In many fields, the spatial clustering of sampled data points has
many consequences. Therefore, several indices have been proposed
to assess the level of clustering affecting datasets (e.g. the Morisita
index, Ripley's Kfunction and Rényi's generalized entropy). The classical
Morisita index measures how many times it is more likely to select
two measurement points from the same quadrats (the data set is covered
by a regular grid of changing size) than it would be in the case
of a random distribution generated from a Poisson process. The multipoint
version (k-Morisita) takes into account k points with k >= 2. The
present research deals with a new development of the k-Morisita index
for (1) monitoring network characterization and for (2) detection
of patterns in monitored phenomena. From a theoretical perspective,
a connection between the k-Morisita index and multifractality has
also been found and highlighted on a mathematical multifractal set.