Spatial statistical techniques for aggregating point objects extracted from high spatial resolution remotely sensed imagery

 Using a local maximum filter, individual trees were extracted from a 1 m spatial resolution IKONOS image and represented as points. The spatial pattern of individual trees was determined to represent forest age (a surrogate for forest structure). Point attributes, based on the spatial pattern of trees, were generated via nearest neighbour statistics and used as the basis for aggregating points into forest structure units. The forest structure units allowed for the mapping of a forested area into one of three age categories: young (1–20 years), intermediate (21–120 years), and mature (>120 years). This research indicates a new approach to image processing, where objects generated from the processing of image data (rather than pixels or spectral values) are subjected to spatial statistical analysis to estimate an attribute relating an aspect of forest structure. Received: 22 April 2002 / Accepted: 23 November 2002     

Unconditional and conditional competing risk models of activity duration and activity sequencing decisions: An empirical comparison

 This paper reports the results of an empirical comparison of various types of competing risk models in predicting the timing and duration of activities. In particular, three types of models are compared: a non-competing risk model, an unconditional competing risk model, and a conditional competing risk model. The models are applied to an activity diary, collected in the Netherlands. The results of the comparison indicate that the conditional competing risk model performs best, indicating that the choice and timing of activities depends on the nature and duration of the activity conducted previously. The specific structure of these dependent transition probabilities are discussed in detail. Several socio-demographic variables are found to be significantly related to the transition probabilities. Received: 19 July 2001 / Accepted: 25 January 2002     

The development of computer networks: First results from a microeconomic model

 Computer networks like the Internet are gaining importance in social and economic life. The accelerating pace of the adoption of network technologies for business purposes is a rather recent phenomenon. Many applications are still in the early, sometimes even experimental, phase. Nevertheless, it seems to be certain that networks will change the socioeconomic structures we know today. This is the background for our special interest in the development of networks, in the role of spatial factors influencing the formation of networks, and consequences of networks on spatial structures, and in the role of externalities. This paper discusses a simple economic model – based on a microeconomic calculus – that incorporates the main factors that generate the growth of computer networks. The paper provides analytic results about the generation of computer networks. The paper discusses (1) under what conditions economic factors will initiate the process of network formation, (2) the relationship between individual and social evaluation, and (3) the efficiency of a network that is generated based on economic mechanisms. Received: 5 July 2000 / Accepted: 28 November 2000     

GPS vector configuration design for monitoring deformation networks

 The performance of geodetic monitoring networks is heavily influenced by the configuration of the measured GPS vectors. As an effective design of the GPS measurements will decrease GPS campaign costs and increase the accuracy and reliability of the entire network, the identification of the preferred GPS vectors for measurement has been highlighted as a core problem in the process of deformation monitoring. An algorithm based on a sensitivity analysis of the network, as dependent upon a postulated velocity field, is suggested for the selection of the optimal GPS vectors. Relevant mathematical and statistical concepts are presented as the basis for an improved method of vector configuration design. A sensitivity analysis of the geodetic geodynamic network in the north of Israel is presented, where the method is examined against two deformation models, the Simple Transform Fault and the Locked Fault. The proposed method is suggested as a means for the improvement of the design of monitoring networks, a common practice worldwide. Received: 30 July 2001 / Accepted: 3 June 2002 Acknowledgments. It is my pleasant duty to thank the Survey of Israel and Dr. E. Ostrovsky for providing the variance–covariance matrix of the G1 network in northern Israel. I would like to thank the reviewers of this paper for their constructive and helpful remarks.     

Combination of spatial networks using an estimated covariance matrix

When combining satellite and terrestrial networks, covariance matrices are used which have been estimated from previous data. It can be shown that the least-squares estimator of the unknown parameters using such an estimated covariance matrix is not necessarily the best. There are a number of cases where a more efficient estimator can be obtained in a different way. The problem occurs frequently in geodesy, since in least-squares adjustment of correlated observations estimated covariance matrices are often used. If the general structure of the covariance matrix is known, results can often be improved by a method called covariance adjustment. The statistical model used in least-squares collocation leads to a type of covariance matrix which fits into this framework. It is shown in which way improvements can be made using a modified approach of principal component analysis. As a numerical example the combination of a satellite and a terrestrial network has been computed with varying assumptions on the covariance matrix. It is shown which types of matrices are critical and where the usual least-squares approach can be applied without hesitation. Finally, a simplified representation of covariances for spatial networks by means of a suitable covariance function is suggested. Paper presented at the International Symposium on Computational Methods in Geometrical Geodesy-Oxford, 2–8 September, 1973.     

Formation of surface spherical harmonic normal matrices and application to high-degree geopotential modeling

 The structure of normal matrices occurring in the problem of weighted least-squares spherical harmonic analysis of measurements scattered on a sphere with random noises is investigated. Efficient algorithms for the formation of the normal matrices are derived using fundamental relations inherent to the products of two surface spherical harmonic functions. The whole elements of a normal matrix complete to spherical harmonic degree L are recursively obtained from its first row or first column extended to degree 2L with only O(L ⁴) computational operations. Applications of the algorithms to the formation of surface normal matrices from geoid undulations and surface gravity anomalies are discussed in connection with the high-degree geopotential modeling. Received: 22 March 1999 / Accepted: 23 December 1999     

Spatial econometrics functions in R: Classes and methods

 Placing spatial econometrics and more generally spatial statistics in the context of an extensible data analysis environment such as R exposes similarities and differences between traditions of analysis. This can be fruitful, and is explored here in relation to prediction and other methods usually applied to fitted models in R. Objects in R may be assigned a class attribute, including fitted model objects. Such fitted model objects may be provided with methods allowing them to be displayed, compared, and used for prediction, and it is of interest to see whether fitted spatial models can be treated in the same way. Received: 26 August 2002 / Revised version: 15 January 2003     

A computational approach for the analysis of changes in polygon distributions

 This paper develops a computational method for analyzing changes in polygon distributions. Unmovable polygons that change discontinuously without explicit functional linkage information are discussed. Six types of primitive events are used to describe the change: 1) generation, 2) disappearance, 3) expansion, 4) shrinkage, 5) union, and 6) division. The change of polygon distributions is decomposed into a combination of these events. A computational procedure for deducing a set of events from polygon distributions of two times is proposed. The method is applied to the analysis of the spatial competition between the major and small chains of convenience stores in Tokyo, Japan. Some empirical findings are shown. Received: 3 August 2000 / Accepted: 6 February 2001     

A bound for the Euclidean norm of the difference between the best linear unbiased estimator and a linear unbiased estimator

 A bound is established for the Euclidean norm of the difference between the best linear unbiased estimator and any linear unbiased estimator in the general linear model. The bound involves the spectral norm of the difference between the dispersion matrices of the two estimators, and the residual sum of squares, all evaluated at the assumed model, but is independent of the provenance of the observation vector at hand. The bound, a straightforward consequence of first principles in Gauss–Markov theory, generalizes previous results on the difference between the best linear unbiased estimator and the ordinary least-squares estimator. In a numerical example from repeated precise levelling, the bound is used to analyse the sensitivity of estimates of vertical motion to the choice of estimator. Received: 9 September 1999 / Accepted: 15 March 2002     

Testing spatial patterns and growth spillover effects in clusters of cities

 This paper analyzes the spatial patterns of households' distribution in clusters of cities and the effects on regional growth using spatial exploratory techniques and a model of growth that incorporates spatial location. Our empirical analysis shows that, over the 1980–1990 period, in Southern New England, patterns of spatial clustering of households did create heterogeneous growth rates in the region. Also, there is evidence that clusters of cities and isolated cities created spillover growth effects in bordering towns. Received: 5 September 2001 / Accepted: 2 August 2002     

The parallel sum of matrices and its application in geodetic adjustments

Summary . It is well known that for the comparison and combination of geodetic networks their heterogeneous datum definitions are well to be considered. Various algorithms have been developed for this purpose. As an alternative concept to deal with hybrid datum problems, the operator parallel sum of matrices is introduced in this paper. To begin with, a definition is given and some basic properties are explained. To demonstrate the usefulness of the operator, two practical applications are given. The first deals with the estimation of parameters describing the deformation of two networks which are to be compared to each other. The second one treats the estimation of parameters representing the heterogeneous datum definitions of two networks which are to be merged into a hybrid network. It will be shown that – regardless of the datum definitions of the preadjusted individual networks – the parallel sum of matrices can be used to simplify the algorithms applied for the estimation of those parameters. Received 15 December 1995; Accepted 24 September 1996     

Determining the size of spatial clusters in focused tests: Comparing two methods by means of simulation in a GIS

 Based on a four-point evaluation system consisting of accuracy, consistency, power, and chance to commit type I errors, this study compares Tango's minimum p (MinP) and Stone's maximum relative risk (MaxRR) methods for detecting focused cluster size through simulations in GIS. It reveals that the MinP method is more effective than the MaxRR method. The MinP method exhibits higher levels of accuracy and consistency; and its power and chance to commit type I errors are similar to the MinP method. The MaxRR method has a tendency to underestimate the cluster size, while the MinP method tends to overestimate the cluster size, particularly when the clusters are relatively big and have high relative risk levels. In addition, the MinP method seems to be most effective in revealing the size of clusters when clusters are neither too strong nor too weak. The lowest detection rates for clustering occur when the clustering signal is relatively weak, which is easily understandable. In practice, it might be useful to use both the methods to estimate a range of possible cluster sizes, where the MaxRR method indicates the lower estimate, while the MinP method gives the higher estimate of the cluster size. Received: 24 August 2002 / Accepted: 20 December 2002     

Finite covariance functions

Because of the full covariance matrices and the computer storage limitations the number of measurements which can be handled by the collocation method simultaneously, is limited. This paper presents a method to compute covariance functions with a finite support yielding sparse covariance matrices. The theoretical background is pointed out and, for the one- and two-dimensional case, special functions are developed which can be combined with the usually used covariance functions to get a “finite covariance function”. Simulated examples to demonstrate the behaviour of different solution methods to solve these special, sparse covariance matrices supplement our investigations.     

Assessing representation error in point-based coverage modeling

 Accurately representing geographic space in a digital environment continues to confound and challenge researchers. Carrying out spatial analysis in a setting where geographic representation is subject to change poses problems to be addressed. In this paper we examine spatial representation in the context of coverage-based location modeling. A geographic region can be represented in a variety of ways. We present an evaluation of spatial representation in the location of facilities that provide coverage oriented services. The analysis shows that the modeling results are sensitive to how spatial demand for service is represented in a digital environment. We develop an approach for evaluating representational appropriateness. This research contributes to spatial analysis integrated in geographic information system environment. Received: 10 January 2001 / Accepted: 8 April 2002     

Estimated population mixing by country and risk cohort for the HIV/AIDS epidemic in Western Europe

 This paper applies a compartmental epidemic model to estimating the mixing relations that support the transfer of HIV infection between risk populations within the countries of Western Europe. To this end, a space-time epidemic model with compartments representing countries with populations specified to be at high (gay men and intravenous drug injectors ever with AIDS) and low (the remainder who are sexually active) risk is described. This model also allows for contacts between susceptible and infectious individuals by both local and international travel. This system is calibrated to recorded AIDS incidence and the best-fit solution provides estimates of variations in the rates of mixing between the compartments together with a reconstruction of the transmission pathway. This solution indicates that, for all the countries, AIDS incidence among those at low risk is expected to remain extremely small relative to their total number. A sensitivity analysis of the low risk partner acquisition rate, however, suggests this endemic state might be fragile within Europe during this century. The discussion examines the relevance of these mixing relationships for the maintenance of disease control. Received: 4 May 2000 / Accepted: 9 July 2000     

Aggregate accessibility to population at the county level: U.S. 1940–2000

 A classic study by Harris (1954) shows a map of U.S. national accessibility. Harris argued that access to population and income represents a critical factor for location analysis. Such maps and analyses are now readily produced by geographical information systems, allowing experimentation with various parameters, and explorations of changes. By comparing changes in these measurements we can develop a synthetic picture of the impacts of population redistribution. This paper offers a comprehensive review of these calculations and illustrates their use with maps from county population in the continental U.S. from 1940 through to 2000. Received: September 2002 / Accepted: January 2003 RID="*" ID="*" Previous versions of this paper were presented to the Initiative in Population Research (IPR) workshop at the Ohio State University (Horner) and to the Center for Spatially Integrated Social Sciences (CSISS) Summer Workshop in Accessibility (O'Kelly). Thanks to the referees for helpful comments.     

Volume-preserving interpolation of a smooth surface from polygon-related data

 The interpolation of continuous surfaces from discrete points is supported by most GIS software packages. Some packages provide additional options for the interpolation from 3D line objects, for example surface-specific lines, or contour lines digitized from topographic maps. Demographic, social and economic data can also be used to construct and display smooth surfaces. The variables are usually published as sums for polygonal units, such as the number of inhabitants in communities or counties. In the case of point and line objects the geometric properties have to be maintained in the interpolated surface. For polygon-based data the geometric properties of the polygon boundary and the volume should be preserved, avoiding redistribution of parts of the volume to neighboring units during interpolation. The pycnophylactic interpolation method computes a continuous surface from polygon-based data and simultaneously enforces volume preservation in the polygons. The original procedure using a regular grid is extended to surface representations based on an irregular triangular network (TIN). Received: 5 October 2000 / Accepted: 20 December 2000     

Spatial analysis in a Markov random field framework: The case of burning oil wells in Kuwait

 This paper discusses a modeling approach for spatial-temporal prediction of environmental phenomena using classified satellite images. This research was prompted by the analysis of change and landscape redistribution of petroleum residues formed from the residue of the burning oil wells in Kuwait (1991). These surface residues have been termed “tarcrete” (El-Baz et al. 1994). The tarcrete forms a thick layer over sand and desert pavement covering a significant portion of south-central Kuwait. The purpose of this study is to develop a method that utilizes satellite images from different time steps to examine the rate-of-change of the oil residue deposits and determine where redistribution is are likely to occur. This problem exhibits general characteristics of environmental diffusion and dispersion phenomena so a theoretical framework for a general solution is sought. The use of a lagged-clique, Markov random field framework and entropy measures is deduced to be an effective solution to satisfy the criteria of determination of time-rate-of-change of the surface deposits and to forecast likely locations of redistribution of dispersed, aggraded residues. The method minimally requires image classification, the determination of time stationarity of classes and the measurement of the level of organization of the state-space information derived from the images. Analysis occurs at levels of both the individual pixels and the system to determine specific states and suites of states in space and time. Convergence of the observed landscape disorder with respect to an analytical maximum provide information on the total dispersion of the residual system. Received: 5 September 2000 / Accepted: 10 July 2001     

Map projection errors in the Weber problem

 When demand points are given as a planar map where projection method is explicitly stated, we usually know the latitudes and longitudes of these points from the map. Then we can solve the Weber problem on the globe, and we do not suffer from errors. This paper analyses how cylindrical projections cause distortion in the Weber problem when demands are distributed on the Northern Hemisphere. First, we demonstrate that planar solutions are always located south of the spherical solution if the Mercator projection, the equirectangular projections with standard parallels near the demands, or the equal-area projection with the same characteristic is chosen. Second, we verify that this geographical tendency is inclined to hold when the demand points, are distributed symmetrically, widely or toward the north. Received: 15 August 2001 / Accepted: 20 April 2002 This paper was partially written while the first author was visiting the Department of Geography at the Catholic University of Louvain, Louvain-la-Neuve, Belgium [1993–1994]. He is grateful for the hospitality of this department. An earlier version of this paper was presented in 1994 at the Seventh Meeting of the European Operational Research Working Group on Locational Analysis in Brussels, and in 1996 at the Fifth World Congress of the Regional Science Association International in Tokyo. The authors would also like to thank the participants as well as three anonymous referees for their constructive comments.     

Learning in neural spatial interaction models: A statistical perspective

 In this paper we view learning as an unconstrained non-linear minimization problem in which the objective function is defined by the negative log-likelihood function and the search space by the parameter space of an origin constrained product unit neural spatial interaction model. We consider Alopex based global search, as opposed to local search based upon backpropagation of gradient descents, each in combination with the bootstrapping pairs approach to solve the maximum likelihood learning problem. Interregional telecommunication traffic flow data from Austria are used as test bed for comparing the performance of the two learning procedures. The study illustrates the superiority of Alopex based global search, measured in terms of Kullback and Leibler's information criterion. Received: December 2001 / Accepted: August 2002 The author gratefully thanks Martin Reismann (Department of Economic Geography & Geoinformatics) for his valuable research assistance.