Local and global spatio-temporal entropy indices based on distance-ratios and co-occurrences distributions

When it comes to characterize the distribution of 'things' observed spatially and identified by their geometries and attributes, the Shannon entropy has been widely used in different domains such as ecology, regional sciences, epidemiology and image analysis. In particular, recent research has taken into account the spatial patterns derived from topological and metric properties in order to propose extensions to the measure of entropy. Based on two different approaches using either distance-ratios or co-occurrences of observed classes, the research developed in this paper introduces several new indices and explores their extensions to the spatio-temporal domains which are derived whilst investigating further their application as global and local indices. Using a multiplicative space-time integration approach either at a macro or micro-level, the approach leads to a series of spatio-temporal entropy indices including from combining co-occurrence and distances-ratios approaches. The framework developed is complementary to the spatio-temporal clustering problem, introducing a more spatial and spatio-temporal structuring perspective using several indices characterizing the distribution of several class instances in space and time. The whole approach is first illustrated on simulated data evolutions of three classes over seven time stamps. Preliminary results are discussed for a study of conflicting maritime activities in the Bay of Brest where the objective is to explore the spatio-temporal patterns exhibited by a categorical variable with six classes, each representing a conflict between two maritime activities.