Complexities in spatial center derivation

Abstract The center of a spatial object or set of objects is a rather straightforward and well understood descriptor. Beyond providing a statistically oriented interpretation of the middle of something, the center often has much significance in terms of locating services and activities, but may also represent a place of political/historical importance, a site that explains the occurrence of events, or a position that avoids conflict. Even so, precise definition and specification of the spatial center is difficult, as many alternatives exist for such a descriptor in practice. This is because different interpretations of a spatial center are inevitable depending on context, theory, and operational nuances. As a result, a range of approaches may reflect the necessary descriptive flexibility, depending on the type of evaluation being carried out. While legacy mathematical and statistical thinking may point to particular alternatives, spatial significance and bias remain questionable for some approaches as they are not generally well understood. Further, a host of other considerations, such as direct and indirect summary along with homogeneous and heterogeneous attribute distribution, contribute additional levels of detail to choices for best characterizing a center. Definitions and approaches used to specify the center of a spatial object, or set of objects, are detailed to demonstrate the significance of spatial context, and are used to show that expanded interpretations are possible.