The Multipoint Morisita Index for the Analysis of Spatial Patterns

TL;DR

This paper introduces a new multipoint Morisita index for analyzing spatial clustering, useful for network characterization and pattern detection, with theoretical links to multifractality.

Contribution

It develops an enhanced k-Morisita index for spatial pattern analysis and explores its connection to multifractality, advancing clustering assessment methods.

Findings

The new index effectively detects spatial patterns.

A theoretical link to multifractality is established.

Applications include network monitoring and pattern detection.

Abstract

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 K-function and R\'enyi'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 greater than or equal to 2. The present research deals with a new development of the k-Morisita index for (1) monitoring network characterization and for (2) the 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.