引用本文: 段悦, 舒红, 胡泓达, 马国锐. 全球MODIS气温数据的修正秩克里金插值分析[J]. 武汉大学学报 ( 信息科学版), 2015, 40(8): 1036-1041.
DUAN Yue, SHU Hong, HU Hongda, MA Guorui. Globle Temperature MODIS Data Interpolation with Fixed Rank Kriging[J]. Geomatics and Information Science of Wuhan University, 2015, 40(8): 1036-1041.
 Citation: DUAN Yue, SHU Hong, HU Hongda, MA Guorui. Globle Temperature MODIS Data Interpolation with Fixed Rank Kriging[J]. Geomatics and Information Science of Wuhan University, 2015, 40(8): 1036-1041.

## Globle Temperature MODIS Data Interpolation with Fixed Rank Kriging

• 摘要: 高维数据插值是大数据分析的一个基本内容,传统克里金插值方法的计算复杂度,是O(n3),即随数据观测量的增大其计算复杂度以3次方速度增长,无法满足实时性应用需求强的克里金插值。修正秩克里金(FRK)方法通过矩阵分解降低大维矩阵的运算维数来简化矩阵计算,提高计算速度。在大数据分析背景下,借助FRK方法对全球MODIS气温数据进行统计建模并计算实现气温数据的插值分析。将其与普通克里金(OK)作对比实验,结果表明,相较于OK方法,FRK方法的插值精度并没有降低;在计算效率方面,使用FRK方法进行插值时,随数据量增大,耗时程度趋于缓慢平稳增长,而同一环境下的OK方法耗时随数据量增大呈指数增长趋势。相对于传统克里金方法,FRK能够在保证插值精度的同时显著降低其计算复杂度,缩短插值时间。

Abstract: High-dimensional data interpolation is a basic content of big data analysis.The computa-tional cost of traditional Kriging is of order n3,which means computational complexity grows as thethird power rate along with the increase number of the observations.So Kriging computing time canhardly meet real-time applications.Thus,Fixed Rank Kriging(FRK)rises in response.To achievehigh computing speed,it simplifies computational complexity by reducing the dimensions of large-di-mensional matrix.Under the background of big data analysis,this paper uses FRK to do the statisti-cal modeling and implement interpolation analysis with the global MODIS temperature.It also givesout Root-Mean-Square standardized which equals to 1.0003through the cross-validation method,indi-cating that FRK can provide high accurate interpolation result.On the side of computational efficien-cy,with increasing data,the computational cost of FRK increases as a slow and steady speed while or-dinary kriging tends to an exponential growth.The conclusion can be drawn from two points above,that is,FRK can reduce computational complexity and shorten interpolation time with high predictionaccuracy when compared with ordinary kriging.

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