the unified tensor analysis of the irregular multi-dimensional spatiotemporal field data(4)At last,a feature analysis system for irregular spatiotemporal field data is designed.This system constructs a unified interface and integrated processing for irregular data such as sparse,dimensional asymmetry and structural heterogeneity,and studies the main modules of data management,data analysis and data visualization.The data structure of irregular space-time field data is designed,and core algorithms such as sparse tensor decomposition,hierarchical tensor decomposition and reconstruction are constructed,and the core tensor decomposition algorithm is transformed in parallel computing.The geographic application of feature-oriented analysis,combined with the actual geo-meteorological reanalysis data,verifies the analytical capabilities of the system's multi-scale feature extraction for sparse tensor data,sparse tensor interpolation of multi-resolution,high-dimensional spatiotemporal field data compression and weak signal extraction of multi-view synthesis.The studies in this thesis show that,the tensor-based analysis methods of irregular spatiotemporal field data,can not only support the analysis of general spatiotemporal data,but also support the feature extraction and data management for irregular spatiotemporal field data that with sparse distribution,dimensional asymmetry and structural heterogeneity.The tensor-based algebraic expression of irregular spatiotemporal field data can support feature measure space construction that unified both basic and irregular measure.On the foundation of multidimensional fusion features revelation of tensor decompositions and dimension expansions of tensor operators,developing decomposition model and solution algorithms of multi-mode tensor with concise parameter and physical intuition for the irregular spatiotemporal field data,can unify the organization,feature analysis and application.