Measuring change similarity of spatial entities: The case of the criminal history of place
Badurek, Christopher A
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Limitations to representations for spatiotemporal data and query languages are well documented in the geographic information systems (GIS) literature. The primary purpose of this study is to develop a method for measuring similarity of change among discrete areal objects and to extend current approaches for representing change in GIS. This research identifies the primary elements necessary for formalizing spatial change query language operators and develops a method for assessing the similarity of spatial change in the context of crime analysis. There are four main goals of this work. First, it is shown that similarity queries require semantics associated with three fundamental elements of this phenomenon: rate, magnitude, and direction of change. Second, based on the fundamental elements derived, a formal description of all possible relations among a target and referent with regard to similarity of change is presented. This formal description demonstrates a set of five basic similarity operators that represent ideal types of possible kinds of similarity of change relationships. A mathematical method based on the fundamental elements is presented by which similarity values can be derived. The usefulness of this model is then demonstrated through a case study of crime in São Paulo, Brazil. Third, the similarity measure is compared to the Structured Query Language (SQL) and Change Description Language (CDL) in order to determine if it is more expressive for reasoning about change among objects. Assessment has shown that it has advantages over these other query languages in efficiency and expressiveness. Fourth, to determine if the similarity query language is effective in practice, its expressiveness is evaluated in regard to requirements of the crime analysis domain. It was determined from this evaluation that the five basic similarity operators that form the basis of the language capture the semantics required for queries of spillover effects in crime data. It is also determined that the resolution of temporal intervals used has a measurable effect on the consistency of query results. The result of these activities has provided a formal model for reasoning about change using the concept of similarity tested in the context of crime applications.