A Comparison of Three Exploratory Methods for Cluster Detection in Spatial Point Patterns

This paper compares the performances of three exploratory methods for cluster detection in spatial point patterns where the at-risk population is known. After reviewing two existing methods, Openshaw et al. (1987) and Besag and Newell (1991), an alternative method is introduced. These three methods are then compared empirically using two point patterns drawn from a disaggregate housing database consisting of 28,832 observations. Each observation in the data set contains attributes of single-family detached dwellings in the City of Amherst, New York. This paper provides some new insights into the performance of the three methods, as previous applications have used spatially aggregated (and hence rather inaccurate) data. The paper also demonstrates the utility of GIS for this type of spatial analysis.     

Local Indicators of Network-Constrained Clusters in Spatial Point Patterns

The detection of clustering in a spatial phenomenon of interest is an important issue in spatial pattern analysis. While traditional methods mostly rely on the planar space assumption, many spatial phenomena defy the logic of this assumption. For instance, certain spatial phenomena related to human activities are inherently constrained by a transportation network because of our strong dependence on the transportation system. This article thus introduces an exploratory spatial data analysis method named l ocal i ndicators of n etwork-constrained c luster s (LINCS), for detecting local-scale clustering in a spatial phenomenon that is constrained by a network space. The LINCS method presented here applies to a set of point events distributed over the network space. It is based on the network K -function, which is designed to determine whether an event distribution has a significant clustering tendency with respect to the network space. First, an incremental K -function is developed so as to identify cluster size more explicitly than the original K -function does. Second, to enable identification of cluster locations, a local K -function is derived by decomposing and modifying the original network K -function. The local K -function LINCS, which is referred to as KLINCS, is tested on the distribution of 1997 highway vehicle crashes in the Buffalo, NY area. Also discussed is an adjustment of the KLINCS method for the nonuniformity of the population at risk over the network. As traffic volume can be seen as a surrogate of the population exposed to a risk of vehicle crashes, the spatial distribution of vehicle crashes is examined in relation to that of traffic volumes on the network. The results of the KLINCS analysis are validated through a comparison with priority investigation locations (PILs) designated by the New York State Department of Transportation.     

Assessing the Cluster Correspondence between Paired Point Locations

Some complex geographic events are associated with multiple point locations. Such events include, but are not limited to, those describing linkages between and among places. The term multi‐location event is used in the paper to refer to these geographical phenomena. Through formalization of the multi‐location event problem, this paper situates the analysis of multi‐location events within the broad context of point pattern analysis techniques. Two alternative approaches (Vector autocorrelation analysis and cluster correspondence analysis) to the spatial dependence of paired‐location events (i.e., two‐location events) are explored, with a discussion of their appropriateness to general multi‐location event problems. The research proposes a framework of cluster correspondence analysis for the detection of local non‐stationarities in the spatial process generating multi‐location events. A new algorithm for local analysis of cluster correspondence is proposed. It is implemented on a large‐scale dataset of vehicle theft and recovery location pairs in Buffalo, New York.     

云冈石窟风化检测研究进展

云冈石窟,作为我国规模最大的古代石窟群,是文化遗产的重要组成部分。由于年代久远,许多石质文物都遭受着严重的风化病害侵蚀,对其风化程度进行检测已经成为石质文物保护中的一项紧迫任务。随着检测技术的不断发展,石质文物风化的检测方法也越来越多,并且每种检测方法都有其侧重的检测目的和优势。本研究综述近几十年内曾使用过的重点检测方法,并分析每种检测方法的原理、优势和局限性,为云冈石窟风化检测和保护提供参考。     

Spatial Characteristics and Comparisons of Interaction and Median Clustering Models

Cluster analysis has been pursued from a number of directions for identifying interesting relationships and patterns in spatial information. A major emphasis is currently on the development and refinement of optimization‐based clustering models for the purpose of exploring spatially referenced data. Within this context, two basic methods exist for identifying clusters that are most similar. An interesting feature of these two approaches is that one method approximates the relationships inherent in the other method. This is significant given that the approximation approach is invariably utilized for cluster detection in spatial and aspatial analysis. A number of spatial applications are investigated which highlight the differences in clusters produced by each model. This is an important contribution because the differences are in fact quite significant, yet these contrasts are not widely known or acknowledged.     

Anisotropic Variance Functions in Geographically Weighted Regression Models

Most standard methods of statistical analysis used in the social and environmental sciences are built upon the basic assumptions of independence, homogeneity, and isotropy. A notable exception to this rule is the collection of methods used in geographical analysis, which have been designed to take into account serial dependence often observed in spatial data. In addition, recent developments, in particular the method of geographically weighted regression, have provided the tools to model non‐stationary processes, and thus evidence that challenges the assumption of homogeneity. The assumption of isotropy, however, although suspect, has received considerably less attention, and there is thus a need for tools to study anisotropy in a more systematic fashion. In this paper we expand the method of geographically weighted regression in a simple yet effective way to explore the topic of anisotropy in spatial processes. We discuss two different estimation situations and exemplify the proposed technical development by means of a case study. The results suggest that anisotropy issues might be a fairly common occurrence in spatial processes and/or in the statistical modeling of spatial processes.     

Geoadditive Models for Regional Count Data: An Application to Industrial Location

We propose a geoadditive negative binomial model (Geo‐NB‐GAM) for regional count data that allows us to address simultaneously some important methodological issues, such as spatial clustering, nonlinearities, and overdispersion. This model is applied to the study of location determinants of inward greenfield investments that occurred during 2003–2007 in 249 European regions. After presenting the data set and showing the presence of overdispersion and spatial clustering, we review the theoretical framework that motivates the choice of the location determinants included in the empirical model, and we highlight some reasons why the relationship between some of the covariates and the dependent variable might be nonlinear. The subsequent section first describes the solutions proposed by previous literature to tackle spatial clustering, nonlinearities, and overdispersion, and then presents the Geo‐NB‐GAM. The empirical analysis shows the good performance of Geo‐NB‐GAM. Notably, the inclusion of a geoadditive component (a smooth spatial trend surface) permits us to control for spatial unobserved heterogeneity that induces spatial clustering. Allowing for nonlinearities reveals, in keeping with theoretical predictions, that the positive effect of agglomeration economies fades as the density of economic activities reaches some threshold value. However, no matter how dense the economic activity becomes, our results suggest that congestion costs never overcome positive agglomeration externalities. Nuestra propuesta se basa en un modelo geoaditivo binomial (Geo‐NB‐GAM) para datos de recuento regionales (regional count data) que nos permitan abordar simultáneamente distintos temas metodológicos importantes como la concentración espacial (clustering), no linealidades y sobre‐dispersión. Este modelo es aplicado al estudio de determinantes de localización de nuevas inversiones de tipo greenfield internas (inward greenfield investments) que se dieron entre 2003 y 2007, en 249 regiones europeas. Luego de presentar el conjunto de datos y de mostrar la presencia de sobre‐dispersión y agrupación (concentración) espacial, examinamos el marco teórico que motiva los determinantes de localización incluidos en el modelo empírico, y resaltamos algunas de las razones por las que las relaciones entre ciertas co‐variables y la variable dependiente podrían ser no lineales. La sección subsiguiente comienza con descripción de las soluciones propuestas por la literatura anterior para abordar la concentración espacial, no linealidades, y sobre‐dispersión, para luego presentar el Geo‐NB‐GAM. El análisis empírico muestra el buen desempeño del Geo‐NB‐GAM. Particularmente, la inclusión del componente geo‐aditivo (una superficie de tendencia espacial suavizada) nos permite controlar heterogeneidades espaciales no observadas que inducen a la concentración espacial. Al permitir no linealidades se revela ‐continuando con las predicciones teóricas‐ que el efecto positivo de las economías de aglomeración se desvanece a medida que la densidad de las actividades económicas alcanza un umbral de valor. Sin embargo, sin importar cuán densa llegue a ser la actividad económica, nuestros resultados sugieren que los costes de congestión nunca superan las externalidades de aglomeración positivas. 本文提出了一种应用于区域统计数据的负二项式地理加性模型,它能够同时处理包括空间聚类、非线性和过度离散等多种重要的方法论问题。将该模型应用于2003‐2007年的249个欧洲案例区,探讨其内部绿地投资的区位因子。在揭示了数据集样本分布具有过度离散与空间聚类特征后,我们对所构建的关于区位驱动因子的实证模型进行了核查,以确定是否遗漏重要变量,并高亮显示为何有些变量与因变量的关系可能是非线性的。本文后续部分首先描述了已有文献在解决空间聚类、非线性与过度离散等情景下的解决方案,并简要介绍了本文的Geo‐NB‐GAM模型。实证分析表明,该模型具有良好的模拟效果,尤其是地理加性成分（一种平滑的空间趋势面）在处理包括空间聚类在内的未被关注的空间异质性。非线性模型揭示出集聚经济的正向效应,随着经济活动密度阈值呈衰减趋势,这一点和理论预测是一致的。然而,本文结果显示无论经济活动的密度呈现何种变化,正向集聚的外部效应仍大于拥挤成本。.     

RECURSIVE ALGORITHMS FOR THE ELIMINATION OF REDUNDANT PATHS IN SPATIAL LAG OPERATORS*

ABSTRACT. Recursive algorithms for the elimination of redundant paths in spatial lag operators are introduced. It is shown that these algorithms have superior computational properties in comparison with the cumbersome procedure proposed by Ross and Harary (1952). A rigorous definition of spatial lag operators is given, while a number of mathematical results and properties are derived. Theoretical and empirical results regarding the performance of the proposed algorithms are presented.     

The Bearing Correlogram: A New Method of Analyzing Directional Spatial Autocorrelation

Extensions of nondirectional spatial autocorrelation techniques to two dimensions have existed for many years, but the results are difficult to compare to the traditional nondirectional techniques and often lack ease of interpretability. This paper reviews the traditional one‐ and two‐dimensional spatial autocorrelation methods and proposes a new directional method which is both easier to compare to nondirectional methods and easier to interpret than previous directional methods.     

From Activity Areas to Occupational Histories: New Methods to Document the Formation of Spatial Structure in Hunter-Gatherer Sites

Over the past five decades, archaeologists have proposed a wide range of methods for the study of spatial organization within hunter-gatherer sites. Many of these methods sought to identify the spatial location of activities based on patterns of behavior observed in ethnographic contexts. While this resulted in productive observations at certain sites, many of these methods were tailored to specific situations and thus could not be applied to a wide range of sites. For example, open-air sites rarely contain preserved bone or features, such as hearths, which were central components to identifying characteristics of site structure. In addition, many of these methods often did not take into consideration the temporal dynamics of the occupation, i.e., that many sites were formed through subsequent occupations of differing duration. This paper proposes the use of two related methods that assume many assemblages are the result of more than one occupation. The methods target the distribution of lithic artifacts, the most ubiquitously preserved of archaeological materials, and accounts for the potential that the final resting place of artifacts was the result of both intentional and unintentional movement by humans and a host of biological and geological processes. The main goal of this paper is to use an understanding of how these processes influenced the formation of site structure to estimate the relative number and duration of occupations for each site in the sample. These new methods will be presented and explained through the study of seven open-air Middle Paleolithic sites in France but are applicable to a wide range of hunter-gatherer sites.     

生态旅游环境承载力预警系统研究

随着生态旅游的兴起,旅游可持续发展概念的提出,国内外对生态旅游环境承载力的研究从理论和实践上不断丰富和完善,但其单维和静态研究成为其研究发展方向上的一块难以逾越的障碍,本文正是在关注旅游生态系统和环境质量的时空演化和变化的基础上,提出运用预警理论和方法来多维分析由于旅游活动导致和产生的旅游环境的变化过程,以解决现今生态旅游环境承载力研究缺乏综合性、系统性、动态性和预警性的现实性问题。同时本文从系统论、控制论、决策论的角度,对生态旅游环境承载力预警系统的结构、特点、运行机制,基本数学模型进行了初步研究。     

Spatial Cluster Detection in Spatial Flow Data

As a typical form of geographical phenomena, spatial flow events have been widely studied in contexts like migration, daily commuting, and information exchange through telecommunication. Studying the spatial pattern of flow data serves to reveal essential information about the underlying process generating the phenomena. Most methods of global clustering pattern detection and local clusters detection analysis are focused on single‐location spatial events or fail to preserve the integrity of spatial flow events. In this research we introduce a new spatial statistical approach of detecting clustering (clusters) of flow data that extends the classical local K‐function, while maintaining the integrity of flow data. Through the appropriate measurement of spatial proximity relationships between entire flows, the new method successfully upgrades the classical hot spot detection method to the stage of “hot flow” detection. Several specific aspects of the method are discussed to provide evidence of its robustness and expandability, such as the multiscale issue and relative importance control, using a real data set of vehicle theft and recovery location pairs in Charlotte, NC.     

Spatial Analysis in Physical Geography and the Challenge of Deterministic Uncertainty

The application of complex and nonlinear dynamical systems (NDS) theory in physical geography and geosciences has proceeded through several stages, and has recently entered a phase where field-testable hypotheses and historical or mechanistic explanations are being generated. However, there are some fundamental challenges. It seems clear that chaos and dynamical self-organization are present, and may be common in earth surface systems, and that these phenomena have spatial manifestations in the landscape. However, NDS theory and methods have been formulated primarily in the temporal domain and are typically ill-suited to real-world spatial data. Spatial analytical methods are not generally capable of distinguishing deterministic complexity and uncertainty from noise. Thus, the detection of the signals of complex deterministic dynamics in real landscapes and spatial data is a major challenge. Entropy-based methods of spatial analysis can be directly linked to nonlinear dynamics, and are at present the best available method to approach this problem. However, there is evidence in the spatial analysis literature suggesting that development of techniques to detect deterministic uncertainty is possible. Pending such a break-through, three general approaches are described, based on spatial analysis of chronosequences, the characteriziation of changes in spatial structure over time, and the spatial-domain testing of specific hypotheses relevant to deterministic uncertainty. Current trends generally suggest a shift in mathematical modeling and spatial analysis in physical geography away from traditional determinism toward approaches that incorporate locational, historical, and scale contingency.     

Probabilistic Regionalization via Evidence Accumulation with Random Spanning Trees as Weak Spatial Representations

Spatial clusters contain biases and artifacts, whether they are defined via statistical algorithms or via expert judgment. Graph-based partitioning of spatial data and associated heuristics gained popularity due to their scalability but can define suboptimal regions due to algorithmic biases such as chaining. Despite the broad literature on deterministic regionalization methods, approaches that quantify regionalization probability are sparse. In this article, we propose a local method to quantify regionalization probabilities for regions defined via graph-based cuts and expert-defined regions. We conceptualize spatial regions as consisting of two types of spatial elements: core and swing. We define three distinct types of regionalization biases that occur in graph-based methods and showcase the use of the proposed method to capture these types of biases. Additionally, we propose an efficient solution to the probabilistic graph-based regionalization problem via performing optimal tree cuts along random spanning trees within an evidence accumulation framework. We perform statistical tests on synthetic data to assess resulting probability maps for varying distinctness of underlying regions and regionalization parameters. Lastly, we showcase the application of our method to define probabilistic ecoregions using climatic and remotely sensed vegetation indicators and apply our method to assign probabilities to the expert-defined Bailey's ecoregions.     

Geographically Weighted Extreme Learning Machine: A Method for Space–Time Prediction

Spatial heterogeneity has been regarded as an important issue in space–time prediction. Although some statistical methods of space–time predictions have been proposed to address spatial heterogeneity, the linear assumption makes it difficult for these methods to predict geographical processes accurately because geographical processes always involve complicated nonlinear characteristics. An extreme learning machine (ELM) has the advantage of approximating nonlinear relationships with a rapid learning speed and excellent generalization performance. However, determining how to incorporate spatial heterogeneity into an ELM to predict space–time data is an urgent problem. For this purpose, a new method called geographically weighted ELM (GWELM) is proposed to address spatial heterogeneity based on an ELM in this article. GWELM is essentially a locally varying ELM in which the parameters are regarded as functions of spatial locations, and geographically weighted least squares is applied to estimate the parameters in a local model. The proposed method is used to analyze two groups of different data sets, and the results demonstrate that the GWELM method is superior to the comparative method, which is also developed to address spatial heterogeneity.     

The marble of the David of Michelangelo: A multi-method analysis of provenance

The origin of the marble block utilised by Michelangelo for sculpting the David has been determined with the aid of a multi-method provenancing procedure including spectroscopic (EPR), isotopic and other miscellaneous variables. Data processing was carried out using discriminant function analysis. The provenancing procedure was split into three sequential steps aimed at obtaining increasing spatial resolution. High values of relevant probabilistic parameters indicate that the David's marble originates from Carrara and, specifically, from the Fantiscritti quarries (Miseglia), thus confirming the assignment proposed in the 19th century on the basis of simple autoptic examination. The role of different provenancing techniques in the three stages of the analysis is briefly discussed, as is the performance of instrumental methods as compared with the ability of a trained human eye.     

Quantifying Interpolation Errors in Urban Airborne Laser Scanning Models

Airborne laser scanning (ALS) is becoming an increasingly popular data capture technique for a variety of applications in urban surface modeling. Raw ALS data are captured and supplied as a 3D point cloud. Many applications require that these data are interpolated onto a regular grid in order that they may be processed. In this article, we identify and analyze the magnitudes and spatial patterning of residuals from ALS models of urban surfaces, at a range of different scales. Previous research has demonstrated the effects of interpolation method and scale upon the nature of error in digital surface models (DSMs), but the size and spatial patterning of such errors have not hitherto been investigated for urban surfaces. The contribution of this analysis is thus to investigate the ways in which different methods may introduce error, and to understand the uncertainty that characterizes urban surface models that are devised for a wide range of applications. The importance of the research is shown using examples of how the different methods may introduce different amounts of error and how the uncertainty information may benefit users of ALS height models. Our analysis uses a range of validation techniques, including split-sample, cross-validation, and jackknifing, to estimate the error created in DSMs of urban areas.     

flowAMOEBA: Identifying Regions of Anomalous Spatial Interactions

This study aims at developing a data‐driven and bottom‐up spatial statistic method for identifying regions of anomalous spatial interactions (clusters of extremely high‐ or low‐value spatial flows), based on which it creates a spatial flow weights matrix. The method, dubbed flowAMOEBA, upgrades a multidirectional optimum ecotope‐based algorithm (AMOEBA) from areal data to spatial flow data through a proper spatial flow neighborhood definition. The method has the potential to dramatically change the way we study spatial interactions. First, it breaks the convention that spatial interaction data are always collected and modeled between spatial entities of the same granularity, as it delineates the OD region of anomalous spatial interactions, regardless of the size, shape, scale, or administrative level. Second, the method creates an empirical spatial flow weights matrix that can handle network autocorrelation embedded in spatial interaction modeling, thus improving related policy‐making or problem‐solving strategies. flowAMOEBA is tested and demonstrated on a synthetic data set as well as a county‐to‐county migration data set.     

大都市中心区生产性服务业集群的空间溢出——以广州市天河区为例

空间溢出对产业集群形成发展具有重要意义。但空间溢出对生产性服务业集群的影响机制并不清楚。本文基于1 km×1 km网格和2013年广州市中心区--天河区的企业经济普查数据，采用空间数据分析技术，识别生产性服务业集群，分析集群特征，探测集群溢出类型。结果发现：①生产性服务业集群区位指向大城市中心区的核心地域，具有五种集群类型分异，空间呈不完全耦合。②生产性服务业集群空间规模受Jocobs型和MAR型两种溢出调控，在MAR型溢出作用下的集群空间规模相对较小。③信息服务业集群的溢出为负效应说明溢出作为一种潜在利益，在转化为集群优势的过程中存在过滤效应。