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.

中文翻译：

---

复杂轨迹结构的演化模式挖掘-以南海中尺度涡旋为例

诸如海洋漩涡和云等实词现象在空间中四处移动时往往会分裂和融合。它们的轨迹通常带有一个或多个分支，因此在本研究中被定义为复杂轨迹。轨迹在结构上可能显示出显着的时空变化，并且其中一些可能比其他轨迹更为突出。在这种现实世界现象的复杂轨迹中识别出突出的结构可以更好地揭示它们的演化过程，甚至为它们背后的驱动因素提供新的启示。已经提出了从简单轨迹（即具有线性结构且没有任何分支的轨迹）中提取周期性模式的方法，重点是挖掘相关的时间，空间或语义信息。不幸，直接使用此类方法检查复杂轨迹是不合适的。这项研究提出了一种新颖的方法，通过考虑固有的空间，时间和拓扑信息来研究复杂轨迹的周期模式。首先，我们使用一系列符号来表示复杂轨迹在其生命周期中的各种结构。然后，我们在PrefixSpan算法的基础上，提出了一种结构演化的周期性模式挖掘（PPSE）算法，并使用它来从符号序列中识别出最大和最频繁的模式（LFP）。我们还确定了潜在的周期性行为。然后使用PPSE方法检查1993年至2016年南海中尺度涡旋的复杂轨迹。越南东南部海洋涡旋的复杂轨迹与南海其他地区的结构演化过程不同，这是生命周期最长，活动范围最广，复杂度最高和最远的LFP所表明的。积极的行为。越南东南部的LFP寿命最长，活动范围最广，复杂性最高，​​行为最活跃。在整个SCS中，我们发现了七个迁移渠道。通过这些通道迁移的涡旋的LFP的时间周期为17-24年。这些通道也是涡流频繁出现的区域，如流场数据所示。最高的复杂性和最活跃的行为。越南东南部的LFP寿命最长，活动范围最广，复杂性最高，​​行为最活跃。在整个SCS中，我们发现了七个迁移渠道。通过这些通道迁移的涡旋的LFP的时间周期为17-24年。这些通道也是涡流频繁出现的区域，如流场数据所示。最高的复杂性和最活跃的行为。越南东南部的LFP寿命最长，活动范围最广，复杂性最高，​​行为最活跃。在整个SCS中，我们发现了七个迁移渠道。通过这些通道迁移的涡旋的LFP的时间周期为17-24年。这些通道也是涡流频繁出现的区域，如流场数据所示。