Exhibited the same kind of unusual behavior (positive or negative) on the same day and if they are very close together or directly connected by a road with no other sites in between. To do this, we create a spatial neighborhood graph G as follows. Each site is associated with a vertex in G. Two vertices are connected by an edge in G if the two corresponding sites are neighbors in the grid cell system or in the road network system we constructed for Rwanda–see Section SI1 in S1 Supporting Information. Two sites are neighbors in the grid cell system if they share an edge or a corner of the grid cells that define them. The road network system connects any two sites based the quickest road paths between their centroids, and does not contain loops, i.e., routes that leave one site, then return to the same site before reaching another destination site. We define two sites as neighbors in the road network system if there does not exist any other site on the quickest route path between them. For a set of sites that had unusual behavior on a particular day, A, the spatial neighborhood graph G induces a subgraph G(A). This is also a graph whose vertices are the set of sites A and whose edges connect those sites in A that are also linked in G. As opposed to G, a subgraph G (A) is not necessarily connected: there could exist sites in A that are not linked by a sequence of edges in this subgraph. The connected components of G(A) (i.e., subgraphs of this graph that are connected) represent the spatial clusters of sites identified by our system. Consider the maps from the second row of Fig. 2. There are 12 sites with higher than normal movement frequency, and 10 of these sites located in the proximity of the Lake Kivu earthquakes belong to one large spatial cluster. The disturbances at these sites were probably caused by the earthquakes. The two remaining sites located in Western Rwanda are farther away from the other 10 sites and from each other, and belong to two other spatial clusters. The anomalous patterns of behavior at these two sites are likely to have been caused by QVD-OPH chemical information events different than the Lake Kivu earthquakes. The number and location of spatial clusters are key for estimating the number and location of outlier events. The number of sites in a single spatial cluster is a key indicator of the possible spatial reach of an event. The more sites in a cluster, the more wide-ranging were the behavioral anomalies, suggesting the wider was the range of the population that was influenced by an event. From another perspective, the largest spatial clusters of sites indicate the most significant events with the largest impact. For example, Figs. 2 and 3 show spatial clusters with one, two,PLOS ONE | DOI:10.1371/journal.pone.0120449 March 25,12 /Spatiotemporal Detection of Unusual Human Population Behaviorand eleven sites per cluster. The impact of the events that caused these clusters was reasonably concentrated in space.ResultsOur anomalous behavior detection system identified many days with unusual calling and movement behavior across multiple sites. Figs. C in S1 Supporting Information show daily time series of the size of the largest spatial clusters of sites that were PX105684 molecular weight extreme positive or negative outliers for one or both of our behavioral measures, call and movement frequency. There are numerous days in which the largest spatial clusters comprise 20, 30 or even more than 60 sites and cover much of the entire country. Here we describe some of th.Exhibited the same kind of unusual behavior (positive or negative) on the same day and if they are very close together or directly connected by a road with no other sites in between. To do this, we create a spatial neighborhood graph G as follows. Each site is associated with a vertex in G. Two vertices are connected by an edge in G if the two corresponding sites are neighbors in the grid cell system or in the road network system we constructed for Rwanda–see Section SI1 in S1 Supporting Information. Two sites are neighbors in the grid cell system if they share an edge or a corner of the grid cells that define them. The road network system connects any two sites based the quickest road paths between their centroids, and does not contain loops, i.e., routes that leave one site, then return to the same site before reaching another destination site. We define two sites as neighbors in the road network system if there does not exist any other site on the quickest route path between them. For a set of sites that had unusual behavior on a particular day, A, the spatial neighborhood graph G induces a subgraph G(A). This is also a graph whose vertices are the set of sites A and whose edges connect those sites in A that are also linked in G. As opposed to G, a subgraph G (A) is not necessarily connected: there could exist sites in A that are not linked by a sequence of edges in this subgraph. The connected components of G(A) (i.e., subgraphs of this graph that are connected) represent the spatial clusters of sites identified by our system. Consider the maps from the second row of Fig. 2. There are 12 sites with higher than normal movement frequency, and 10 of these sites located in the proximity of the Lake Kivu earthquakes belong to one large spatial cluster. The disturbances at these sites were probably caused by the earthquakes. The two remaining sites located in Western Rwanda are farther away from the other 10 sites and from each other, and belong to two other spatial clusters. The anomalous patterns of behavior at these two sites are likely to have been caused by events different than the Lake Kivu earthquakes. The number and location of spatial clusters are key for estimating the number and location of outlier events. The number of sites in a single spatial cluster is a key indicator of the possible spatial reach of an event. The more sites in a cluster, the more wide-ranging were the behavioral anomalies, suggesting the wider was the range of the population that was influenced by an event. From another perspective, the largest spatial clusters of sites indicate the most significant events with the largest impact. For example, Figs. 2 and 3 show spatial clusters with one, two,PLOS ONE | DOI:10.1371/journal.pone.0120449 March 25,12 /Spatiotemporal Detection of Unusual Human Population Behaviorand eleven sites per cluster. The impact of the events that caused these clusters was reasonably concentrated in space.ResultsOur anomalous behavior detection system identified many days with unusual calling and movement behavior across multiple sites. Figs. C in S1 Supporting Information show daily time series of the size of the largest spatial clusters of sites that were extreme positive or negative outliers for one or both of our behavioral measures, call and movement frequency. There are numerous days in which the largest spatial clusters comprise 20, 30 or even more than 60 sites and cover much of the entire country. Here we describe some of th.
