Smooth Pycnophylactic Interpolation Produced by Density-Equalising Map Projections

Velika količina kvantitativnih geoprostornih podataka prikuplja se i spaja u diskretne popisne jedinice (npr. zemlje ili države). Glatka piknofilaktička interpolacija ima za cilj pronaći glatku, nenegativnu funkciju tako da je integral površine nad svakom popisnom jedinicom jednak agregiranim podacima. Konvencionalno, glatka piknofilaktička interpolacija dobiva se algoritmom staničnog automata koji pretvara po dijelovima konstantnu funkciju u približno glatku funkciju definiranu na mreži koordinata na karti u ekvivalentnoj projekciji. Alternativni pristup, kojeg je predložio Tobler (1976), je konstruirati kartografsku projekciju s ujednačavanjem gustoće u kojoj su područja popisnih jedinica proporcionalna agregiranim podacima. Piknofilaktička interpolacija može se dobiti iz Jakobijana te projekcije. U ovom radu opisujemo primjenu softvera za tu metodu. Iako rješenja nisu nužno optimalna u smislu unaprijed definiranih kvantitativnih mjera glatkoće, naša metoda je računski učinkovita i potencijalno se može koristiti zajedno s drugim metodama da bi se ubrzala konvergencija prema optimalnom rješenju.A large amount of quantitative geospatial data is collected and aggregated in discrete enumeration units (e.g. countries or states). Smooth pycnophylactic interpolation aims to find a smooth, nonnegative function such that the area integral over each enumeration unit is equal to the aggregated data. Conventionally, smooth pycnophylactic interpolation is achieved by a cellular automaton algorithm that converts a piecewise constant function into an approximately smooth function defined on a grid of coordinates on an equal-area map. An alternative approach, proposed by Tobler in 1976, is to construct a density-equalising map projection in which areas of enumeration units are proportional to the aggregated data. A pycnophylactic interpolation can be obtained from the Jacobian of this projection. Here, we describe a software implementation of this method. Although solutions are not necessarily optimal in terms of predefined quantitative measures of smoothness, our method is computationally efficient and can potentially be used in tandem with other methods to accelerate convergence towards an optimal solution

IMPORTANCIA DE LOS ESPACIOS COMUNES: UNA ADAPTACIÓN DE LA TÉCNICA DE INTERPOLACIÓN ESPACIAL INVERSE DISTANCE WEIGHTED (IDW) EN LA PREDICCIÓN DE DATOS SOCIOECONÓMICOS AUSENTES

Disponer de estadísticas socioeconómicas microterritoriales no es frecuente a pesar de los esfuerzos de instituciones oficiales de generarlas, particularmente en el caso de lugares de difícil acceso y/o despoblados. En este documento, las autoras recurren al uso de técnicas de interpolación espacial para predecir microdatos de variables socioeconómicas ausentes. En particular, se utiliza la técnica del Inverso de la Distancia (IDW), conocida por su facilidad de implementación e interpretación. El IDW estima el valor de una variable desconocida a través de la ponderación inversa de la distancia a valores cercanos conocidos. Tal asunción se basa en la ley geográfica de Tobler de que “todo está relacionado con todo, pero las cosas cercanas están más relacionadas entre sí que las distantes”. Para mejorar la estimación de la predicción, se propone una nueva especificación de IDW compuesta por una función gravitatoria, en que la distancia inversa (variable de fricción) se combina específicamente con la longitud relativa de la frontera común entre dos unidades espaciales (variable de atracción). Probamos el funcionamiento de esta función para predecir los ingresos disponibles en algunos municipios metropolitanos en Madrid (España). La eficacia de las predicciones espaciales se evalúa mediante el error medio cuadrático (EMC) por el método de la validación cruzada, el error producto de las diferencias entre los valores reales e interpolados y el coeficiente de correlación entre los valores reales y estimados

Spatial reallocation of areal data - a review

The analysis of socio-economic data often implies the combination of data bases originating from different administrative sources so that data have been collected on several separate partitions of the zone of interest into administrative units. It is therefore necessary to reallocate the data from the source spatial units to the target spatial units. We propose a review of the literature on statistical methods of spatial reallocation rules (spatial interpolation). Indeed one can distinguish several types of reallocation depending on whether the initial data and the final output are areal data or point data. We concentrate here on the areal-to-areal change of support case when initial and final data have an areal support with a particular attention to disaggregation for continuous data. There are three main types of such techniques: proportional weighting schemes also called dasymetric methods, smoothing techniques and regression based interpolation

Analysis of Data of Different Spatial Support: A Multivariate Process Approach

Inherent to a spatial variable is the unit of support at which it is measured. In many studies, variables are observed at different support. For example, disease rates might be measured at an aggregated level while temperature is usually measured at specific points. It is still an interesting problem to study the relationship of variables having different support. However, it may be a different problem to statistically model the relationship of variables of different support, particularly when the supports do not have a hierarchical structure. Currently, cokriging, the use of one or more spatial variables to predict another variable, is applied to variables of the same support. In this work, I extend cokriging for use with variables of different support by constructing a nonparametric cross-covariance matrix. This method is flexible as it applies to any marginal spatial model and is suited to large datasets because it uses latent variables which can assist with dimension reduction. The proposed nonparametric method is demonstrated with two correlated variables which are measured at different spatial units. In addition, the method is implemented using two algorithms; one which yields an optimized matrix (Wang, 2011) and the other which produces an approximately optimized matrix but is computationally more efficient (Hu 2013). The results show that the method is appropriate for predicting data of different support and that it outperforms some competing methods with respect to predictive performance. Furthermore, as expected, the approximately optimized matrix does not perform as well as the alternative algorithm, but it performs better than the comparative methods

Developing Population Grid with Demographic Trait: An Example for Milwaukee County, Wisconsin

Population grids have been widely used in estimating population in environmental justice studies and emergency management. The currently available population grids are only for total population. There is an increasing need for population grids that have not only total population but also populations of different age, gender, race, and ethnicity. This study explores the methodology to develop these population grids endowed with the demographic characteristics. Areal interpolation methods are used to transfer total population at census blocks to the cells of the grid. Kernel density method is used to estimate the relative probability of population of different subgroups at the cells, and to disaggregate total population into subgroups. Population grids of black, white, and other, as well as populations of age 20 to 34 and age 65 and over, are derived for Milwaukee County, Wisconsin. Applications of the population grids demonstrate their potentials

GIS-based urban land use characterization and population modeling with subpixel information measured from remote sensing data

This dissertation provides deeper understanding on the application of Vegetation-Impervious Surface-Soil (V-I-S) model in the urban land use characterization and population modeling, focusing on New Orleans area. Previous research on the V-I-S model used in urban land use classification emphasized on the accuracy improvement while ignoring the discussion of the stability of classifiers. I developed an evaluation framework by using randomization techniques and decision tree method to assess and compare the performance of classifiers and input features. The proposed evaluation framework is applied to demonstrate the superiority of V-I-S fractions and LST for urban land use classification. It could also be applied to the assessment of input features and classifiers for other remote sensing image classification context. An innovative urban land use classification based on the V-I-S model is implemented and tested in this dissertation. Due to the shape of the V-I-S bivariate histogram that resembles topological surfaces, a pattern that honors the Lu-Weng’s urban model, the V-I-S feature space is rasterized into grey-scale image and subsequently partitioned by marker-controlled watershed segmentation, leading to an urban land use classification. This new approach is proven to be insensitive to the selection of initial markers as long as they are positioned around the underlying watershed centers. This dissertation links the population distribution of New Orleans with its physiogeographic conditions indicated by the V-I-S sub-pixel composition and the land use information. It shows that the V-I-S fractions cannot be directly used to model the population distribution. Both the OLS and GWR models produced poor model fit. In contrast, the land use information extracted from the V-I-S information and LST significantly improved regression models. A three-class land use model is fitted adequately. The GWR model reveals the spatial nonstationarity as the relationship between the population distribution and the land use is relatively poor in the city center and becomes stronger towards the city fringe, depicting a classic urban concentric pattern. It highlighted that New Orleans is a complex metropolitan area, and its population distribution cannot be fully modeled with the physiogeographic measurements

Les méthodes d'interpolation pour données sur zones

Le résumé en français n'a pas été communiqué par l'auteur.The combination of several socio-economic data bases originating from different administrative sources collected on several different partitions of a geographic zone of interest into administrative units induces the so called areal interpolation problem. This problem is that of allocating the data from a set of source spatial units to a set of target spatial units. At the European level for example, the EU directive ’INSPIRE’, or INfrastructure for Spatial InfoRmation, encourages the states to provide socio-economic data on a common grid to facilitate economic studies across states. In the literature, there are three main types of such techniques: proportional weighting schemes, smoothing techniques and regression based interpolation. We propose a theoretical evaluation of these statistical techniques for the case of count related data. We find extensions of some of these methods to new cases : for example, we extend the ordinary dasymetric weightingmethod to the case of an intensive target variable Y and an extensive auxiliary quantitative variable X and we introduce a scaled version of the Poisson regression method which satisfies the pycnophylactic property. We present an empirical study on an American database as well as an R-package for implementing these methods

The effect of work related mechanical stress on the peripheral temperature of the hand

The evolution and developments in modern industry have resulted a wide range of occupational activities, some of which can lead to industrial injuries. Due to the activities of occupational medicine, much progress has been made in transforming the way that operatives perform their tasks. However there are still many occupations where manual tasks have become more repetitive, contributing to the development of conditions that affect the upper limbs. Repetitive Strain Injury is one classification of those conditions which is related to overuse of repetitive movement. Hand Arm Vibration Syndrome is a subtype of this classification directly related to the operation of instruments and machinery which involves vibration. These conditions affect a large number of individuals, and are costly in terms of work absence, loss of income and compensation. While such conditions can be difficult to avoid, they can be monitored and controlled, with prevention usually the least expensive solution. In medico-legal situations it may be difficult to determine the location or the degree of injury, and therefore determining the relevant compensation due is complicated by the absence of objective and quantifiable methods. This research is an investigation into the development of an objective, quantitative and reproducible diagnostic procedure for work related upper limb disorders. A set of objective mechanical provocation tests for the hands have been developed that are associated with vascular challenge. Infrared thermal imaging was used to monitor the temperature changes using a well defined capture protocol. Normal reference values have been measured and a computational tool used to facilitate the process and standardise image processing. These objective tests have demonstrated good discrimination between groups of healthy controls and subjects with work related injuries but not individuals, p<0.05, and are reproducible. A maximum value for thermal symmetry of 0.5±0.3ºC for the whole upper limbs has been established for use as a reference. The tests can be used to monitor occupations at risk, aiming to reduce the impact of these conditions, reducing work related injury costs, and providing early detection. In a medico-legal setting this can also provide important objective information in proof of injury and ultimately in objectively establishing whether or not there is a case for compensation