Spatial Entropy Measures

In this chapter, we start by highlighting the drawbacks of using traditional entropy measures for the analysis of environmental data. Then, we present the main approaches available in the literature for the consideration of the spatial dimension in entropy indices. In particular, Sect. 2.2 contains Batty’s approach to spatial entropy for geographical data, and its extension for the inclusion of a neighbourhood system. Section 2.3 outlines the other main branch of proposals, based on the simultaneous consideration of couples (or sets) of realizations occurring at a certain distance over space. The following Sect. 2.4 presents a recent proposal for the simultaneous inclusion of all distances within the observation area. Such spatial entropy measure satisfies the additivity property of partial terms into a global value over a set of distance classes, and exploits the decomposition of entropy proposed in Information Theory to quantify the contribution of space to the system’s heterogeneity. All proposals are offered under a unified notation, pros and cons of each approach are highlighted, and their ability to draw conclusions is compared, in order to guide the reader to the most suitable option for the study at hand. The final Sects. 2.5 and 2.6 show the practical work on two case studies with a focus on result interpretation and on the explanation of the essential R code for the main steps.