Real-word phenomena, such as ocean eddies and clouds, tend to split and merge while they are moving around within a space. Their trajectories usually bear one or more branches and are accordingly defined as complex trajectories in this study. The trajectories may show significant spatiotemporal variations in terms of their structures and some of them may be more prominent than the others. The identification of prominent structures in the complex trajectories of such real-world phenomena could better reveal their evolution processes and even shed new light on the driving factors behind them. Methods have been proposed for the extraction of periodic patterns from simple trajectories (i.e., those with linear structure and without any branches) with a focus on mining the related temporal, spatial or semantic information. Unfortunately, it is not appropriate to directly use such methods to examine complex trajectories. This study proposes a novel method to study the periodic patterns of complex trajectories by considering the inherent spatial, temporal and topological information. First, we use a sequence of symbols to represent the various structures of a complex trajectory over its lifespan. We then, on the basis of the PrefixSpan algorithm, propose a periodic pattern mining of structural evolution (PPSE) algorithm and use it to identify the largest and most frequent patterns (LFPs) from the symbol sequence. We also identify potential periodic behaviors. The PPSE method is then used to examine the complex trajectories of the mesoscale eddy in the South China Sea (SCS) from 1993 to 2016. The complex trajectories of ocean eddies in the southeast of Vietnam show are different from other regions in the SCS in terms of their structural evolution processes, as indicated by the LFPs with the longest lifespan, the widest active range, the highest complexity, and the most active behaviors. The LFP in the southeast of Vietnam has the longest lifespan, the widest active range, the highest complexity, and the most active behaviors. Across the SCS, we found seven migration channels. The LFPs of the eddies that migrate through these channels have a temporal cycle of 17–24 years. These channels are also the regions where eddies frequently emerge, as revealed by flow field data.
Clustering Complex Trajectories Based on Topologic Similarity and Spatial Proximity: A Case Study of the Mesoscale Ocean Eddies in the South China Sea