We show a new approach for detecting hotspots in spatial analysis based on the extended Gustafson-Kessel clustering method encapsulated in a Geographic Information System (GIS) tool. This algorithm gives (in the bidimensional case) ellipses as cluster prototypes to be considered as hotspots on the geographic map and we study their spatiotemporal evolution. The data consist of georeferenced patterns corresponding to positions of Taliban’s attacks against civilians and soldiers in Afghanistan that happened during the period 2004–2010. We analyze the formation through time of new hotspots, the movement of the related centroids, the variation of the surface covered, the inclination angle, and the eccentricity of each hotspot. 1. Introduction Hotspot detection is a known spatial clustering process in which it is necessary to detect spatial areas on which specific events thicken [1]; the patterns are the events georeferenced as points on the map; the features are the geographical coordinates (latitude and longitude) of any event. Hotspot detection is used in many disciplines, as in crime analysis [2–4], for analyzing where crimes occur with a certain frequency, in fire analysis [5] for studying the phenomenon of forest fires, and in disease analysis [6–9] for studying the localization and the focuses of diseases. Generally speaking, for detecting more accurately the geometrical shapes of hotspot areas algorithms based on density [10, 11] are used and they measure the spatial distribution of patterns on the area of study, but these algorithms have a high computational complexity. In [5, 12, 13] a new hotspot detection method based on the extended fuzzy C-means algorithm (EFCM) [14, 15] was proposed, which is a variation of the famous fuzzy C-means (FCM) algorithm that detects cluster prototypes as hyperspheres. With respect to the FCM algorithm, the EFCM algorithm has the advantages of determining recursively the optimal number of clusters and being robust in the presence of noise and outliers. In [5, 12, 13] the EFCM is encapsulated in a GIS tool for detecting hotspots as circles displayed on the map. The pattern event dataset is partitioned according to the time of the event’s detection, so each subset is corresponding to a specific time interval. The authors compare the hotspots obtained in two consecutive years by studying their intersection on the map. In this way it is possible to follow the evolution of a particular phenomenon studying how its incidence is shifting and spreading through time. In this paper we present a new hotspot detection method based
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