Representation and Spatial Analysis in Geographic Information Systems

Abstract

A common-perhaps modal-representation of geography in spatial analysis and geographic information systems is native (unexamined) objects interacting based on simple distance and connectivity relationships within an empty Euclidean space. This is only one possibility among a large set of geographic representations that can support quantitative analysis. Through the vehicle of GIS, many researchers are adopting this representation without realizing its assumptions or its alternatives. Rather than locking researchers into a single representation, GIS could serve as a toolkit for estimating and exploring alternative geographic representations and their analytical possibilities. The article reviews geographic representations, their associated analytical possibilities and relevant computational tools in the combined spatial analysis and GIScience literatures. The discussion identifies several research and development frontiers, including analytical gaps in current GIS software.A common-perhaps modal-representation of geography in spatial analysis (SA) and geographic information systems (GIS) is native (unexamined) objects interacting based on simple distance and connectivity relationships within an empty Euclidean plane. This representation has essentially remained untouched since its inception during the birth of quantitative geography and computer cartography, an era characterized by scarce geographic data, weak computers, and crude spatial algorithms. It is only one possibility among a large set that can support ''analysis,'' or the ability to measure and infer quantitative properties and relationships. 1 The Euclidean model is useful in many contexts, such as cartography, navigation, and many types of analysis. However, there may be latent explanatory power in geographic space not captured by the Euclidean model and consequently missed by SA techniques and GIS-based analysis based on this georepresentation. Representation and analysis are closely linked: mathematical and computational tools, however powerful, cannot extract more information than is latent in a representation.Through the vehicle of GIS, many researchers are adopting the Euclidean model and its related analytical possibilities without realizing its assumptions or its alternatives. Rather than locking researchers into a single representation, GIS could serve as a toolkit for estimating and exploring alternative geographic representations and their analytical possibilities for a given geographic phenomenon or problem. Reconsidering and expanding the geographic representation model underpinning both SA and GIS is an unexplored avenue for improving analytical capabilities of both.Theories and techniques for alternative geographic representations and analyses exist in the SA and geographic information science (GIScience) literatures. 2 SA has a small but steady current of literature on representation issues in analysis, including theories of geographic space and techniques for estimating distance metrics, analyzing geographic relationships between spatial...

The Minkowski approach for choosing the distance metric in geographically weighted regression

“…Here, p can be chosen to approximate known distance types. For example, Miller and Wentz (2003) show that TT in an urban setting could be represented by p values ranging from 1 to 2. Furthermore, as each individual GWR calibration is independent from each other, it would be straightforward to apply parallel computing techniques (e.g.…”

“…For example, Shahabi et al (2002) and Shahid et al (2009) use Minkowski distance to approximate road distances and TTs. Love et al (1988), cited by Miller and Wentz (2003), indicate that the value of p typically ranges from 1 to 2 for representing the true travel distance at urban and regional scales. For a spatial model that is adapted to use Minkowski distances, optimal values of p and θ are commonly found that minimize some goodness-of-fit (GoF) criteria.…”

Exploring Regionalization in the Network Urban Space

“…The most common perspective is to replace the Euclidean distance measures with network distances (Miller and Wentz 2003). Spatial optimization models often treat network distances between locations either as a quantitative measure such as in a point location model (Church and Murray 2008b) or as a virtual link network that is transformed from relationships between neighboring objects.…”

Spatiotemporal enabled Content-based Image Retrieval

“…There is little here to suggest a sustained research theme of alternative models of space. As Mark and Frank note, "except for geodesics on cost surfaces, nonEuclidean geometries have not made significant inroads into mainstream geographic models" (1996,17), a claim substantially true today, which also hints at the crux of the problem: the lockin effects of existing GIS, regardless of the efforts of GIScientists (Miller and Wentz 2003). Of course, computation does require reduction and abstraction of events to textual, numeric, or otherwise programmatically understood representations (Ullman 1997, Drucker 2009).…”