Further developments of a fuzzy set map comparison approach

Fuzzy set map comparison offers a novel approach to map comparison.The approach is specifically aimed at categorical raster maps and applies fuzzy set techniques, accounting for fuzziness of location and fuzziness of category, to create a similarity map as well as an overall similarity statistic: the Fuzzy Kappa. To date, the calculation of the Fuzzy Kappa (or K-fuzzy) has not been formally derived, and the documented procedure was only valid for cases without fuzziness of category. Furthermore, it required an infinitely large, edgeless map. This paper presents the full derivation of the Fuzzy Kappa; the method is now valid for comparisons considering fuzziness of both location and category and does not require further assumptions. This theoretical completion opens opportunities for use of the technique that surpass the original intentions. In particular, the categorical similarity matrix can be applied to highlight or disregard differences pertaining to selected categories or groups of categories and to distinguish between differences due to omission and commission.     

Fuzzy set approach to assessing similarity of categorical maps

For the evaluation of results from remote sensing and high-resolution spatial models it is often necessary to assess the similarity of sets of maps. This paper describes a method to compare raster maps of categorical data. The method applies fuzzy set theory and involves both fuzziness of location and fuzziness of category. The fuzzy comparison yields a map, which specifies for each cell the degree of similarity on a scale of 0 to 1. Besides this spatial assessment of similarity also an overall value for similarity is derived. This statistic corrects the cell-average similarity value for the expected similarity. It can be considered the fuzzy equivalent of the Kappa statistic and is therefore called K_Fuzzy. A hypothetical case demonstrates how the comparison method distinguishes minor changes and fluctuations within patterns from major changes. Finally, a practical case illustrates how the method can be useful in a validation process.     

A spatial heterogeneity-based rough set extension for spatial data

When classical rough set (CRS) theory is used to analyze spatial data, there is an underlying assumption that objects in the universe are completely randomly distributed over space. However, this assumption conflicts with the actual situation of spatial data. Generally, spatial heterogeneity and spatial autocorrelation are two important characteristics of spatial data. These two characteristics are important information sources for improving the modeling accuracy of spatial data. This paper extends CRS theory by introducing spatial heterogeneity and spatial autocorrelation. This new extension adds spatial adjacency information into the information table. Many fundamental concepts in CRS theory, such as the indiscernibility relation, equivalent classes, and lower and upper approximations, are improved by adding spatial adjacency information into these concepts. Based on these fundamental concepts, a new reduct and an improved rule matching method are proposed. The new reduct incorporates spatial heterogeneity in selecting the feature subset which can preserve the local discriminant power of all features, and the new rule matching method uses spatial autocorrelation to improve the classification ability of rough set-based classifiers. Experimental results show that the proposed extension significantly increased classification or segmentation accuracy, and the spatial reduct required much less time than classical reduct.     

基于空间分析方法的中国区域差异研究

利用中国1952~2000年各省区的人口、土地利用和人均GDP等数据,采用空间分析方法对中国区域社会经济发展差异问题进行了实证研究。对中国大陆的几何中心、可利用土地、人口和GDP总量的空间中心计算表明,空间中心统计是一种简单有效刻画要素空间分布的方法。通过对中国各省区人均GDP的空间自相关系数Moran's I的计算,表明中国社会经济发展主要指标存在强烈的空间自相关,空间分析方法不失为一种深入理解区域经济格局及其变化的重要和有益的方法。对不同年度的Moran's I和Local Moran I的分析也揭示了中国区域经济格局的时空变化规律。     

AutoLogistic方法在土地利用格局模拟中的应用——以张家界市永定区为例

土地利用/ 土地覆被变化(LUCC) 是当前研究全球变化的重要内容, 而区域土地利用 格局模拟是LUCC 研究的核心内容之一。以张家界市永定区为研究单元, 根据由2005 年土地 利用现状图和数字高程模型数据源得到的土地利用、地形、河流以及道路等空间数据, 对区 域土地利用类型空间格局的空间自相关性特征进行了建模研究, 并通过在传统Logistic 模型 中引入描述空间自相关性的成份, 实现了能够考虑自相关性因素的回归分析模型 (AutoLogistic 模型), 同时应用该模型对区域土地利用格局进行了模拟和分析。结果显示, 通 过与没有考虑空间自相关性的回归模型(传统Logistic 模型) 相比较, 该模型显示了更好的拟 合优度和更高的拟合准确率(耕地、林地、建设用地及未利用地的ROC 值分别从0.851、 0.913、0.877 和0.852 提高到0.893、0.940、0.907 和0.863)。研究结果说明了基于 AutoLogistic 方法的土地利用格局的相关性建模在一定意义上是合理的。同时研究结果也可以 为永定区及其相似地区的土地利用规划决策提供更为科学的依据。     

Identifying strengths and limitations of pan-European forest cover maps through spatial comparison

Detailed and harmonized information on spatial forest distribution is an essential input for forest-related environmental assessments, in particular, for biomass and growing stock modeling. In the last years, several mapping approaches have been developed in order to provide such information for Europe in a harmonized way. Each of these maps exhibits particular properties and varies in accuracy. Yet, they are often used in parallel for different modeling purposes. A detailed spatial comparison seemed necessary in order to provide information on the advantages and limitations of each of these forest cover maps in order to facilitate their selection for modeling purposes.

This article confronts the high-resolution forest cover map recently developed by the Joint Research Centre for the year 2000 (FMAP2000) with previously existing maps for the same time period: the CORINE Land Cover 2000 (CLC2000) and the Calibrated European Forest Map 1996 (CEFM1996). The spatial comparison of these three maps was carried out based on forest proportion maps of 1 km derived from the original maps. To characterize differences according to biogeographic regions, two criteria were used: detail of thematic content within each map and local spatial agreement.

Concerning thematic content, CLC2000 displayed a surfeit of non-forested areas at the cost of low forest proportions, while FMAP2000 showed a more balanced distribution likely to preserve more detail in forest spatial pattern. Good spatial agreement was found for CLC2000 and FMAP2000 within about 70% of the study area, while only 50% agreement was found when compared with CEFM1996. The largest spatial differences between all maps were found in the Alpine and Mediterranean regions. Reasons for these might be different input data and classification techniques and, in particular, the calibration of CEFM1996 to reported national statistics.     

Modeling spatially non-stationary land use/cover change in the lower Connecticut River Basin by combining geographically weighted logistic regression and the CA-Markov model

Simulating land use/cover change (LUCC) and determining its transition rules have been a focus of research for several decades. Previous studies used ordinary logistic regression (OLR) to determine transition rules in cellular automata (CA) modeling of LUCC, which often neglected the spatially non-stationary relationships between driving factors and land use/cover categories. We use an integrated geographically weighted logistic regression (GWLR) CA-Markov method to simulate LUCC from 2001–2011 over 29 towns in the Connecticut River Basin. Results are compared with those obtained from the OLR-CA-Markov method, and the sensitivity of LUCC simulated by the GWLR-CA-Markov method to the spatial non-stationarity-based suitability map is investigated. Analysis of residuals indicates better goodness of fit in model calibration for geographically weighted regression (GWR) than OLR. Coefficients of driving factors indicate that GWLR outperforms OLR in depicting the local suitability of land use/cover categories. Kappa statistics of the simulated maps indicate high agreement with observed land use/cover for both OLR-CA-Markov and GWLR-CA-Markov methods. Similarity in simulation accuracy between the methods suggests that the sensitivity of simulated LUCC to suitability inputs is low with respect to spatial non-stationarity. Therefore, this study provides critical insight on the role of spatial non-stationarity throughout the process of LUCC simulation.     

Comparison of land cover maps using fuzzy agreement

A generic problem associated with different land cover maps that cover the same geographical area is the use of different legend categories. There may be disagreement in many areas when comparing different land cover products even though the legend shows the same or very similar land cover class. To capture the uncertainty associated with both differences in the legend and the difficulty in classification when comparing two land cover maps, expert knowledge and a fuzzy logic framework are used to map the fuzzy agreement. The methodology is illustrated by comparing the Global Land Cover 2000 data set and the MODIS global land cover product. Overall accuracy measures are calculated, and the spatial fuzzy agreement between the two land cover products is provided. This approach can be used to improve the overall confidence in a land cover product, since areas of severe disagreement can be highlighted, and areas can be identified that require further attention and possible re-mapping.     

A Review of “Turf Wars: Discourse,Diversity, and the Politics of Place”

The spatial correlation, or colocation, of two or more variables is a fundamental issue in geographical analysis but has received much less attention than the spatial correlation of values within a single variable, or autocorrelation. A recent paper by Leslie and Kronenfeld (2011) contributes to spatial correlation analysis in its development of a colocation statistic for categorical data that is interpreted in the same way as a location quotient, a frequently used measure in human geography and other branches of regional analysis. Geographically weighted colocation measures for categorical data are further developed in this article by generalizing Leslie and Kronenfeld's global measure as well as specifying a local counterpart for each global statistic using two different types of spatial filters: fixed and adaptive. These geographically weighted colocation quotients are applied to the spatial distribution of housing types to demonstrate their utility and interpretation.     

Using autologistic spatial models to simulate the distribution of land-use patterns in Zhangjiajie, Hunan Province

Nowadays, spatial simulation on land use patterns is one of the key contents of LUCC. Modeling is an important tool for simulating land use patterns due to its ability to integrate measurements of changes in land cover and the associated drivers. The conventional regression model can only analyze the correlation between land use types and driving factors, but cannot depict the spatial autocorrelation characteristics. Land uses in Yongding County, which is located in the typical karst mountain areas in northwestern Hunan province, were investigated by means of modeling the spatial autocorrelation of land use types with the purpose of deriving better spatial land use patterns on the basis of terrain characteristics and infrastructural conditions. Through incorporating components describing the spatial autocorrelation into a conventional logistic model, we constructed a regression model (Autologistic model), and used this model to simulate and analyze the spatial land use patterns in Yongding County. According to the comparison with the conventional logistic model without considering the spatial autocorrelation, this model showed better goodness and higher accuracy of fitting. The distribution of arable land, wood land, built-up land and unused land yielded areas under the ROC curves (AUC) was improved to 0.893, 0.940, 0.907 and 0.863 respectively with the autologistic model. It is argued that the improved model based on autologistic method was reasonable to a certain extent. Meanwhile, these analysis results could provide valuable information for modeling future land use change scenarios with actual conditions of local and regional land use, and the probability maps of land use types obtained from this study could also support government decision-making on land use management for Yongding County and other similar areas.     

Use of the weighted Kappa coefficient in classification error assessment of thematic maps

Abstract

The weighted Kappa coefficient is applied to the comparison of thematic maps. Weighted Kappa is a useful measure of accuracy when the map classes are ordered, or when the relative seriousness of the different possible errors may vary. The calculation and interpretation of weighted Kappa are demonstrated by two examples from forest surveys. First, the accuracy of thematic site quality maps classified according to an ordinal scale is assessed. Error matrices are derived from map overlays, and two different sets of agreement weights are used for the calculation. Weighted Kappa ranges from 0.34 to 0.55, but it does not differ significantly between two separate areas. Secondly, weighted Kappa is calculated for a tree species cover classified according to a nominal scale. Weights reflecting the economic loss for the forest owner due to erroneous data are used for the computation. The value of weighted Kappa is 0.56.     

基于空间自相关的闽台城镇建设用地分布研究

空间自相关是一种重要的空间统计方法, 用来检验某种地理现象或某一属性值的整体分 布状况, 判断此现象或属性值在空间上是否有聚集特性存在。本文利用2002 年ASTER 影像数据 作为遥感数据源提取闽台建设用地信息, 闽台建设用地密度的分布呈现出沿台湾海峡呈对称集 聚分布的态势。通过建设用地密度的空间自相关分析, 显示闽台建设用地空间分布整体上呈显著 的空间正相关, 集聚现象明显; 而在局部上则呈现出不同的空间结构形态, 建设用地高密度区主 要集聚分布在闽东南沿海的闽江口、厦门湾和泉州湾三大城镇密集区及台湾西部的台北、台中和 高雄三大都会区。这种空间相关关系的探讨对于认识闽台人口和社会经济的空间分布及福建省 建设用地未来的发展具有重要的意义, 也对福建省社会经济发展政策的制定提供重要参考依据。     

Spatial autocorrelation and data uncertainty in the American Community Survey: a critique

ABSTRACT

We argue that the use of American Community Survey (ACS) data in spatial autocorrelation statistics without considering error margins is critically problematic. Public health and geographical research has been slow to recognize high data uncertainty of ACS estimates, even though ACS data are widely accepted data sources in neighborhood health studies and health policies. Detecting spatial autocorrelation patterns of health indicators on ACS data can be distorted to the point that scholars may have difficulty in perceiving the true pattern. We examine the statistical properties of spatial autocorrelation statistics of areal incidence rates based on ACS data. In a case study of teen birth rates in Mecklenburg County, North Carolina, in 2010, Global and Local Moran’s I statistics estimated on 5-year ACS estimates (2006–2010) are compared to ground truth rate estimates on actual counts of births certificate records and decennial-census data (2010). Detected spatial autocorrelation patterns are found to be significantly different between the two data sources so that actual spatial structures are misrepresented. We warn of the possibility of misjudgment of the reality and of policy failure and argue for new spatially explicit methods that mitigate the biasedness of statistical estimations imposed by the uncertainty of ACS data.     

A Review of “Hot,Flat and Crowded: Why We Need a Green Revolution—And How It Can Renew America”

Based on a county-level Chinese industry survey data set, this article aims to extend the agglomeration literature by applying and comparing selected combination indexes of geographical concentration that incorporate both traditional indexes of inequality and measures of spatial autocorrelation at the global level and by applying and comparing a new measure, the focal location quotient (FLQ), to the local Moran's I, a commonly used local indicator of spatial association, at the county level. At the global level, the results show that the combination indexes used are generally effective for comparing the extent of geographical concentration across industries, and they could serve as useful dependent variables in modeling agglomeration effects across industries. At the local level, specific spatial patterns of production concentrations are identified for textiles, machinery, food manufacturing, and the electronics and telecommunication industries. FLQ tends to generate more generalized patterns than does the local Moran statistic. Mapping the local statistics is useful in supplementing the global measures, and those maps tend to support the results of the global combination indexes.     

中国土壤土层厚度的空间变异性特征

以全国第二次土壤普查的1627个土壤剖面资料为基础,在地质统计学和地理信息系统的支持下,以变异函数为基本工具初步分析中国土壤土层厚度的空间变异特征,并应用普通克里格法进行最优无偏线性插值,制作出分辨率为30km×30km的中国土壤土层厚度的空间分布图。结果表明:中国土壤土层厚度具有较好的可迁性和空间结构性特点,实验变异函数值的变化趋势基本上随着距离的增加逐渐上升,拟合变程在680km以上,土壤厚度的相关性可大于680km,土层厚度具有明显的块状或连续分布的特点     

基于不同尺度的中国区域经济差异

采用变异系数、泰尔指数、空间自相关和尺度方差等统计方法从地带、省级、地级和县级4 个尺度对1998-2009 年中国区域经济差异进行测度和空间格局比较分析。① 差异测度研究表明, 自1998 年以来, 中国区域经济差异在4 个尺度上均表现出扩大的趋势;省级、地级和县级单元人均GDP具有显著的空间自相关性, 其中地级和县级人均GDP的空间自相关程度呈扩大趋势。② 尺度方差及其分解研究表明, 尺度方差及其构成大小依次排列均为县级、地级、省级、地带, 即尺度越小, 尺度方差越大, 对区域经济差异的贡献份额也越大。③ 空间格局研究表明, 不同尺度区域经济空间关联格局总体相对稳定, HH类型集聚区大多分布于东部沿海地区, LL类型在中西部地区的大规模集聚是不同尺度区域经济空间自相关性的主要原因;各尺度显著空间关联类型对总体空间自相关和区域经济差异的影响各不相同。     

Testing local spatial autocorrelation using k-order neighbours

The analysis of local spatial autocorrelation for spatial attributes has been an important concern in geographical inquiry. In this paper, we propose a concept and algorithm of k-order neighbours based on Delaunay's triangulated irregular networks and redefine Getis and Ord's (1992) local spatial autocorrelation statistic as G_i(k) with weight coefficient w_ij(k) based on k-order neighbours for the study of local patterns in spatial attributes. To test the validity of these statistics, an experiment is performed using spatial data of the elderly population in Ichikawa City, Chiba Prefecture, Japan. The difference between the weight coefficients of the k-order neighbours and distance parameter to measure the spatial proximity of districts located in the city centre and near the city limits is found by Monte-Carlo simulation.     

中国区域经济发展收敛的空间计量分析

通过空间计量经济学经济收敛标准分析方法的扩展,就中国240 个地级及以上城市的经济增长收敛性展开讨论。运用Moran's I 探讨中国区域经济空间相关模式与集聚,发现1990-2007 年间人均GDP水平显示出强烈的全局正自相关,且局部空间结构相对稳定,各城市要脱离原来的集群有一定困难。文章指出收敛标准分析存在错误方程设定,空间计量分析方法是合适的。空间计量分析结果表明中国城市间存在绝对β收敛,与非空间模型相比收敛速度显著提高且可信,空间因素在区域经济增长与收敛过程中起到重要作用。但敏感性分析显示,绝对收敛的同一稳态以及在空间上并不稳健。从机制看,中国城市间同时存在新古典增长理论和新增长理论所强调的趋同机制。最后,对促进绝对收敛的区域政策进行了讨论,并提出通过模拟经济收敛过程,是判断区域政策有效性的重要工具。     

Variation in land cover classification due to individual interpreter assessment: a case study of farmland mapping in Norway

Visual interpretations of remote sensing images are required when producing land cover/use maps for management purposes. Human assessment is viewed as an advantage during the interpretation process. However, large mapping projects require several interpreters, and the possibility of inter-operator variability during classification work may affect map usage. In this study, five skilled interpreters from the Norwegian Forest and Landscape Institute independently updated the national Norwegian land resource dataset (AR5) in the same two study areas using the same orthophotos. Cross-tabulations were obtained, and class agreement, overall agreement, kappa agreement and fuzzy Kappa (K_fuzzy) were calculated. Most disagreements occurred in fragmented and complex landscapes, particularly with closely related classes. What can be regarded as an acceptable level of agreement depends on the intended map use and should be based on sensitivity tests exploring the effects of interpreter variation on specific applications of the map product. Finally, the threshold is a political decision based on thorough consideration of the economic and non-economic consequences of the variation tolerated in the maps produced.     

A Cartographic Analysis Using Spatial Filter Logistic Model Specifications for Implementing Mosquito Control in Kenya

Negative spatial autocorrelation (NSA), the tendency for dissimilar neighboring values to cluster on a map, may go undetected in statistical analyses of immature Anopheles gambiae s.l., a leading malaria mosquito vector in Sub-Saharan Africa. Unquantified NSA generated from an inverse variance-covariance matrix may generate misspecifications in an An. gambiae s.l. habitat model. In this research, we used an eigenfunction decomposition algorithm based on a modified geographic connectivity matrix to compute the Moran's I statistic, to uncover hidden NSA in a dataset of georeferenced An. gambiae s.l. habitat explanatory predictor variables spatiotemporally sampled in Malindi and Kisumu, Kenya. The Moran's I statistic was decomposed into orthogonal synthetic map patterns. Global tests revealed that |z_MC|s generated were less than 1.11 for the presence of latent autocorrelation. The algorithm captured NSA in the An. gambiae s.l. habitat data by quantifying all non-normal random variables, space-time heterogeneity, and distributional properties of the spatial filters.