Hierarchical granular hotspots detection

  • Ferdinando Di MartinoEmail author
  • Witold Pedrycz
  • Salvatore Sessa
Methodologies and Application


We present a hierarchical model based on the extended fuzzy C-means (EFCM) clustering algorithm to develop a granular view of hotspots on a geographic map. The objective is to establish an overview of the spatial distribution of a phenomenon when the relevant data are partitioned into different datasets. The EFCM algorithm is applied to each dataset to detect local hotspots, represented as circles, on the map. The local hotspots constitute information granules at lower level of abstraction in the model. A weighted EFCM algorithm is then applied to a dataset formed by the centers of all the local hotspots to extract circular prototypes, defined as global hotspots, which constitute information granules at the higher level, and hence, they deliver a global overview of the spatial distribution of the phenomenon on the map. Two indices related to the essential criteria of the principle of justifiable granularity are used. The results demonstrate that the most justifiable overview is obtained by using the radius of the local hotspot as weight. Comparisons with a hierarchical model based on FCM algorithm show that our algorithm gives a better granular view of the phenomenon with respect to the latter.


Hotspot EFCM wEFCM Information granule 



This research was performed under the auspices of GCNS-INDAM. No specific grant from funding agencies or economic supports in the public, commercial, or not-for-profit sectors was received during this research.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Dipartimento di Architettura and Centro Interdipartimentale di Ricerca “A. Calza Bini”Università degli Studi di Napoli Federico IINaplesItaly
  2. 2.Department of Electrical and Computer EngineeringUniversity of AlbertaEdmontonCanada

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