Estimating Population Attribute Values in a Table: “Get Me Started in” Iterative Proportional Fitting

Iterative proportional fitting (IPF) is a technique that can be used to adjust a distribution reported in one data set by totals reported in others. IPF is used to revise tables of data where the information is incomplete, inaccurate, outdated, or a sample. Although widely applied, the IPF methodology is rarely presented in a way that is accessible to nonexpert users. This article fills that gap through discussion of how to operationalize the method and argues that IPF is an accessible and transparent tool that can be applied to a range of data situations in population geography and demography. It offers three case study examples where IPF has been applied to geographical data problems; the data and algorithms are made available to users as supplementary material.     

Performance of shape indices and classification schemes for characterising perceptual shape complexity of building footprints in GIS

Shape characterisation is important in many fields dealing with spatial data. For this purpose, numerous shape analysis and recognition methods with different degrees of complexity have so far been developed. Among them, relatively simple indices are widely used in spatial applications, but their performance has not been investigated sufficiently, particularly for building footprints (BFs). Therefore, this article focuses on BF shape characterisation with shape indices and classification schemes in a GIS environment. This study consists of four phases. In the first phase, the criteria for BF shape complexity were identified, and accordingly, benchmark data was constructed by human experts in three shape complexity categories. In the second phase, 18 shape indices were selected from the literature and automatically computed in GIS. The performance of these indices was then statistically assessed with histograms, correlation matrix and boxplots, and consequently four indices were found to be appropriate for further investigation. In the third phase, two new indices (Equivalent Rectangular index and Roughness index) were proposed with the objective to measure some BF shape characteristics more efficiently. The proposed indices also were found to be appropriate with the same statistical assessment procedures. In the final phase, BF shape complexity categories were created with the pairs of six appropriate indices and four choropleth mapping classification schemes (equal intervals, natural break, standard deviation, and custom) in GIS. The performance of the index–scheme pairs was assessed against the benchmark data. The findings demonstrated that both new indices and two of the selected indices (Convexity and Rectangularity) delivered higher performance. The custom classification scheme was found more ideal to reveal absolute shape complexity with the index value ranges derived from the boxplots while the other classification schemes were more appropriate to reveal relative shape complexity.     

Entropy-Maximizing and the Iterative Proportional Fitting Procedure

In a recent paper, Wong outlined the benefits of the IPF procedure, which he claimed had received little attention from geographers. This follow-up paper introduces a large literature, ignored by Wong, which uses that procedure, but within the context of another mathematical model. Its application is illustrated with new analyses of recent voting patterns in Great Britain.     

Combining Sample and Census Data in Small Area Estimates: Iterative Proportional Fitting with Standard Software*

The combination of detailed sample data with less detailed but fully enumerated marginal subtotals is the focus of a wide range of research. In this article we advocate careful modeling of sample data, followed by Iterative Proportional Fitting (IPF). The modeling aims to estimate accurately the interaction or odds ratios of complex tables, which is information not contained in the marginal subtotals. IPF ensures consistency with the subtotals. We advance this work in three practical ways. First, we show that detailed small‐area estimates of both counts and proportional distributions usually gain accuracy by combining data for larger areas containing the small areas, and we illustrate the multilevel framework to achieve these estimates. Second, we find that a general classification or socioeconomic typology of the small areas is even more associated with the within‐area interactions than is membership of the larger area. Third, we show how the Statistical Package for the Social Sciences (SPSS) can be used for IPF in any number of dimensions and with any structure of constraining marginal subtotals. Throughout, we use an example taken from the 1991 U.K. Census. These data allow us to evaluate various methods combining 100 percent tabulations and the Samples of Anonymised Records.     

Response to Commentaries by Craig Campbell,Lyle Courtney and Walter G. Hardwick,and John E. Chappell,Jr.

Abstract

The combination of detailed sample data with less detailed but fully enumerated marginal subtotals is the focus of a wide range of research. In this article we advocate careful modeling of sample data, followed by Iterative Proportional Fitting (IPF). The modeling aims to estimate accurately the interaction or odds ratios of complex tables, which is information not contained in the marginal subtotals. IPF ensures consistency with the subtotals. We advance this work in three practical ways. First, we show that detailed small-area estimates of both counts and proportional distributions usually gain accuracy by combining data for larger areas containing the small areas, and we illustrate the multilevel framework to achieve these estimates. Second, we find that a general classification or socioeconomic typology of the small areas is even more associated with the within-area interactions than is membership of the larger area. Third, we show how the Statistical Package for the Social Sciences (SPSS) can be used for IPF in any number of dimensions and with any structure of constraining marginal subtotals. Throughout, we use an example taken from the 1991 U.K. Census. These data allow us to evaluate various methods combining 100 percent tabulations and the Samples of Anonymised Records.

     

The selection of internal migration models for European regions

"A full multiregional projection model requires migration data that are simultaneously classified by age and gender and region of origin and region of destination. Except for a very small number of regions, these data requirements are so high that aggregation of the data (which is equivalent to simplification of the model) is called for. This paper investigates the extent to which the full internal migration matrix can be simplified without seriously affecting the performance of the resulting multiregional model. Using IPF (iterative proportional fitting) methods, a log-linear analysis of alternative model specifications is made, using data for Italy, the Netherlands and the UK....A reasonable balance between goodness-of-fit and parsimony is found for the model in which time interacts with the main effects only (i.e. with age/sex, with origin and with destination)."     

小波基及其参数对遥感影像融合图像质量的影响

IHS和小波变换结合的融合方法已成为多源遥感影像信息聚合的有效途径,但小波基与小波分解层数等参数对影像融合质量影响的很多细节需进一步研究。该文以SPOT遥感影像为数据,在Matlab软件环境下进行小波簇、不同序号小波基及分解层数的图像融合,用信息熵、平均梯度和标准偏差3指标对融合图像的质量进行评价。结论如下:第1层小波分解的融合图像质量差异不大;其余小波分解层数下融合影像的质量因小波基而异,如coif5s、ym5、dmey对小波分解层数不敏感,db1、bior3.1则具有分段响应的敏感特征,其中,rbio3.1在小波分解层数为4时,融合图像失真;不同簇的小波基对融合图像质量的影响也各异。结果表明,小波基等参数的选取直接影响到遥感影像融合的效果。     

THE LOCATIONAL CONCENTRATION OF GROUP HOMES IN TORONTO1

This paper contributes to the ongoing debate on the concentration of social service facilities within North American cities. The location quotient and the coefficient of localization are applied to data on Adult Services, Children's Services and psychiatric group homes (residential care facilities) in Metropolitan Toronto. Results demonstrate a high degree of localization in all three categories, particularly the psychiatric, and could be used in the formulation of placement policies to relieve certain areas of the inner city of the social and economic pressures created by group home concentration.     

Implementation of the Iterative Proportion Fitting Algorithm for Geostatistical Facies Modeling

In geostatistics, most stochastic algorithm for simulation of categorical variables such as facies or rock types require a conditional probability distribution. The multivariate probability distribution of all the grouped locations including the unsampled location permits calculation of the conditional probability directly based on its definition. In this article, the iterative proportion fitting (IPF) algorithm is implemented to infer this multivariate probability. Using the IPF algorithm, the multivariate probability is obtained by iterative modification to an initial estimated multivariate probability using lower order bivariate probabilities as constraints. The imposed bivariate marginal probabilities are inferred from profiles along drill holes or wells. In the IPF process, a sparse matrix is used to calculate the marginal probabilities from the multivariate probability, which makes the iterative fitting more tractable and practical. This algorithm can be extended to higher order marginal probability constraints as used in multiple point statistics. The theoretical framework is developed and illustrated with estimation and simulation example.     

基于作息空间思想的人口统计数据空间化方法

探讨了基于作息空间思想的人口统计数据空间化方法。定义居住和工作的活动空间范围为作息空间,并结合土地利用类型数据和泰森多边形构建了作息空间,以作息空间人口密度作为人口空间分布的表达方式。对辽宁省2005年人口统计数据进行了实例分析,精度优于传统的面积权重内插法,结果的地图渲染能够表现受自然因素和社会经济因素影响的人口分布特征。该方法不涉及复杂的权重计算过程,也可以避免主观因素的干扰,简单易行,有较强的实用性。     

Web data mining for automatic inventory of geohazards at national scale

In this study, we present a fully automated procedure to analyze online news using data mining techniques. It is then used to compile and continually update a geohazard database. The procedure is based on new technologies that publish news on the internet, i.e., the news is analyzed, georeferenced and attributed to a category of geohazards (the current categories are landslides, floods and earthquakes). A continuous flow of georeferenced events is established to populate and update the geodatabase automatically and in near-real time. We tested the procedure for 2 years at a national scale, creating a geodatabase containing more than 20,000 news items concerning geohazards that occurred in Italy. This procedure enables continuous feedback from events in the real world, such that information about geohazards can be fully exploited rapidly (compared to traditional techniques based on remote sensing, field surveys and historical inventories).     

圣保罗大都市区社会空间分异研究——多元统计方法在城市连绵区的应用

空间数据和地理信息系统在城市规划和决策中应用的重要性日见凸显。主要原因在于：重要的人口数据和社会变动经常表现出一定的空间特性,这种特性可以通过空间分析和统计方法被认识和解释。应用多元分析的空间分类方法编制圣保罗大都市区社会分异地图并进行相关分析。研究的主要数据来自2000年巴西全国人口普查,其中包括了圣保罗大都市的所有行政区和39个自治市的21774个人口普查区。为了把都市连绵区从数据全集中分离出来,我们采用混合技术进行互补分析,即在2000年4月30日的陆地卫星7号图像中绘制一个个多边形,这些被识别出来的多边形就是人口普查区。然后,通过目视解译出假彩色多边形集合。应用空间分类评分程序将这些多边形分成五类,并建立人口普查区的数目、覆盖的面积和都市连绵区之间的关系。这种多元分析方法是基于变量的均衡化来生成易于用分级统计图描述平均值,以促进可视化和后续的空间分布分析。基于多元分析的空间分类方法研究,清楚地展现了圣保罗大都市最重要的社会特征,也说明城市社会地图方法和多元分析的空间分类方法在大都市区的管理、公共政策规划和复杂决策中具有重要的应用价值。     

Developing parallel procedures for line simplification

Abstract

This paper explores parallel programming issues that are relevant to the efficient implementation of spatial data handling procedures on current parallel computers through sample implementations of the Douglas line simplification procedure. Using source code-equivalent implementations of the Douglas procedure, this paper analyses the performance characteristics of two parallel implementations, compares their performance characteristics to those of a sequential implementation, and identifies critical components of the parallel implementations that enhance or inhibit their overall performance values. The results of this work show that the selection of appropriate interprocessor communication and load balancing strategies are crucial to obtaining large speedup values over comparable sequential implementations.     

移动GIS中GML数据压缩技术研究

目前利用GML实现多源异构移动GIS空间数据资源整合时,存在数据压缩的"瓶颈"问题。在分析移动计算环境中GML数据压缩特性(语义同构、时空拓扑特性保持以及自适应网络流量动态调整压缩结构)的基础上,利用语义编码构造整体空间,并通过语义空间聚类与小波变换分析,构建移动GIS中GML数据压缩模型。实验表明:该压缩模型在压缩比、直接读取压缩数据以及在无线网络上传输压缩数据3方面均具有较好的性能,对移动GIS数据共享集成的理论与技术研究具有一定的参考价值。     

Automated classifications of topography from DEMs by an unsupervised nested-means algorithm and a three-part geometric signature

An iterative procedure that implements the classification of continuous topography as a problem in digital image-processing automatically divides an area into categories of surface form; three taxonomic criteria–slope gradient, local convexity, and surface texture–are calculated from a square-grid digital elevation model (DEM). The sequence of programmed operations combines twofold-partitioned maps of the three variables converted to greyscale images, using the mean of each variable as the dividing threshold. To subdivide increasingly subtle topography, grid cells sloping at less than mean gradient of the input DEM are classified by designating mean values of successively lower-sloping subsets of the study area (nested means) as taxonomic thresholds, thereby increasing the number of output categories from the minimum 8 to 12 or 16. Program output is exemplified by 16 topographic types for the world at 1-km spatial resolution (SRTM30 data), the Japanese Islands at 270 m, and part of Hokkaido at 55 m. Because the procedure is unsupervised and reflects frequency distributions of the input variables rather than pre-set criteria, the resulting classes are undefined and must be calibrated empirically by subsequent analysis. Maps of the example classifications reflect physiographic regions, geological structure, and landform as well as slope materials and processes; fine-textured terrain categories tend to correlate with erosional topography or older surfaces, coarse-textured classes with areas of little dissection. In Japan the resulting classes approximate landform types mapped from airphoto analysis, while in the Americas they create map patterns resembling Hammond's terrain types or surface-form classes; SRTM30 output for the United States compares favorably with Fenneman's physical divisions. Experiments are suggested for further developing the method; the Arc/Info AML and the map of terrain classes for the world are available as online downloads.     

Comparing English,Mandarin, and Russian hydrographic and terrain categories

The paper compares hydrographic and terrain categories in the geospatial data standards of the United States, Taiwan, and Russian Federation where the dominant languages used are from different language families. It aims to identify structural and semantic differences between similar categories across three geospatial data standards. By formalizing the data standard structures and identifying the properties that differentiate sibling categories in each geospatial data standard using well-known formal relations and quality universals, we develop a common basis on which hydrographic and terrain categories in the three data standards can be compared. The result suggests that all the three data standards structure categories with a mixture of relations even though most of them are well-known relations in top-level ontologies. Similar categories can be found across all the three standards. Cases of categories from different standards carrying identical meaning are rare. Partial overlaps in the meaning of the similar categories can be a direct result of different quality universals at work in defining and distinguishing these categories, or in the case of these categories being ordered by size, the threshold values for distinguishing the categories are ambiguous and language-dependent. Understanding these differences avoids incorrect mappings of categories in multilingual applications. More importantly, it provides a starting point for more effective mapping between hydrographic and terrain categories between English, Mandarin, and Russian.     

IMPROVEMENTS TO THE CLASSIFICATION PERFORMANCE OF RDA

Regularized discriminant analysis has proven to be a most effective classifier for problems wheretraditional classifiers fail because of a lack of sufficient training samples,as is often the case in high-dimensional settings.However,it has been shown that the model selection procedure of regularizeddiscriminant analysis,determining the degree of regularization,has some deficiencies associated with it.We propose a modified model selection procedure based on a new appreciation function.By means ofan extensive simulation it was shown that the new model selection procedure performs better than theoriginal one.We also propose that one of the control parameters of regularized discriminant analysis beallowed to take on negative values.This extension leads to an improved performance in certain situations.The results are confirmed using two chemical data sets.     

Interest in intermediate soft-classified maps in land change model validation: suitability versus transition potential

This study compares two types of intermediate soft-classified maps. The first type uses land use/cover suitability maps based on a multi-criteria evaluation (MCE). The second type focuses on the transition potential between land use/cover categories based on a multi-layer perceptron (MLP). The concepts and methodological approaches are illustrated in a comparable manner using a Corine data set from the Murcia region (2300 km², Spain) in combination with maps of drivers that were created with two stochastic, discretely operating, commonly used tools (MCE in CA_MARKOV and MLP in Land Change Modeler). The importance of the different approaches and techniques for the obtained results is illustrated by comparing the specific characteristics of both approaches by validating the suitability versus transition potential maps to each other using a Spearman correlation matrix and, between the Corine maps, using classical ROC (receiver operating characteristic) statistics. Then, we propose a new use of ROC statistics to compare these intermediate soft-classified maps with their respective hard-classified maps of the models for each category. The validation of these results can be beneficial in choosing a suitable model and provide a better understanding of the implications of the different modeling steps and the advantages and limitations of the modeling tools.     

The statistical relationship between unconfined compressive strengths and the frequency distributions of slope gradients — A case study in northern Hungary

This paper focuses on the question of whether there is a deterministic connection between the slope gradient and unconfined compression strength (UCS) as a lithological factor and on describing the nature of this connection. Moreover, the authors determined the sensitive statistical parameters in the statistical surface analyses. The surface analyses were carried out in an area extending over 1500 km² in northern Hungary and containing parts of the uplifted Palaeozoic and Mesozoic basement and the semi-consolidated material of the Palaeogene and Neogene molasse sediments.The 67 geological formations of the area were grouped into 10 petrophysical categories characterised by unconfined compressive strength as a petrophysical parameter. The geological database was the digitalized geological map of North Hungarian Region (1 : 100 000). The digital topographic database was based on 10 m contour lines of 1 : 50 000 maps, the digital elevation model was generated by kriging interpolation. Three topographic models were created with resolutions of 25 × 25, 50 × 50 and 100 × 100 m per pixels.Evident correlation can be shown between the UCS and the relative frequency of the slope gradient. The adequate regression procedure is the power regression for low slope category values while logarithmic regression is applicable at high slope angles. Based on the characteristic of the relationship and the value of r², slope category intervals can be identified the relative frequency of which is proven to be determined by the UCS. These intervals are found to be between 4–10%, 10–16%, 16–22%, 22–44% and over 44%.Using the determination equations of slope gradient between 4–10% and over 44%, the UCS of the bedrock can be calculated approximately as the average value of the two calculated results. So the quotient of the frequency of these two category intervals can be regarded as an important morphometric index for a given bedrock.From the aspect of petrophysical characteristics, the rock with UCS between 6 and 86 MPa were proven to be deterministic for the slope development i.e. in the determination of the slope category frequencies. Applying the relative frequency of slope gradients a relative erosion resistance of the petrophysical categories can be calculated.Considering the determination coefficients, among the statistical parameters of the distribution of slope category values the standard deviation, mode, mean and median proved to be determined by the UCS of the bedrock.     

Automatic model for finding the one-dimensional magnetotelluric problem

Summary. A method is described for finding a resistivity model that fits given magnetotelluric data in the one-dimensional case. The procedure is automatic and objective in that no a priori model structure is imposed. Starting with a uniform half space derived directly from the data, the procedure gradually transforms the half space to one with a continuous and smooth resistivity distribution whose response fits the measured data. The method is illustrated by application to two magnetotelluric data sets.