Yukio Sadahiro

Accuracy of areal interpolation: A comparison of alternative methods

Abstract. This paper discusses the accuracy of spatial data estimated by areal interpolation, a process of transferring data from one zonal system to another. A stochastic model is proposed which represents areal interpolations in diverse geographic situations. The model is used to examine the relationship between estimation accuracy and the spatial distribution of estimation error from a theoretical viewpoint. The analysis shows that the uniformity in error distribution improves the accuracy of areal interpolation. Four areal interpolation methods are then assessed through numerical examinations. From this it is found that the accuracy of simple interpolation methods heavily depends on the appropriateness of their hypothetical distributions, whereas the accuracy of intelligent methods depends on the fitness of the range of supplementary data for that of true distribution.

Accuracy of count data transferred through the areal weighting interpolation method

This paper analyses the accuracy of count data transferred from a zonal system to an incompatible zone through the areal weighting interpolation method. To treat a variety of situations in a theoretical framework, stochastic models representing areal weighting interpolation are developed. The relationship between the accuracy of estimates and the size of source zones is analytically investigated by use of a proposed model. The results strongly suggested that smaller zones give better estimates on a wide range of zonal systems. The effect of the shape of source zones and the target zone on estimation accuracy is also numerically examined, and is also found to be significant.

Variation in count data transferred from a set of irregular zones to a set of regular zones through the point-in-polygon method

This paper deals with variation in transferred data from a set of irregular zones (called source zones) to a set of regular zones (called target zones) through the point-in-polygon method (i.e., the method that transfers the attribute value of a source zone to a target zone if a representative point of the source zone is included in the target zone). First,the variation is written as a mathematical equation. Second, it is shown that among regular lattices of target zones, a regular hexagonal lattice gives the minimum variation. However, the difference in variation between a square lattice and a regular hexagonal lattice is very small. Third, under the condition that an allowable variation is less than 5 per cent (which is usually acceptable in practice), the safest (the most conservative) rule supported by a theory is that the point-in-polygon method should be used when the diameter of every source zone is less than 4 per cent of the length of the edge of a square cell. Last, a practical rule based upon e...

A computational approach for the analysis of changes in polygon distributions

Abstract. 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.

Cluster Perception in the Distribution of Point Objects

This paper aims to develop a model representing cluster perception in the distribution of point objects. Three spatial factors—that is, proximity, concentration, and density change—are considered to cause cluster perception. To measure these factors, two spatial notions based on the density of point objects are proposed: local density and relative local density. These densities are defined as the functions of a location in a map, and indicate how points are distributed around the location. Cluster perception is represented as a probabilistic function of the measures derived from the relative local density, and its likelihood is shown for model estimation. An experiment in cluster perception indicates that the model is significantly valid, and some empirical findings related to the heterogeneity of map readers in cluster perception are shown.

Implementing spatial segregation measures in R.

Reliable and accurate estimation of residential segregation between population groups is important for understanding the extent of social cohesion and integration in our society. Although there have been considerable methodological advances in the measurement of segregation over the last several decades, the recently developed measures have not been widely used in the literature, in part due to their complex calculation. To address this problem, we have implemented several newly proposed segregation indices in R, an open source software environment for statistical computing and graphics, as a package called seg. Although there are already a few standalone applications and add-on packages that provide access to similar methods, our implementation has a number of advantages over the existing tools. First, our implementation is flexible in the sense that it provides detailed control over the calculation process with a wide range of input parameters. Most of the parameters have carefully chosen defaults, which perform acceptably in many situations, so less experienced users can also use the implemented functions without too much difficulty. Second, there is no need to export results to other software programs for further analysis. We provide coercion methods that enable the transformation of our output classes into general R classes, so the user can use thousands of standard and modern statistical techniques, which are already available in R, for the post-processing of the results. Third, our implementation does not require commercial software to operate, so it is accessible to a wider group of people.

An illusion of spatial hierarchy: spatial hierarchy in a random configuration

In this paper we show the properties of a spatial hierarchy found in a random configuration in which points are randomly placed on a plane and ranks are randomly assigned to these points. First we show a method of detecting a spatial hierarchy in a configuration of ranked points on a plane (not necessarily the random configuration). Second, using this method we obtain the spatial hierarchy of the random configuration mentioned above, and examine its properties theoretically as well as numerically with the Monte Carlo simulation. From this examination, we find that the spatial hierarchy of the random configuration shares more or less similar properties with Christallers spatial hierarchy. Stated explicitly, the shape of dominant regions is hexagonal on average; the areas of the same rank centers are fairly homogeneous; the K value defined by Christaller is almost constant. The constant K of the random configuration is close to seven, implying that the spatial hierarchy of the random configuration is close to Christallers hierarchy of the administrative principle. These results explain to a certain extent why spatial hierarchies are often observed in the real world. At the same time, these results give us a warning. Even if we find a spatial hierarchy in the real world, we should question whether or not the observed hierarchy is a seeming hierarchy like the spatial hierarchy in the random configuration.

Exploratory Method for Analyzing Changes in Polygon Distributions

In this paper I develop an exploratory method for analyzing changes in polygon distributions. Changes are deduced from a set of polygon distributions of different times, and represented by a directed graph. Three viewpoints for representing individual changes are proposed: topology, size, and direction. They are described qualitatively, and used for exploratory analysis of spatiotemporal distribution of changes. In addition to individual changes, their sequences are analyzed through classification, visualization, and calculation of summary statistics. The method proposed is applied to the analysis of changes in market areas of a convenience-store chain in Tokyo, Japan. The empirical study reveals the spatial structure of changes in a global scale.

Analysis of surface changes using primitive events

This paper develops a method for analysing changes in a surface, a scalar function defined over a two-dimensional region. The method is based on the topological method for static surfaces that uses critical points (peaks, bottoms, and cols) and their connecting lines. To extend the topological method to spatiotemporal domain, four types of primitive events are proposed: (1) generation, (2) disappearance, (3) movement, and (4) switch. The change of a surface is described by a combination of these primitives. From surfaces of two times a set of primitive events that cause the change is deduced. They are stored in GIS as spatial objects with attributes, and their spatio-temporal pattern is visually analysed. To test the validity of the method, the change of a retail cluster in Shinjuku and Shibuya area in Tokyo is analysed. The empirical study yielded some interesting findings that help us understand changes in the spatial structure of retailing.

Statistical methods for analyzing the distribution of spatial objects in relation to a surface

Abstract. This paper develops statistical methods for analyzing the distribution of spatial objects—points, convex polygons, and line segments—in relation to a surface. We propose statistics for measuring the relationship between the distribution of these objects and a surface and derive their expectations and variances under the null hypothesis that the objects are independently and randomly distributed. The statistics are approximately distributed according to the normal distribution under the null hypothesis, which enables us to test the significance of the spatial relationships statistically. Using the proposed methods, we empirically analyze the distribution of convenience stores in relation to the distribution of population in a suburb of Osaka, Japan. Some empirical findings are shown.