一种面向异质性时空场数据分析的张量模型

A Tensor Model for Heterogeneous Spatial-Temporal Field Data Analysis

面向高维数据分析的张量方法在应用于异质性时空数据时,易造成特征估计偏差问题,而建立从局部到整体的特征分析框架有助于提升异质性张量分析的准确性,但该分析框架构建涉及不同维度、不同结构时空数据对象,进而会增加时空数据模型的复杂度。该文从张量模型的特性出发,利用张量算子分别建立张量子空间和张量块的数据组织与表达结构,以时空场数据的面向对象表达为基础,定义适用于异质性时空场数据的类与操作,并将该数据模型应用于异质性时空场数据分析方法设计。基于气象再分析数据的实验表明:该文的数据模型可有效支撑高维时空场数据的统一组织与表达,在支撑异质性时空场数据的特征提取方面较经典的张量分析方法具有更高的准确性。

When applying to heterogeneous spatio-temporal field data,high dimensional tensor analysis methods can result in estimation biases.Establishment of a local-to-global feature analysis framework can improve the accuracies of tensor analysis,yet the framework will increase the complexity of data model due to the involvement of data objects with distinct dimensions and data structures.In this paper,we start from the characteristics of the tensor model to establish the data organization and expression structure for tensor subspace and tensor block using tensor operators.Based on the object-oriented representation of spatial-temporal field data,we define the classes and operations of data model which are applicable to heterogeneous spatial-temporal field data,and further design the data analysis methods with the model.The validation results based on meteorological reanalysis data show that the data model can effectively support a unified organization and representation of heterogeneous spatial-temporal field data and outperforms traditional tensor-based methods in supporting the feature extraction of dimensionally asymmetric and structurally heterogeneous spatial-temporal field data.