Academic journal article Geographical Analysis

Assessing the Cluster Correspondence between Paired Point Locations

Academic journal article Geographical Analysis

Assessing the Cluster Correspondence between Paired Point Locations

Article excerpt

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 w 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.

1. INTRODUCTION

Many spatial phenomena can be conceptualized as elemental events of zero dimension and can be represented as a single set of points for geographical investigation. The well-established techniques of spatial statistics (Diggle 1983; Upton and Fingleton 1985; Boots and Getis 1988; Bailey and Gatrel] 1995; Fotheringham, Brunsdon, and Charlton 2000) provide methodological support for the analysis of such point patterns. When multiple sets of zero-dimensional events interact with each other during certain geographical processes (e.g., the coexistence and interdependence of different species of trees), multivariate spatial point analysis techniques exist to represent and analyze the distribution of multiple point sets (Diggle 1983). By extending the spatial statistical analysis of single point sets to that of multiple point sets, these techniques enable a broader set of research questions to be addressed, such as whether the pattern in the occurrences of one type of event is related to that of another.

Besides simple geographical processes that link each event to a single location, some geographical events exhibit the added complexity of association with multiple point locations. Such events include, but are not limited to, those describing some linkage between and among places. The linking can be based on physical connections, functional interactions, or any other process relating one place to another. Such is the case of geospatial lifelines, a special class of spatiotemporal data identified and defined by Mark and Egenhofer (1998) as "continuous set[s] of positions occupied by an object in geographic space over some time period." Migration and journey-to-work associating origins with destinations, information exchange connecting places through telecommunication, and crime events developing spatial relationships between criminals' base locations and the corresponding offense sites are but three examples of such complex geographical phenomena. To provide a complete description of these complex phenomena, related analysis will have to take into consideration the association of multiple locations through a single geographical event. In this paper, we use the term multi-location events to refer to such complex geographical phenomena.

The most important aspect for multi-location events is that a certain point from one location set is associated with a specific point from another location set through the construction of a specific event. For example, any work trip links a specific residential place with a specific workplace. Because of the structure embedded in multi-location events, techniques of multivariate spatial pattern analysis cannot effectively describe their spatial pattern. Multivariate spatial pattern analysis considers the points belonging to distinct location sets to be generated by independent processes. …

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