基于因子分析的混合像元分解方法研究
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摘要
遥感数据是对连续分布空间事物电磁辐射信息的离散记录，由于混合像元的存在，传统的像元级遥感分类难以达到应用需求，混合像元组分分解可获取像元内各地物端元的丰度，对于提高遥感信息提取精度及深度具有重要意义。
因子分析是对多样品、多变量观测数据进行综合分析解释的一种多元分析方法，其基本思想是通过对变量或样品间相似矩阵的研究，将错综复杂的多个变量或样品归结为少数的因子，在信息损失极少的前提下分析原始变量或样品的组合关系，进而求取具有主导作用的本质因素。
本文在深入研究因子分析模型和线性光谱混合模型的原理及其数理关联的基础上，利用兴城地区多光谱遥感影像数据，分别采用Q型因子分析方法和线性光谱分解方法进行混合像元组分分解，对比二者解混结果，重点分析了因子得分、因子负载的专题意义及典型地物景观的因子组分特征，并确定了因子负载的制图方法。论文主要研究成果如下：
1．将因子分析方法用于混合像元分解是避免由纯净端元选择不当引起影响混合像元分解结果精度的一种新方法。其中，Q型的因子得分代表变量与因子的相关性，与混合光谱模型中的端元光谱相对应；Q型的因子负载代表样品与因子的相关性，与线性光谱混合模型中的组分丰度相对应。
2．多光谱遥感数据进行Q型因子分析的流程为：首先利用代表性样品-变量数据矩阵求解因子负载和因子得分，而后将因子得分应用于全部像元样品而得到因子负载。
3．Q型因子负载与线性光谱混合像元分解对比结果显示，各类典型地物的相似系数（夹角余弦）为0.6396～0.9985，平均为0.894，表明二者具有较高的相似程度。同时，通过对典型地物/景观的因子组分特征的分析，可实现基于因子负载的深度信息挖掘，包括地物类别的细分以及异常信息提取。
4．本研究对占信息总量99.085%的前三个因子进行了物理意义解释，分别定义为土壤、植被、水体因子。根据旋转后的因子负载矩阵，海水、水库在水体因子上均具有最大负载，针叶林、阔叶林在植被因子上均具有最大负载，草被灌木、耕地、城镇和道路在土壤因子上均具有最大负载。
Remote sensing data records electromagnetic radiation information ofcontinuous distribution things in space. Because of the existence of mixed pixels, thetraditional remote sensing classification is difficult to meet the application needs,spectral unmixing can obtain end member abundance in the mix-pixel, so spectralunmixing has important significance in improving the accuracy and depth of remotesensing application.
Factor analysis is a multivariate analysis method which makes compre-hensive analysis on observed data of multiple variables and multiple samples, its basicidea is based on the study about the similarity matrix of variable or sample, and sumsthe perplexing many variable or samples up to a few factors, and makes analysis onthe combination relation of variable of sample under the premise of the least amountof information loss, then gets the leading role essential factors.
This paper studies both the model of factor analysis and linear spectral mixingmodel and their relationship, for the ETM data of the region of Xingcheng area, andthe spectrum of the mixture is decomposed by the use of factor analysis model andlinear spectral mixing model, and compares the two results. In the paper, I emphasizesthe geological significance of factor loadings and factor scores, and analysis the factorcomponent of typical ground landscape, at last confirm the mapping method of factorloadings imagine. The main conclusions are as follows:
First, the model of factor analysis and linear spectral mixing are most intimatelyassociated with numerical relationship. Among them, factor scores in Q-mode factoranalysis represents the correlation of the variables and the factors, and it correspondsto the end members of linear spectral mixing model; factor loadings in Q-mode factoranalysis represents the correlation of the samples and the factors, and it corresponds tothe abundance.
Second, based on ETM data, Q-mode factor analysis should be carried onfollowed the steps below: solve the factor loadings and factor scores using of therepresentative sample-variable data matrix, and calculate the factor loadings of thefull scene according to the got factor score.
Third, analysised the two results we can see, the similarity coefficient of allkinds of typical features is0.6396-0.9985, with an average of0.894. It shows that the factor analysis can be used for spectral unmixing, at the same time, after the analysisof the components characteristics of the typical features/landscape, it can realizeDepth information mining based on factor loading, including both the classification ofthe terrain category and the altered information extraction.
The last, this study shows the physical significance explanation of the first threefactors which contains99.085%of the total information, and defines as soil、vegetation and water factor. According to the rotation factor loading matrix, water、reservior both have the maximum factor loading in the water factor, and coniferousforest、broad-leaved forest has the maximum factor loading in the vegetation factors,and grass shrubs、farmland、town and roads have the maximum factor loading in thesoil factor.
因子分析是对多样品、多变量观测数据进行综合分析解释的一种多元分析方法，其基本思想是通过对变量或样品间相似矩阵的研究，将错综复杂的多个变量或样品归结为少数的因子，在信息损失极少的前提下分析原始变量或样品的组合关系，进而求取具有主导作用的本质因素。
本文在深入研究因子分析模型和线性光谱混合模型的原理及其数理关联的基础上，利用兴城地区多光谱遥感影像数据，分别采用Q型因子分析方法和线性光谱分解方法进行混合像元组分分解，对比二者解混结果，重点分析了因子得分、因子负载的专题意义及典型地物景观的因子组分特征，并确定了因子负载的制图方法。论文主要研究成果如下：
1．将因子分析方法用于混合像元分解是避免由纯净端元选择不当引起影响混合像元分解结果精度的一种新方法。其中，Q型的因子得分代表变量与因子的相关性，与混合光谱模型中的端元光谱相对应；Q型的因子负载代表样品与因子的相关性，与线性光谱混合模型中的组分丰度相对应。
2．多光谱遥感数据进行Q型因子分析的流程为：首先利用代表性样品-变量数据矩阵求解因子负载和因子得分，而后将因子得分应用于全部像元样品而得到因子负载。
3．Q型因子负载与线性光谱混合像元分解对比结果显示，各类典型地物的相似系数（夹角余弦）为0.6396～0.9985，平均为0.894，表明二者具有较高的相似程度。同时，通过对典型地物/景观的因子组分特征的分析，可实现基于因子负载的深度信息挖掘，包括地物类别的细分以及异常信息提取。
4．本研究对占信息总量99.085%的前三个因子进行了物理意义解释，分别定义为土壤、植被、水体因子。根据旋转后的因子负载矩阵，海水、水库在水体因子上均具有最大负载，针叶林、阔叶林在植被因子上均具有最大负载，草被灌木、耕地、城镇和道路在土壤因子上均具有最大负载。
Remote sensing data records electromagnetic radiation information ofcontinuous distribution things in space. Because of the existence of mixed pixels, thetraditional remote sensing classification is difficult to meet the application needs,spectral unmixing can obtain end member abundance in the mix-pixel, so spectralunmixing has important significance in improving the accuracy and depth of remotesensing application.
Factor analysis is a multivariate analysis method which makes compre-hensive analysis on observed data of multiple variables and multiple samples, its basicidea is based on the study about the similarity matrix of variable or sample, and sumsthe perplexing many variable or samples up to a few factors, and makes analysis onthe combination relation of variable of sample under the premise of the least amountof information loss, then gets the leading role essential factors.
This paper studies both the model of factor analysis and linear spectral mixingmodel and their relationship, for the ETM data of the region of Xingcheng area, andthe spectrum of the mixture is decomposed by the use of factor analysis model andlinear spectral mixing model, and compares the two results. In the paper, I emphasizesthe geological significance of factor loadings and factor scores, and analysis the factorcomponent of typical ground landscape, at last confirm the mapping method of factorloadings imagine. The main conclusions are as follows:
First, the model of factor analysis and linear spectral mixing are most intimatelyassociated with numerical relationship. Among them, factor scores in Q-mode factoranalysis represents the correlation of the variables and the factors, and it correspondsto the end members of linear spectral mixing model; factor loadings in Q-mode factoranalysis represents the correlation of the samples and the factors, and it corresponds tothe abundance.
Second, based on ETM data, Q-mode factor analysis should be carried onfollowed the steps below: solve the factor loadings and factor scores using of therepresentative sample-variable data matrix, and calculate the factor loadings of thefull scene according to the got factor score.
Third, analysised the two results we can see, the similarity coefficient of allkinds of typical features is0.6396-0.9985, with an average of0.894. It shows that the factor analysis can be used for spectral unmixing, at the same time, after the analysisof the components characteristics of the typical features/landscape, it can realizeDepth information mining based on factor loading, including both the classification ofthe terrain category and the altered information extraction.
The last, this study shows the physical significance explanation of the first threefactors which contains99.085%of the total information, and defines as soil、vegetation and water factor. According to the rotation factor loading matrix, water、reservior both have the maximum factor loading in the water factor, and coniferousforest、broad-leaved forest has the maximum factor loading in the vegetation factors,and grass shrubs、farmland、town and roads have the maximum factor loading in thesoil factor.
引文
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[3]柏延臣,王劲峰.遥感信息的不确定性研究[M],北京:地质出版社,2003.
[4] Charles Ichoku, Arnon Karnieli. A review of mixture modeling techniques for sub-pixel landcover estimation[J].Remote Sensing Reviews,1996,13:161-186.
[5]朱述龙.基于混合像元的遥感图像分类技术[J].解放军测绘学院学报,1995,12(4):226-229．
[6]陶秋香.非线性混合光谱模型及植被高光谱遥感分类若干问题研究[D].青岛:山东科技大学,2004.
[7] J.Bowles, P.Palmadesso, J.Antoniades, et al. Use of filter vectors in hyperspectral dataanalysis[J]. Proc.SPIE,1995,2552:148-157.
[8] J C.Harsanyi, C I Chang. Hyperspectral Image Classification and Dimensionality Reduction:An Orthogonal Subspace Projection Approach. IEEE Trans Geosci Remote Sens,1994,7,(32):779-785.
[9]李新蕊.主成分分析、因子分析、聚类分析的比较与应用[J].山东教育学院学报,2007,6:23-26.
[10]李卫东.应用多元统计分析[M].北京:北京大学出版社,2008.
[11] Richard A.Johnson,DeanW.Wiehern著,陆漩译,实用多元统计分析,清华大学出版社,2001.4.
[12] Renner R M. A constrained least-squares subroutine for adjusting negative estimated elementconcentrations to zero[J]. Computers&Geosciences,1993,19(9):1351-1360.
[13]罗红霞,龚健雅.线性和非线性光谱混合模型模拟土壤、植被混合光谱的效果分析[J].测绘通报,2005,5:5-10
[14] Gregory P. Asner, David B. Lobell. A Biogeophysical Approach for Automated SWIRUnmixing of Soils and Vegetation[J]. Remote Sensing of Environment,2000.74:99–112.
[15] G. P. ASNER and K. B. HEIDEBRECHT. Spectral unmixing of vegetation, soil and drycarbon cover in arid regions: comparing multispectral and hyperspectral observations[J].International Journal of Remote Sensing,2002,23(19):3939-3958.
[16] Braun Matthias, Herold Martin. Mapping imperviousness using NDVI and linear spectralunmixing of ASTER data in the Cologne-Bonn region (Germany)[J].SPIE10th InternationalSymposium on Remote Sensing,2003,9,8-12.
[17] Conghe Song. Spectral mixture analysis for sub-pixel vegetation fractions in the urbanenvironment: How to incorporate endmember variability?[J]. Remote Sensing ofEnvironment,2005,95:248-263.
[18] Ruiliang Pu, Peng Gong. Spectral mixture analysis for mapping abundance of urban surfacecomponents from the Terra/ASTER data[J]. Remote Sensing of Environment.2008,112:939-954.
[19] Fernando López Pe a, Juan Luís Crespo. Unmixing Low-Ratio Endmembers inHyperspectral Images Through Gaussian Synapse ANNs[J]. IEEE,2010,59(7):1834-1840.
[20] G I Metternicht, A Fermont. Estimating Erosion Surface Features by Linear MixtureModeling[J]. Remote Sensing of Environment,1998,64:254-265.
[21]陶秋香,陶华学,张连蓬,等.线性混合光谱模型在植物高光谱遥感分类中的应用研究[J].勘察科学技术,2004(1):21-24.
[22]肖青,闻建光,柳钦火,等.混合光谱分解模型提取水体叶绿素含量的研究[J].遥感学报,2007,4,10(4):559-567.
[23]应天玉,李明泽,范文义.基于IDL的混合光谱分解模型的实现[J].东北林业大学学报,2007,11,35(11):70-73.
[24]岳文泽,吴次芳.基于混合光谱分解的城市不透水面分布估算[J].遥感学报,2007,11,11(6):914-922.
[25]陈健飞,林征,陈颖彪.基于高光谱线性混合光谱分解识别人工地物[J].应用基础与工程科学学报,2009,17(2):206-218.
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