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In a spatio-temporal data set, identifying spatio-temporal clusters is difficult because of the coupling of time and space and the interference of noise. Previous methods employ either the window scanning technique or the spatio-temporal distance technique to identify spatio-temporal clusters. Although easily implemented, they suffer from the subjectivity in the choice of parameters for classification. In this article, we use the windowed kth nearest (WKN) distance (the geographic distance between an event and its kth geographical nearest neighbour among those events from which to the event the temporal distances are no larger than the half of a specified time window width [TWW]) to differentiate clusters from noise in spatio-temporal data. The windowed nearest neighbour (WNN) method is composed of four steps. The first is to construct a sequence of TWW factors, with which the WKN distances of events can be computed at different temporal scales. Second, the appropriate values of TWW (i.e. the appropriate temporal scales, at which the number of false positives may reach the lowest value when classifying the events) are indicated by the local maximum values of densities of identified clustered events, which are calculated over varying TWW by using the expectation-maximization algorithm. Third, the thresholds of the WKN distance for classification are then derived with the determined TWW. In the fourth step, clustered events identified at the determined TWW are connected into clusters according to their density connectivity in geographic-temporal space. Results of simulated data and a seismic case study showed that the WNN method is efficient in identifying spatio-temporal clusters. The novelty of WNN is that it can not only identify spatio-temporal clusters with arbitrary shapes and different spatio-temporal densities but also significantly reduce the subjectivity in the classification process. [ABSTRACT FROM AUTHOR]

When two spatial point processes are overlaid, the one with the higher rate is shown as clustered points, and the other one with the lower rate is often perceived to be background. Usually, we consider the clustered points as feature and the background as noise. Revealing these point clusters allows us to further examine and understand the spatial point process. Two important aspects in discerning spatial cluster features from a set of points are the removal of noise and the determination of the number of spatial clusters. Until now, few methods were able to deal with these two aspects at the same time in an automated way. In this study, we combine the nearest-neighbour (NN) method and the concept of density-connected to address these two aspects. First, the removal of noise can be achieved using the NN method; then, the number of clusters can be determined by finding the density-connected clusters. The complexity for finding density-connected clusters is reduced in our algorithm. Since the number of clusters depends on the value of k (the k th nearest neighbour), we introduce the concept of lifetime for the number of clusters in order to measure how stable the segmentation results (or number of clusters) are. The number of clusters with the longest lifetime is considered to be the final number of clusters. Finally, a seismic example of the west part of China is used as a case study to examine the validity of our method. In this seismic case study, we discovered three seismic clusters: one as the foreshocks of the Songpan quake ( M = 7.2), and the other two as aftershocks related to the Kangding-Jiulong ( M = 6.2) quake and Daguan quake ( M = 7.1), respectively. Through this case study, we conclude that the approach we proposed is effective in removing noise and determining the number of feature clusters. [ABSTRACT FROM AUTHOR]

Abstract: Clustered events are usually deemed as feature when several spatial point processes are overlaid in a region. They can be perceived either as a precursor that may induce a major event to come or as offspring triggered by a major event. Hence, the detection of clustered events from point processes may help to predict a forthcoming major event or to study the process caused by a major event. Nevertheless, the locations of existing clustered events alone are not sufficient to identify the area susceptible to a potential major future event or to predict the potential locations of similar future events, so it is desirable to know the shape and the size of the region (the “territory” of feature events) that the feature process occupies. In this paper, the support domain of feature (SDF), the region over which any feature event has the equivalent likelihood to occur, is employed to approximate the “territory” of feature events. A method is developed to delineate the SDF from a region containing spatial point processes. The method consists of three major steps. The first is to construct a discrimination function for separating feature points from noise points. The second is to divide the entire area into a regular mesh of points and then compute a fuzzy membership value for each grid point belonging to the SDF. The final step is to trace the boundary of the SDF. The algorithm was applied to two seismic cases for evaluation, one is the Lingwu earthquake and the other is the Longling earthquakes. Results show that the main earthquakes in both areas as well as most aftershocks triggered by them fell into the estimated SDFs. The case study of Longling shows that the algorithm can deal with a region containing more than two processes. [Copyright &y& Elsevier]