On integrating size and shape distributions into a spatio-temporal information entropy framework

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.