%0 Journal Article
%@ 1874-8961
%A Pei, Tao
%A State Key Laboratory of Resources and Environmental Information System, Institute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences, 11A, Datun Road Anwai, Beijing 100101, China,
%D 2011
%F epos:1283
%I Springer Verlag
%J Mathematical Geosciences
%K Nearest-neighbor · Feature · Noise · Cluster · Poisson process · Complete spatial randomness
%N 3
%P 345-362
%T A Nonparametric Index for Determining the Numbers of Events in Clusters
%U https://episodesplatform.eu/eprints/1283/
%V 43
%X The task of discriminating between heterogeneity and complete spatial randomness (CSR) for a given point process can be divided into three subtasks: the identification of the point pattern; the determination of the sizes of clusters; and the estimation of the numbers of events in dominant clusters. Many studies have been performed regarding the first and second subtasks. However, limited work has been done on the third aspect; hence, the determination of the number of events in each dominant cluster is still an unsolved problem. In this paper, we provide a solution by constructing a new index which is defined as the ratio between the variance of the (k + 1)th nearest distance and that of the kth nearest distance. Our method can be divided into two phases: the detection of point pattern and the estimation of the numbers of events in dominant clusters. These phases can be estimated by the val- ues at which the index abruptly decreases to be less than 1. A comparative study between the existing indices and our index shows the following: (i) our index can in- dicate the numbers of events in dominant clusters in a relatively objective way, which is different from the K-function revealing the sizes of clustered patterns; (ii) it is a nonparametric index and is easy to implement; and (iii) it demonstrates the highest detection power for differentiating between heterogeneity and CSR. The simulations and two seismic case studies also confirmed the correctness of our method.