On Integrating Size and Shape Distributions into a Spatio-Temporal Information Entropy Framework

Abstract

Understanding the structuration of spatio-temporal information is a common endeavour to many disciplines and application domains, e.g., geography, ecology, urban planning, epidemiology. Revealing the processes involved, in relation to one or more phenomena, is often the first step before elaborating spatial functioning theories and specific planning actions, e.g., epidemiological modelling, urban planning. To do so, the spatio-temporal distributions of meaningful variables from a decision-making viewpoint, can be explored, analysed separately or jointly from an information viewpoint. Using metrics based on the measure of entropy has a long practice in these domains with the aim of quantification of how uniform the distributions are. However, the level of embedding of the spatio-temporal dimension in the metrics used is often minimal. This paper borrows from the landscape ecology concept of patch size distribution and the approach of permutation entropy used in biomedical signal processing to derive a spatio-temporal entropy analysis framework for categorical variables. The framework is based on a spatio-temporal structuration of the information allowing to use a decomposition of the Shannon entropy which can also embrace some existing spatial or temporal entropy indices to reinforce the spatio-temporal structuration. Multiway correspondence analysis is coupled to the decomposition entropy to propose further decomposition and entropy quantification of the spatio-temporal structuring information. The flexibility from these different choices, including geographic scales, allows for a range of domains to take into account domain specifics of the data; some of which are explored on a dataset linked to climate change and evolution of land cover types in Nordic areas.

Spatial-Temporal Characteristic Analysis of Ethnic Toponyms Based on Spatial Information Entropy at the Rural Level in Northeast China

“…In this study, a constraint diagram was constructed for the toponymic points, and the Voronoi region corresponding to each point was obtained. For each polygon in the Voronoi region, the thematic information entropy contained in it was calculated according to Equation (11). The N j is the total number of polygon neighbors, and n j is the number of neighbors of the polygon's theme type.…”

“…Some scholars, based on the concept of landscape ecology, have patched size distribution and permutation entropy into biomedical signal processing, from which the framework of spatial and temporal entropy analysis of a class of variables is derived. This framework, which can coordinate the classical methods related to entropy with the latest literature, and better consider the spatial-temporal embedding of information as well as the method of containing entropy, has been applied using land cover evolution data as an example [11]. At present, it is generally believed that map information needs to be measured.…”

Assessing the impact of major historical events on urban landscapes via local entropy measures

“…The application of Shannon entropy to spatial urban data has been pioneered by [17], and since then replicated in a number of studies, including [18], [19]. Shannon entropy is an intuitive measure of the heterogeneity of the distribution {p k } k .…”

Understanding the expansion of Italian metropolitan areas: A study based on entropy measures

“…Another approach to spatial entropy starts from a transformation of the study variable (O’Neill et al., 1988) and accounts for distance between realizations. Recently, Leibovici and Claramunt (2019) extend the method to spatiotemporal studies with the consideration of the size of the land cover patch. The same approach is the basis for a series of papers by Altieri et al.…”