Figure 1
Example of the different steps of the algorithm for DBSCAN with periodic boundary conditions: (a) original input dataset, (b) periodic extension by ϵ (step 1), (c) DBSCAN of the extended dataset (step 2), (d) final clustering after linking and resolving equivalent clusters (steps 3 & 4). This is a 2D example with periodicity L and neighborhood ϵ = 0.06 L.
Figure 2
1D example of DBSCAN clustering with periodic boundary conditions with periodicity L and neighborhood ϵ = 0.05 L. The example shows the raw data (a) and the clustering (b), where different colors represent different clusters, while black points indicate noise points that do not belong to a cluster.
Figure 3
2D example of DBSCAN clustering with doubly periodic boundary conditions (a,b) and with singly periodic boundary conditions (c,d) where in the latter the left and right boundaries are periodic while the top and bottom boundaries are open. The periodicity is L and neighborhood is ϵ = 0.08 L. Panels and colors are as in Figure 2.
Figure 4
3D example of DBSCAN clustering with triply periodic boundary conditions with periodicity L and neighborhood ϵ = 0.08 L. Panels and colors are as in Figure 2.
Figure 5
Example of DBSCAN clustering on a real dataset of light particles in turbulence in a 3D triply periodic domain with periodicity L and neighborhood ϵ = 0.009 L. Light particles tend to cluster in high-vorticity regions of the flow in filamentary structures. Colors show the six largest clusters of particles as identified by the algorithm. Other clusters are colored in gray for readability.