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.     

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.     

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.     

Nonparametric Significance Test for Discovery of Network‐Constrained Spatial Co‐Location Patterns

Spatial co‐location patterns are useful for understanding positive spatial interactions among different geographical phenomena. Existing methods for detecting spatial co‐location patterns are mostly developed based on planar space assumption; however, geographical phenomena related to human activities are strongly constrained by road networks. Although these methods can be simply modified to consider the constraints of networks by using the network distance or network partitioning scheme, user‐specified parameters or priori assumptions for determining prevalent co‐location patterns are still subjective. As a result, some co‐location patterns may be wrongly reported or omitted. Therefore, a nonparametric significance test without priori assumptions about the distributions of the spatial features is proposed in this article. Both point‐dependent and location‐dependent network‐constrained summary statistics are first utilized to model the distribution characteristics of the spatial features. Then, by using these summary statistics, a network‐constrained pattern reconstruction method is developed to construct the null model of the test, and the prevalence degree of co‐location patterns is modeled as the significance level. The significance test is evaluated using the facility points‐of‐interest data sets. Experiments and comparisons show that the significance test can effectively detect network‐constrained spatial co‐location patterns with less priori knowledge and outperforms two state‐of‐the‐art methods in excluding spurious patterns.     

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.     

Local Indicators of Spatial Association—LISA

The capabilities for visualization, rapid data retrieval, and manipulation in geographic information systems (GIS) have created the need for new techniques of exploratory data analysis that focus on the “spatial” aspects of the data. The identification of local patterns of spatial association is an important concern in this respect. In this paper, I outline a new general class of local indicators of spatial association (LISA) and show how they allow for the decomposition of global indicators, such as Moran's I, into the contribution of each observation. The LISA statistics serve two purposes. On one hand, they may be interpreted as indicators of local pockets of nonstationarity, or hot spots, similar to the G_i and G*_i statistics of Getis and Ord (1992). On the other hand, they may be used to assess the influence of individual locations on the magnitude of the global statistic and to identify “outliers,” as in Anselin's Moran scatterplot (1993a). An initial evaluation of the properties of a LISA statistic is carried out for the local Moran, which is applied in a study of the spatial pattern of conflict for African countries and in a number of Monte Carlo simulations.     

Constructing the Spatial Weights Matrix Using a Local Statistic

Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W , based on the principle that spatial structure should be considered in a two‐part framework, those units that evoke a distance effect, and those that do not. Our two‐variable local statistics model (LSM) is based on the G_i* local statistic. The local statistic concept depends on the designation of a critical distance, d_c, defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well‐known spatial weights matrix specifications—two different contiguity configurations, three different inverse distance formulations, and three semi‐variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran's I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.     

The Spatial Distribution of French Agricultural Cooperatives: An Exploratory Spatial Data Analysis

Abstract

This paper studies the spatial dynamics of French agricultural cooperatives using the recently developed exploratory spatial data analysis tool. Analysis at the level of French districts in 1995 and 2005 shows strong evidence for global and local spatial autocorrelations in the geographical distribution of agricultural cooperatives. The presence of spatial disparities between French districts is confirmed by the detection of such specific spatial patterns as district clusters, a group of neighbouring districts with the same high or low level of agricultural cooperative activities. A typology of all the different Regions is developed to examine the specific spatial patterns of the agricultural cooperative activities. The results indicate that major organizational changes in cooperatives do not significantly modify the initial dynamics concerning the location of activities.     

The Detection of Clusters Using a Spatial Version of the Chi-Square Goodness-of-Fit Statistic

A test statistic for the detection of spatial clusters is developed by generalizing the common chi-square goodness-of-fit test. The paper includes a discussion of the relationship between the statistic and other associated statistics, and provides an analysis of both its null distribution and power. The paper concludes with the development of a local version of the statistic and an application to leukemia clustering in central New York.     

The Detection of Clusters Using a Spatial Version of the Chi-Square Goodness-of-Fit Statistic

A test statistic for the detection of spatial clusters is developed by generalizing the common chi-square goodness-of-fit test. The paper includes a discussion of the relationship between the statistic and other associated statistics, and provides an analysis of both its null distribution and power. The paper concludes with the development of a local version of the statistic and an application to leukemia clustering in central New York.     

Spatial and environmental impacts on adverse birth outcomes in Ontario

This study assesses the overall spatial variations and neighbourhood‐level “hot spots” of low birth weight and preterm birth incidence within three public health units in Ontario, Canada. The analysis uses a stepwise approach of intra‐class correlation analysis, a spatial scan statistic, and multilevel spatial modeling. Results show that neighbourhood level variation accounts for only 2–3 percent of the total variation of adverse birth outcomes in the study area. However, strong spatial autocorrelation is observed at the neighbourhood level, and spatial clusters of relatively high adverse birth outcome rates exist in areas that are associated with environmental risks, including pollution sources and proximity to highways. Thus, although estimated neighbourhood impacts on adverse birth outcomes are small compared with those of individual‐level risks, local high potential environmental risk areas are identifiable. Environmental surveillance and spatial statistical analysis should be conducted regularly by local health authorities to identify and monitor the impact of environmental changes on health in general and on birth outcomes in particular. Specific community‐oriented health interventions may be required to reduce observed local health impacts.     

Exploring Spatial Patterns Using an Expanded Spatial Autocorrelation Framework

Spatial autocorrelation (SA) is regarded as an important dimension of spatial pattern. SA measures usually consist of two components: measuring the similarity of attribute values and defining the spatial relationships among observations. The latter component is often represented by a spatial weights matrix that predefines spatial relationship between observations in most measures. Therefore, SA measures, in essence, are measures of attribute similarity, conditioned by spatial relationship. Another dimension of spatial pattern can be explored by controlling observations to be compared based upon the degree of attribute similarity. The resulting measures are spatial proximity measures of observations, meeting predefined attribute similarity criteria. Proposed measures reflect degrees of clustering or dispersion for observations meeting certain levels of attribute similarity. An existing spatial autocorrelation framework is expanded to a general framework to evaluate spatial patterns and can accommodate the proposed approach measuring proximity. Analogous to the concept of variogram, clustergram is proposed to show the levels of spatial clustering over a range of attribute similarity, or attribute lags. Specific measures based on the proposed approach are formulated and applied to a hypothetical landscape and an empirical example, showing that these new measures capture spatial pattern information not reflected by traditional spatial autocorrelation measures.     

Ecological Inference and Spatial Variation of Individual Behavior: National Divide and Elections in Catalonia

When in geography one reconstructs individual behavior starting from aggregated data through ecological inference, a crucial aspect is the spatial variation of individual behavior. Basic ecological inference methods treat areas as if they were all exchangeable, which in geographical applications is questionable due to the existence of contextual effects that relate to area location and induce spatial dependence. Here that assumption is avoided by basing ecological inference on a model that simultaneously does a cluster analysis, grouping together areas with similar individual behavior, and an ecological inference analysis in each cluster, estimating the individual behavior in the areas of each group. That allows one to capture most of the spatial dependence and summarize the individual behavior at a local level through the behavior estimated for each cluster. This approach is used to investigate vote switching in Catalonia, where voters split across a national allegiance divide on top of the ideological divide. That leads to Catalans having a lot of options to choose from, and to them voting differently depending on whether the election is for the Catalan parliament or for the Spanish parliament. To investigate that, the results in the two most recent pairs of such elections are analyzed by simultaneously clustering areas based on the similarity of their vote and vote switch patterns, and estimating one vote switch pattern for each cluster. As a result, Catalonia is partitioned into four clusters that have a strong spatial structure, with all the areas in the same cluster having similar demographic composition. The estimated vote switch patterns are quite different across clusters but very similar across pairs of elections, and they help assess how the differential voter turnout and the strategic dual vote effects vary in space.     

p‐Functional Clusters Location Problem for Detecting Spatial Clusters with Covering Approach

Regionalization or districting problems commonly require each individual spatial unit to participate exclusively in a single region or district. Although this assumption is appropriate for some regionalization problems, it is less realistic for delineating functional clusters, such as metropolitan areas and trade areas where a region does not necessarily have exclusive coverage with other regions. This paper develops a spatial optimization model for detecting functional spatial clusters, named the p‐functional clusters location problem (p‐FCLP), which has been developed based on the Covering Location Problem. By relaxing the complete and exhaustive assignment requirement, a functional cluster is delineated with the selective spatial units that have substantial spatial interaction. This model is demonstrated with applications for a functional regionalization problem using three journey‐to‐work flow datasets: (1) among the 46 counties in South Carolina, (2) the counties in the East North Central division of the US Census, and (3) all counties in the US. The computational efficiency of p‐FCLP is compared with other regionalization problems. The computational results show that detecting functional spatial clusters with contiguity constraints effectively solves problems with optimality in a mixed integer programming (MIP) approach, suggesting the ability to solve large instance applications of regionalization problems.     

A Supplemental Indicator of High-Value or Low-Value Spatial Clustering

Most test statistics for detecting spatial clustering cannot distinguish between low-value spatial clustering and high-value spatial clustering, and none is designed to explicitly detect high-value clustering, low-value clustering, or both. To fill this void in practice, we introduce an adjustment procedure that can supplement common two-sided spatial clustering tests so that a one-sided conclusion can be reached. The procedure is applied to Moran's I and Tango's C _G in both simulated and real-world spatial patterns. The results show that the adjustment procedure can account for the influence of low-value clusters on high-value clustering and vice versa. The procedure has little effect on the original global testing methods when there is no clustering. When there is a clustering tendency, the procedure can unambiguously distinguish the existence of high-value clusters or low-value clusters or both.     

Exploring Goodness-of-Fit and Spatial Correlation Using Components of Tango's Index of Spatial Clustering

The ability to detect anomalies such as spatial clustering in data sets plays an important role in spatial data analysis, leading to interest in test statistics identifying patterns exhibiting significant levels of clustering. Toward this end, Tango (1995) proposed a statistic (and its associated distribution under a null hypothesis of no clustering) assessing overall patterns of spatial clustering in a set of observed regional counts. Rogerson (1999) observed that Tango's index may be decomposed into the summation of two distinct statistics, the first mirroring standard tests of goodness-of-fit (GOF), and the second an index of spatial association (SA) similar to Moran's I . In this article, we investigate the effectiveness of Rogerson's expression of Tango's statistic in separating GOF from SA in data sets containing clusters. We simulate data under the null hypothesis of no clustering as well as two alternative hypotheses. The first alternative hypothesis induces a poor fit from the null hypothesis while maintaining independent observations and the second alternative hypothesis induces spatial dependence while maintaining fit. Using Rogerson's decomposition and leukemia incidence data from upstate New York, we show graphically that one is unable to statistically distinguish poor fit from autocorrelation.     

Spatial/temporal mismatch: a conflation protocol for Canada Census spatial files

The Canada census is one of the chief sources of demographic and socio-economic data for researchers in this country. Census variables are linked to geography files that allow researchers using geographic information systems (GIS) to view and analyze spatial data. Some of the most useful analysis, however, is based on changes in attribute values over time and space. Analysis of spatio- temporal events such as shifting migration patterns or changes in the distribution of health status permits a more dimensioned perspective than the viewing of static spatial phenomena. The analysis of spatio-temporal phenomena is limited by major changes in the spatial framework (e.g., location of road networks and other spatial entities) between national censuses. This paper addresses this limitation by (i) illustrating the extent of spatial mismatch between the 1996 and the 2001 census; (ii) examining attempts to rectify this problem in other jurisdictions and (iii) presenting a 'made-in-Canada' solution for conflation of census geometries. We believe that this solution will enhance the ability of Canadian researchers to describe and analyze socio-economic, health and demographic shifts across time and space. The research is supported by an ftp site for downloading the census geography rectification software presented in this paper.     

Refining the definition of cultural levels at Karabi Tamchin: a quantitative approach to vertical intra-site spatial analysis

The visual identification of archaeological levels can be difficult when stratigraphy is complex. This study emphasizes the importance of three-dimensional intra-site spatial analysis as a means of testing the integrity of archaeological levels, including the identification of palimpsest deposits. A geographical information system (GIS) is applied to a three-dimensional spatial analysis of lithic and bone distributions from Karabi Tamchin, a Middle Palaeolithic site from the Crimea, Ukraine. K-means statistical clustering is combined with a series of data transformations to identify and interpret the vertical and horizontal spatial organization of the site. The results indicate that K-means cluster analysis, used in conjunction with GIS, provides an exceptional method of identifying discrete clusters of archaeological materials in three dimensions. Through an analysis of cluster contents within levels, it is possible to reconstruct and compare patterns of spatial organization at Karabi Tamchin, contributing to current debates regarding the cognitive complexity of Neanderthal populations.     

Space–Time Sequential Similarity for Identifying Factors of Activity‐Travel Pattern Segmentation: A Measure of Sequence Alignment and Path Similarity

The article develops a new method that compares activity‐travel patterns in both terms of the sequential order of activities and the shape of activity‐travel trajectory in time and space. The similarity of the list of activities and their order between activity‐travel patterns are computed by a sequence alignment method. The shape of activity‐travel trajectory is compared between the patterns using a path similarity technique that captures the direction and speed of a movement from the current location and the duration of staying at each location. The comparison results, therefore capture how people move around in three‐dimensional space–time choreography that indicates how people conduct which activities in what order. A total of 1,000 individuals are sampled from the data of 2016 Household Travel Survey, South Korea. The data provide the information of individual activity‐travel behavior and personal characteristics. The suggested method computes the pairwise distance matrix, and Ward clustering algorithm segments the pattern groups of similar activity sequences and space–time trajectories. A CHAID analysis then associates personal and household characteristics with the pattern groups to identify important factors for the segmentation. The analysis provides a significant implication in both terms of research and practice in transportation.