The detection of finite-time coherent particle sets in Lagrangian trajectory data, using data-clustering techniques, is an active research field at the moment. Yet, the clustering methods mostly employed so far have been based on graph partitioning, which assigns each trajectory to a cluster, i.e. there is no concept of noisy, incoherent trajectories. This is problematic for applications in the ocean, where many small, coherent eddies are present in a large, mostly noisy fluid flow. Here, for the first time in this context, we use the density-based clustering algorithm of OPTICS (ordering points to identify the clustering structure; Ankerst et al., 1999) to detect finite-time coherent particle sets in Lagrangian trajectory data. Different from partition-based clustering methods, derived clustering results contain a concept of noise, such that not every trajectory needs to be part of a cluster. OPTICS also has a major advantage compared to the previously used density-based spatial clustering of applications with noise (DBSCAN) method, as it can detect clusters of varying density. The resulting clusters have an intrinsically hierarchical structure, which allows one to detect coherent trajectory sets at different spatial scales at once. We apply OPTICS directly to Lagrangian trajectory data in the Bickley jet model flow and successfully detect the expected vortices and the jet. The resulting clustering separates the vortices and the jet from background noise, with an imprint of the hierarchical clustering structure of coherent, small-scale vortices in a coherent, large-scale background flow. We then apply our method to a set of virtual trajectories released in the eastern South Atlantic Ocean in an eddying ocean model and successfully detect Agulhas rings. We illustrate the difference between our approach and partition-based k-means clustering using a 2D embedding of the trajectories derived from classical multidimensional scaling. We also show how OPTICS can be applied to the spectral embedding of a trajectory-based network to overcome the problems of k-means spectral clustering in detecting Agulhas rings.

中文翻译：

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轨迹的排序揭示了拉格朗日粒子数据中的分层有限时间相干集：在南大西洋检测Agulhas环

使用数据聚类技术检测拉格朗日轨迹数据中的有限时间相干粒子集是当前的活跃研究领域。然而，到目前为止，最常用的聚类方法是基于图划分的，该图划分将每个轨迹分配给一个簇，即没有嘈杂的，不连贯的轨迹的概念。这对于在海洋中的应用是有问题的，在海洋中，在大的，主要是嘈杂的流体流中存在许多小的，连贯的涡流。在这里，在这种情况下，我们首次使用基于密度的OPTICS聚类算法（排序点来识别聚类结构； Ankerst等人，1999）在拉格朗日轨迹数据中检测有限时间相干粒子集。与基于分区的聚类方法不同，派生的聚类结果包含噪声的概念，因此并非每个轨迹都需要成为聚类的一部分。与以前使用的基于噪声的应用程序基于密度的空间聚类（DBSCAN）方法相比，OPTICS还具有一个主要优势，因为它可以检测不同密度的聚类。产生的群集具有固有的层次结构，该群集使人们可以立即检测不同空间尺度上的相干轨迹集。我们将OPTICS直接应用于Bickley射流模型流中的拉格朗日轨迹数据，并成功检测到预期的涡旋和射流。产生的聚类将涡旋和射流与背景噪声分开，在一个连贯的，大型背景流中，具有连贯的，小规模的涡旋的分层聚类结构的烙印。然后，我们将我们的方法应用于在涡流海洋模型中在南大西洋东部释放的一组虚拟轨迹，并成功检测到Agulhas环。我们说明了我们的方法与基于分区的方法之间的区别k-均值使用从经典多维缩放获得的轨迹的2D嵌入进行聚类。我们还展示了如何将OPTICS应用于基于轨迹的网络的光谱嵌入，以克服在检测Agulhas环时k均值光谱聚类的问题。