Seamless multivariate affine error-in-variables transformation and its application to map rectification

Affine transformation that allows the axis-specific rotations and scalars to capture the more transformation details has been extensively applied in a variety of geospatial fields. In tradition, the computation of affine parameters and the transformation of non-common points are individually implemented, in which the coordinate errors only of the target system are taken into account although the coordinates in both target and source systems are inevitably contaminated by random errors. In this article, we propose the seamless affine error-in-variables (EIV) transformation model that computes the affine parameters and transforms the non-common points simultaneously, importantly taking into account the errors of all coordinates in both datum systems. Since the errors in coefficient matrix are involved, the seamless affine EIV model is nonlinear. We then derive its least squares iterative solution based on the Euler–Lagrange minimization method. As a case study, we apply the proposed seamless affine EIV model to the map rectification. The transformation accuracy is improved by up to 40%, compared with the traditional affine method. Naturally, the presented seamless affine EIV model can be applied to any application where the transformation estimation of points fields in the different systems is involved, for instance, the geodetic datum transformation, the remote sensing image matching, and the LiDAR point registration.     

Introducing scale parameters for adjusting area objects in GIS based on least squares and variance component estimation

In this paper, a least‐squares based cadastral parcel area adjustment in geographic information systems (GIS) is developed based on (1) both the areas and coordinates being treated as observations with errors; and (2) scale parameters being introduced to take the systematic effect into account in the process of cadastral map digitization. The area condition equation for cadastral parcel considerations of scale parameters and geometric constraints is first constructed. The effects of the scale error on area adjustment results are then derived, and statistical hypothesis testing is presented to determine the significance of the scale error. Afterwards, Helmert's variance component estimation based on least‐squares adjustment using the condition equation with additional parameters is proposed to determine the weight between the coordinate and area measurements of the parcel. Practical tests are conducted to illustrate the implementation of the proposed methods. Four schemes for solving the inconsistencies between the registered areas and the digitized areas of the parcels are studied. The analysis of the results demonstrates that in the case of significant systematic errors in cadastral map digitization, the accuracies of the adjusted coordinates and areas are improved by introducing scale parameters to reduce the systematic error influence in the parcel area adjustment. Meanwhile, Helmert's variance component estimation method determines more accurate weights of the digitized coordinates and parcel areas, and the least‐squares adjustment solves the inconsistencies between the registered areas and the digitized areas of the parcels.     

基于NDVI与偏最小二乘回归的荒漠化地区植被覆盖度高光谱遥感估测

以星载高光谱影像Hyperion为数据源,系统比较了NDVI与偏最小二乘回归（PLS）估测荒漠化地区植被覆盖度的能力,模型的建立（n=46）与独立检验所用样本（n=10）均为地面实测数据。研究结果表明,基于星载高光谱数据的NDVI与PLS模型可以有效地估测荒漠化地区植被覆盖度。相比于宽波段NDVI（RMSEP=10.5618）及基于803.3/671.02 nm计算的标准高光谱NDVI（RMSEP=8.3863）,选择特定高光谱波段（823.65/701.55 nm）构建的NDVI预测植被覆盖度的误差明显较低（RMSEP=6.5189）。基于高光谱所有波段原始反射率、一阶导数及包络线去除光谱的PLS回归模型表现,要明显优于仅利用两个波段信息的NDVI,其中基于原始反射率的PLS回归模型表现最佳,RMSEP为4.4998,约为因变量平均值的23%。     

Geographically neural network weighted regression for the accurate estimation of spatial non-stationarity

ABSTRACT

Geographically weighted regression (GWR) is a classic and widely used approach to model spatial non-stationarity. However, the approach makes no precise expressions of its weighting kernels and is insufficient to estimate complex geographical processes. To resolve these problems, we proposed a geographically neural network weighted regression (GNNWR) model that combines ordinary least squares (OLS) and neural networks to estimate spatial non-stationarity based on a concept similar to GWR. Specifically, we designed a spatially weighted neural network (SWNN) to represent the nonstationary weight matrix in GNNWR and developed two case studies to examine the effectiveness of GNNWR. The first case used simulated datasets, and the second case, environmental observations from the coastal areas of Zhejiang. The results showed that GNNWR achieved better fitting accuracy and more adequate prediction than OLS and GWR. In addition, GNNWR is applicable to addressing spatial non-stationarity in various domains with complex geographical processes.     

Positional uncertainty in manually digitized map data

Digital map coordinates represent the locations of real world entities. As such, differences can exist between the ‘tru’ and digital database coordinates of those entities. This paper reports on a statistical characterization of positional error in manually-digitized and map-registered point data, the relative contribution of point type and operator to digitization error, and the effects of map media type on the positional uncertainty associated with registration.

Manually-digitized point data were collected by four operators from mylar and paper maps. Point locations for a number of different feature types were sampled from United States Geological Survey (USGS) 1:24 000 scale maps. Linear models were used to estimate the variance components due to among-operator, map media, point type and registration effects. The statistical distribution of signed distance deviations for manually-digitized data was leptokurtic relative to a random normal variate. Unsigned deviations averaged 0-054 mm. Squared distance deviations were not different from a Chi-square random variate. Variance components indicate that among-operator differences in positional uncertainty were large and statistically significant, while differences among point type were small and non-significant. Signed distance deviations associated with a first-order afhne followed a normal distribution. Unsigned distance deviations associated with a first-order affinc transformation averaged 0068mm, and squared distance deviations were distributed as a Chi-square. Differences in transformation accuracy were not related to type of map media.     

Diatom-based inference models and reconstructions revisited: methods and transformations

Different calibration methods and data manipulations are being employed for quantitative paleoenvironmental reconstructions, but are rarely compared using the same data. Here, we compare several diatom-based models [weighted averaging (WA), weighted averaging with tolerance-downweighting (WAT), weighted averaging partial least squares, artificial neural networks (ANN) and Gaussian logit regression (GLR)] in different situations of data manipulation. We tested whether log-transformation of environmental gradients and square-root transformation of species data improved the predictive abilities and the reconstruction capabilities of the different calibration methods and discussed them in regard to species response models along environmental gradients. Using a calibration data set from New England, we showed that all methods adequately modelled the variables pH, alkalinity and total phosphorus (TP), as indicated by similar root mean square errors of prediction. However, WAT had lower performance statistics than simple WA and showed some unusual values in reconstruction, but setting a minimum tolerance for the modern species, such as available in the new computer program C² version 1.4, resolved these problems. Validation with the instrumental record from Walden Pond (Massachusetts, USA) showed that WA and WAT reconstructed most closely pH and that GLR reconstructions showed the best agreement with measured alkalinity, whereas ANN and GLR models were superior in reconstructing the secondary gradient variable TP. Log-transformation of environmental gradients improved model performance for alkalinity, but not much for TP. While square-root transformation of species data improved the performance of the ANN models, they did not affect the WA models. Untransformed species data resulted in better accordance of the TP inferences with the instrumental record using WA, indicating that, in some cases, ecological information encoded in the modern and fossil species data might be lost by square-root transformation. Thus it may be useful to consider different species data transformations for different environmental reconstructions. This study showed that the tested methods are equally suitable for the reconstruction of parameters that mainly control the diatom assemblages, but that ANN and GLR may be superior in modelling a secondary gradient variable. For example, ANN and GLR may be advantageous for modelling lake nutrient levels in North America, where TP gradients are relatively short.     

RECENT DEVELOPMENTS IN MULTIVARIATE CALIBRATION

With the goal of understanding global chemical processes,environmental chemists have some of the mostcomplex sample analysis problems.Multivariate calibration is a tool that can be applied successfully inmany situations where traditional univariate analyses cannot.The purpose of this paper is to reviewmultivariate calibration,with an emphasis being placed on the developments in recent years.The inverseand classical models are discussed briefly,with the main emphasis on the biased calibration methods.Principal component regression(PCR)and partial least squares(PLS)are discussed,along with methodsfor quantitative and qualitative validation of the calibration models.Non-linear PCR,non-linear PLSand locally weighted regression are presented as calibration methods for non-linear data.Finally,calibration techniques using a matrix of data per sample(second-order calibration)are discussed briefly.     

地理数据线性回归中的稳健估计方法

在线性回归中，常用最小二乘估计求线性方程的回归系数。但最小二乘估计受异常值影响较大，当样本数据存在异常值时，估计出的回归系数会产生较大偏差。稳健估计是最小二乘估计的改进，能在不排除异常数据的情况下，达到减弱异常数据对结果的影响。利用稳健估计提出黄土地区沟谷密度与侵蚀量的回归方程，并和最小二乘估计得到的回归方程比较，前者具有更回归效果。     

基于改进植被指数土壤水分遥感反演

以渭-库绿洲为例,基于Landsat8 OLI遥感数据,考虑到短波红外特征与土壤水分有很好的关联,将短波红外波段引入可见光-近红外波段构成的传统植被指数中,旨在建立新的植被指数监测土壤水分。基于改进前后共8种植被指数,通过灰色关联分析（GRA）筛选出3种高关联度植被指数,再用偏最小二乘回归（PLSR）进行建模,然后用该模型对研究区土壤水分反演,并对其空间分布格局进一步分析。结果显示：（1）在传统植被指数的基础上引入信息量较大的短波红外,可大幅度降低植被指数间的VIF,消除其多重共线性。（2）通过GRA分析可知,改进后的植被指数与土壤水分之间的关联度均要高于传统植被指数。（3）通过GRA分析筛选出3种高关联度植被指数建立得到精度较高,稳定性较好的PLSR模型,并反演研究区土壤水分分布状况,土壤水分总体上至西向东,由北到南降低,然而土壤水分最小值主要分布在绿洲—荒漠交错带,使得交错带成为“生态裂谷”。研究表明：将短波红外波段引入到可见光-近红外植被指数中,建立的新植被指数可获得较好的土壤水分空间分布反演结果。     

A new methodology for measuring coastline recession using buffering and non‐linear least squares estimation

Coastline recession is one of the best indicators of coastal erosion. Three methods for computing coastline recession – the baseline approach, the dynamic segmentation approach and the area‐based approach – have been used, each of which has one or more drawbacks. To overcome these problems, a new methodology for measuring coastline recession is proposed, using buffering and non‐linear least squares estimation. The proposed method was compared with the three existing methods with respect to two simulated cases and two real coastlines. Test results confirmed that the new method is more reliable than the three other methods, all of which are susceptible to variability of recession, scale, number of line segments, length of coastlines and direction of the baseline. The proposed method, incorporating two physically meaningful values – magnitude and variability of coastline recession according to the mean and standard deviation of coastline offsets, respectively – presents itself as an effective alternative method of assessing coastline recession.     

MLR和PLSR的沙壤土盐分含量光谱检测对比研究

为了快速有效检测南疆地区典型土壤（沙壤土）的盐分含量变化,利用光谱仪和电导仪测得南疆阿拉尔市红枣种植区盐渍土近红外高光谱和电导率数据,基于7种不同光谱预处理方法和2种特征波长选择算法,分别建立多元线性回归（MLR）和偏最小二乘回归（PLSR）的土壤盐分监测模型。结果表明：7种预处理方法中,归一化,多元散射,变量标准化和一阶导数能够有效提高土壤盐分的预测模型精度。基于多元逐步回归（SMR）波长选择方法的多元线性回归（SMLR）模型的R_val²>0.948 9,RPD>6.294 9,RMSEP<0.435 6;基于连续投影算法（SPA）的多元线性回归（SPA-MLR）模型的R_val²>0.956 8,RPD>6.922 1,RMSEP<0.361 6,预测结果要优于偏最小二乘回归（PLSR）模型,其中基于归一化处理后的SMLR和SPA-MLR的预测精度最为理想,分别为R_val²=0.979 2,RPD=9.907 8,RMSEP=0.287 6和R_val²=0.980 5,RPD=10.50,RMSEP=0.278 3,而且筛选的特征波长较少。说明归一化是更有效的光谱预处理方法,多元线性回归（MLR）更适合建立南疆典型沙壤土盐分含量的预测模型。     

Diatom-based water chemistry reconstructions from northern Sweden: a comparison of reconstruction techniques

The diatom composition in surface sediments from 119 northern Swedish lakes was studied to examine the relationship with lake-water pH, alkalinity, and colour. Diatom-based predictive models, using weighted-averaging (WA) regression and calibration, partial least squares (PLS) regression and calibration, and weighted-averaging partial least squares (WA-PLS) regression and calibration, were developed for inferences of water chemistry conditions. The non-linear response between the diatom assemblages and pH and alkalinity was best modelled by weighted-averaging methods. The lowest prediction error for pH was obtained using weighted averaging, with or without tolerance downweighting. For alkalinity there was still some information in the residual structure after extracting the first weighted-averaging component, which resulted in a slight improvement of predictions when using a two component WA-PLS model. The best colour predictions were obtained using a two component PLS model. Principal component analysis (PCA) of the prediction errors, with some characteristics of the training set included as passive variables, was performed to compare the results for the different alkalinity predictive models. The results indicate that calibration techniques utilizing more than one component (PLS and WA-PLS) can improve the predictions for lakes with diatom taxa that have broad tolerances. Furthermore, we show that WA-PLS performs best compared with the other techniques for those lakes that have a high relative abundance of the most dominant taxa and a corresponding low sample heterogeneity.     

THE PERFORMANCE OF LEAST SQUARES AND ROBUST REGRESSION IN THE CALIBRATION OF ANALYTICAL METHODS UNDER NON-NORMAL NOISE DISTRIBUTIONS

By means of Monte Carlo simulations a comparison has been made between ordinary least squaresregression and robust regression. The robust regression procedure is based on the Huber estimate and iscomputed by means of the iteratively reweighted least squares algorithm. The performance of bothprocedures has been evaluated for estimation of the parameters of a calibration function and fordetermination of the concentration of unknown samples. The influence of the distributionalcharacteristics skewness and kurtosis has been studied, and the number of measurements used forconstructing the calibration curve has also been taken into account, Under certain conditions robustregression offers an advantage over least squares regression.     

Accuracy assessment of georectified aerial photographs: Implications for measuring lateral channel movement in a GIS

Aerial photographs are commonly used to measure planform river channel change. We investigated the sources and implications of georectification error in the measurement of lateral channel movement by testing how the number (6–30) and type (human versus natural landscape features) of ground-control points (GCPs) and the order of the transformation polynomial (first-, second-, and third-order) affected the spatial accuracy of a typical georectified aerial photograph. Error was assessed using the root-mean-square error (RMSE) of the GCPs as well as error in 31 independent test points. The RMSE and the mean and median values of test-point errors were relatively insensitive to the number of GCPs above eight, but the upper range of test-point errors showed marked improvement (i.e., the number of extreme errors was reduced) as more GCPs were used for georectification. Using more GCPs thus improved overall georectification accuracy, but this improvement was not indicated by the RMSE, suggesting that independent test-points located in key areas of interest should be used in addition to RSME to evaluate georectification error.The order of the transformation polynomial also influenced test-point accuracy; the second-order polynomial function yielded the best result for the terrain of the study area. GCP type exerted a less consistent influence on test-point accuracy, suggesting that although hard-edged points (e.g., roof corners) are favored as GCPs, some soft-edged points (e.g., trees) may be used without adding significant error. Based upon these results, we believe that aerial photos of a floodplain landscape similar to that of our study can be consistently georectified to an accuracy of approximately ± 5 m, with 10% chance of greater error. The implications of georectification error for measuring lateral channel movement are demonstrated with a multiple buffer analysis, which documents the inverse relationship between the size of the buffers applied to two channel centerlines and the magnitude of change detected between them. This study demonstrates the importance of using an independent test-point analysis in addition to the RSME to evaluate and treat locational error in channel change studies.     

A ROBUST PLS PROCEDURE

A robust partial least squares(PLS)regression algorithm is developed.This is achieved by substitutionof the univariate regression steps in the iterative PLS2 algorithm by a robust alternative.The anglebetween loading vectors from both perturbed and unperturbed solutions is used as a measure ofrobustness.By means of a perturbation study on a structure-activity data set,it is demonstrated thatthe stability of the robust method is superior to standard PLS.     

土壤粒径空间预测方法研究综述

土壤粒径（砂粒、粉粒和黏粒）是各种陆表过程和生态系统服务评估等模型的关键参数。作为一种土壤成分数据,土壤粒径的空间预测方法有和为1（或100%）等特殊要求,其空间分布精度受预测方法影响较大。本文针对土壤粒径相较于其他土壤属性的特殊性,提出了土壤粒径空间预测方法框架,综述了土壤粒径数据变换、空间插值和精度验证等系列方法,总结了提升土壤粒径空间预测精度的各种途径,包括通过有效的数据变换改善数据分布、结合数据分布特点选择合适的预测方法、结合辅助变量提升制图精度和分布合理性、使用混合模型提升插值精度、使用多成分联合模拟模型提升预测的系统性等。最后,提出了今后土壤粒径空间预测方法研究的未来方向,包括从考虑数据变换原理和机制角度改善数据分布、发展多成分联合模拟模型和高精度曲面建模方法,以及引入土壤粒径函数曲线并与随机模拟结合等。     

长江经济带经济增长与资源环境的协同效应及其驱动力分析

基于人口、资源、环境与经济、社会协调发展的视角,引入生态系统服务价值评价方法构建资源环境成本核算模型以及经济增长与资源环境的协调发展度、相对协调发展度模型,对长江经济带区域经济增长与资源环境的协同效应进行分析、并以偏最小二乘回归方法对其驱动因素进行解析。计算出1983–2012年长江经济带7省2市资源环境成本由4736.55×10^12元攀升至15 359.45×10^12元、占全国同期比重由31.1%降至19.7%,协调发展度由0.295升至1.506,各时段相对协调发展度均高于全国平均水平;1983、1993、2003年3个时段驱动长江经济带区域经济增长与资源环境协调发展的主要因素是资源环境成本相对较低,研究区对推动我国经济、社会协调发展均做出较大贡献;2012年以后随着我国第一、三产业增加值整体上持续增加,长江经济带的比较优势趋于弱化。未来,长江经济带有关省市应积极完善主体功能区规划实施细则,抓住机遇持续推进产业结构调整,通过各个层面实施生态恢复补偿、提高资源利用效率、降低环境损失成本等提高经济发展质量,进一步促进区域经济增长与资源、环境协调发展。     

The Sinusoidal Projection: A New Importance in Relation to Global Image Data

The reprojection of image data causes the loss or duplication of original pixel values. This research investigated the feasibility of using the sinusoidal projection for global image database construction. Specifically, reprojection accuracies were tested with geographic latitude and longitude coordinates, and the Hammer‐Aitoff, Eckert IV, Mollweide, and sinusoidal projections. Reprojections between these five global projections and the Universal Transverse Mercator (UTM) projection and referencing system were performed using fifty‐four sample datasets. A statistical analysis of categorical accuracy, a measure describing the omission of pixel values during reprojection, was conducted. Geographic coordinates and the sinusoidal projection both showed very high accuracy rates (100.0 percent and 99.5 percent respectively) when sample datasets were reprojected from UTM. The geographic coordinates, however, showed very low accuracy (65.3 percent) when sample datasets were reprojected to the UTM projection, while the sinusoidal projection showed the highest accuracy (98.4 percent). The results strongly suggest that the sinusoidal projection is very accurate and efficient for building global image databases.     

仿射变换法在航天MSS数据变换中的应用

航天MSS数据数字纠正、MSS图象复盖地图资料、遥感图象配置区界的模拟试验等结果表明,仿射变换法可分别满足平地与山区1:25万和1:100万的地理制图的精度要求。     

Estimation of pH optima and tolerances of diatoms in lake sediments by the methods of weighted averaging,least squares and maximum likelihood,and their use for the prediction of lake acidity

Ecological optima and tolerances with respect to autumn pH were estimated for 63 diatom taxa in 47 Finnish lakes. The methods used were weighted averaging (WA), least squares (LS) and maximum likelihood (ML), the two latter methods assuming the Gaussian response model.WA produces optimum estimates which are necessarily within the observed lake pH range, whereas there is no such restriction in ML and LS. When the most extreme estimates of ML and LS were excluded, a reasonably close agreement among the results of different estimation methods was observed. When the species with unrealistic optima were excluded, the tolerance estimates were also rather similar, although the ML estimates were systematically greater.The parameter estimates were used to predict the autumn pH of 34 other lakes by weighted averaging. The ML and LS estimates including the extreme optima produced inferior predictions. A good prediction was obtained, however, when prediction with these estimates was additionally scaled with inverse squared tolerances, or when the extreme values were removed (censored). Tolerance downweighting was perhaps more efficient, and when it was used, no additional improvement was gained by censoring. The WA estimates produced good predictions without any manipulations, but these predictions tended to be biased towards the centroid of the observed range of pH values.At best, the average bias in prediction, as measured by mean difference between predicted and observed pH, was 0.082 pH units and the standard deviation of the differences, measuring the average random prediction error, was 0.256 pH units.