基于多尺度最小二乘支持向量机优化的克里金插值方法

doi:10.3724/SP.J.1047.2017.01001

地球信息科学学报 ›› 2017, Vol. 19 ›› Issue (8): 1001-1010.doi: 10.3724/SP.J.1047.2017.01001

• 地球信息科学理论与方法 • 下一篇

基于多尺度最小二乘支持向量机优化的克里金插值方法

车磊^1,²(), 王海起^1,^*(), 费涛¹, 闫滨¹, 刘玉¹, 桂丽¹, 陈冉¹, 翟文龙¹

1. 中国石油大学（华东）地球科学与技术学院,青岛 266580
2. 中国电波传播研究所青岛分所,青岛 266107

收稿日期:2016-10-31 修回日期:2017-06-20 出版日期:2017-08-20 发布日期:2017-08-20
通讯作者: 王海起 E-mail:cheleiyouxiang@163.com;wanghaiqi@upc.edu.cn
作者简介:
作者简介：车磊（1990-）,男,硕士生,研究方向为地图制图学与地理信息工程。E-mail: cheleiyouxiang@163.com
基金资助:
国家自然科学基金项目(41471322);山东省自然科学基金项目(ZR2012DM010)

Kriging Interpolation Method Optimized by Multi-scale Least Squares Support Vector Machine

CHE Lei^1,²(), WANG Haiqi^1,^*(), FEI Tao¹, YAN Bin¹, LIU Yu¹, GUI Li¹, CHEN Ran¹, ZHAI Wenlong¹

1. School Of Geosciences, China University of Petroleum (East China), Qingdao 266580, China
2. China Research Institute of Radiowave Propagation Qingdao Branch, Qingdao 266107, China;

Received:2016-10-31 Revised:2017-06-20 Online:2017-08-20 Published:2017-08-20
Contact: WANG Haiqi E-mail:cheleiyouxiang@163.com;wanghaiqi@upc.edu.cn

摘要/Abstract

摘要：

克里金插值方法根据待估位置点、已知样本数据点的位置关系和区域化变量的空间相关性,实现空间加权估计,满足估计的无偏性和最优性。传统方法理论模型形状固定且选择具有人为主观性,无法反映空间数据的变化趋势及其空间多尺度特征。本文为解决上述问题,提出了一种基于多尺度最小二乘支持向量机优化的克里金插值方法,此方法为拟合实验变异函数提供了一种新的思路。从实际样本数据的变化趋势出发,采用最小二乘支持向量机拟合实验变异函数,并利用不同尺度小波核反映不同尺度下的空间变化。最后,实验环节包括模拟和应用,模拟主要验证经多尺度最小二乘支持向量机优化后插值方法的科学有效性以及准确性,应用主要研究青岛市PM_2.5浓度时空分布特征,为城市生态科学防护及控制提供理论依据。结果表明,基于多尺度最小二乘支持向量机优化的克里金插值方法能够更好地刻画变异函数,反映不同尺度下的空间变化细节,从而在一定程度上提高插值的精度,是一种可选的克里金插值方法。

关键词: 克里金插值, 最小二乘支持向量机, 变异函数, 多尺度, 小波核函数

Abstract:

Kriging interpolation method realizes spatial weighted estimation that meets the unbiasedness and optimality according to the position relationship between the estimated location sites and the known sample sites and regionalized variable spatial correlation. Traditional theoretical model shape is fixed and chosen with subjectivity, which can't reflect the changing trend and multi-scale spatial characteristics. The choice of scale and the treatment of scale effects also need to be considered. To solve the problems above, we propose a method of kriging interpolation optimized by multi-scale least squares support vector machine (LS-SVM), which provides a new idea for fitting experimental variogram. Starting from the changing trend of the actual sample data, least squares support vector machine fits experimental variogram and the results conform to the spatial changing trend of data itself. Secondly, the wavelet kernel as the LS-SVM kernel function, parameters can be adjusted according to different parts of the nuclear, which is flexible and variable. Finally, the multi-scale wavelet kernel using wavelet multi-resolution characteristics, can reflect the different details of spatial changes, to avoid the single scale LS-SVM ignoring the spatial details of the problem. Followed that, the experiment includes simulation and application. Experimental simulation mainly verifies scientific validity and accuracy by the optimized interpolation of multi-scale least squares support vector machine. Meanwhile, experimental application research of PM_2.5 concentrations of temporal and spatial distribution provides the theoretical basis for city ecological protection and controlling. Final results show that kriging interpolation algorithm optimized by multi-scale least squares support vector machine is superior to the traditional method and single scale optimized kriging interpolation algorithm. It would be better to depict the variation function and reflect the different scales of spatial changes in details to further improve the accuracy of the interpolation to some extent, which is an optional kriging interpolation method.

Key words: kriging interpolation, least squares support vector machine, variogram, multi-scale, wavelet kernel function

车磊, 王海起, 费涛, 闫滨, 刘玉, 桂丽, 陈冉, 翟文龙. 基于多尺度最小二乘支持向量机优化的克里金插值方法[J]. 地球信息科学学报, 2017, 19(8): 1001-1010.DOI:10.3724/SP.J.1047.2017.01001

CHE Lei,WANG Haiqi,FEI Tao,YAN Bin,LIU Yu,GUI Li,CHEN Ran,ZHAI Wenlong. Kriging Interpolation Method Optimized by Multi-scale Least Squares Support Vector Machine[J]. Journal of Geo-information Science, 2017, 19(8): 1001-1010.DOI:10.3724/SP.J.1047.2017.01001

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类别	球状模型	指数模型	高斯模型	单尺度 LS-SVM（RBF）	单尺度 LS-SVM (wave)	二尺度 LS-SVM (wave)
MAE	39.43	40.86	110.46	39.81	39.09	38.54
RMSE	56.21	57.33	154.82	56.78	55.97	55.70

指标类别	高斯模型	指数模型	球状模型	单尺度 LS-SVM（RBF）	单尺度 LS-SVM (wave)	二尺度 LS-SVM (wave)
MAE	14.41	12.52	12.54	12.47	12.46	12.42
RMSE	17.66	15.73	15.77	15.57	15.57	15.31

指标类别	高斯模型	指数模型	球状模型	单尺度 LS-SVM（RBF）	单尺度 LS-SVM (wave)	二尺度 LS-SVM (wave)
MAE	3.62	3.47	3.49	3.56	3.44	3.44
RMSE	4.54	4.20	4.27	4.58	4.23	4.19

基于多尺度最小二乘支持向量机优化的克里金插值方法

Kriging Interpolation Method Optimized by Multi-scale Least Squares Support Vector Machine

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