高维时空场数据的层次张量建模与分析方法

项目名称： 高维时空场数据的层次张量建模与分析方法

项目编号： No.41471319

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 天文学、地球科学

项目作者： 袁林旺

作者单位： 南京师范大学

项目金额： 100万元

中文摘要： 地理时空场数据是表征具有连续时空变化的地理对象及地理过程的主要形式，具有海量及高维等特点。从数学基础上寻找高维时空场数据的代数化表达，进而有效利用抽象数学的运算空间和计算算子进行算法构造与优化是提升高维时空场数据表达与分析能力的重要途径。本项目引入具有严格数学理论基础的张量结构，借鉴函数逼近的思想，研究基于维度树结构的层次张量分解与重构算法，实现与计算机表达与检索结构一致的多维地理时空数据集数据组织与建模表达方法，并实现对高维时空场数据的压缩存储。在此基础上，基于层次张量的维度融合表达和维度分层结构，研究面向时空过程的动态数据的张量分解与重构的计算模式，构建普适的、多维融合的高维地理时空场数据分析与高效计算方法，实现传统地理分析方法在层次张量模型下的对接与重构，从而为复杂地理时空数据的组织存储、特征检索与高效计算提供基础理论支撑，并为复杂地理时空数据的结构特征、演化行为分析提供方法支撑。

中文关键词： 海量数据；时空场；分层张量；数据建模；地理信息系统

英文摘要： Geographic spatio-temporal field data is the main form of representing the geographic objects and geographic processes with continuous spatio-temporal variation. Finding the algebraic expression for high dimensional spatio-temporal field data from mathematic basic and constructing and optimizing the algorithms using effectively the calculating space and operators of abstract mathematics is the important way to improve the expression, storage, retrieval and analysis of high-dimension spatio-temporal field data. This project directs at the expression, organization, retrieval and analysis needs of high dimensional geographic spatio-temporal field data. The tensor structure based on strict mathematic theory is introduced to research the tensor dimension tree-based hierarchical tensor decomposition model and further construct the data organization, compression storage, effective retrieval and modeling expression methods of multi-dimensional geographic spatio-temporal dataset based on hierarchical tensor, which borrow ideas from the function approximation. The spatio-temporal process oriented tensor decomposition and reconstruction calculating model of dynamic data is studied to build the universal and multidimensional syncretic analyzing and calculating methods for high-dimension geographic spatio-temporal field data and realize the docking and reconstructing of conventional geographic analyzing methods in hierarchical tensor model, which is based on dimensional syncretic expression and dimensional layered structure of hierarchical tensor. It provides the basic theory support for the organization, dynamic storage and feature retrieval of complicated geographic spatio-temporal data, and it also supplies the methods support for the structural feature and evolution behavior analyzing of complex geographic spatio-temporal data.

英文关键词： Massive Data;Spatial-temporal Field;Hierarchical Tensor;data modeling;GIS