Abstract The discovery of patterns in spatial and spatio-temporal data is crucial across scientific disciplines studying natural phenomena to enhance our understanding of the real world. These phenomena display complex patterns, necessitating novel specialized pattern mining techniques. In this paper, we introduce Vortex Correlation Clustering which aims to identify a subgroup of such complex pattern, namely correlated groups of objects oriented along a vortex. This can be achieved by adapting the Circle Hough Transform, already known from image analysis. The presented adaptations not only allow to cluster objects depending on their relative location next to each other, but also allows to take the orientation of individual objects into consideration. A multi-step approach allows to analyze and aggregate cluster candidates, allowing a certain deviation from the reference shape in the final clusters. Further adaptations allow to analyze clusters along a third dimension, which allows to reflect the shape of real-world objects in a three dimensional space. We evaluate our approach upon a real world application, to cluster particle simulations composing such shapes. Our approach outperforms comparable methods for this application, both in terms of effectiveness and efficiency. Additionally, we discuss how the adaptation enables further analysis capabilities. For instance, in the presented use case, the introduced approach allows to additionally analyze clusters throughout the depth of the water. So far, this is not feasible with existing approaches.

A special focus in data mining is to identify agglomerations of data points in spatial or spatio-temporal databases. Multiple applications have been presented to make use of such clustering algorithms. However, applications exist, where not only dense areas have to be identified, but also requirements regarding the correlation of the cluster to a specific shape must be met, i.e. circles. This is the case for eddy detection in marine science, where eddies are not only specified by their density, but also their circular-shaped rotation. Traditional clustering algorithms lack the ability to take such aspects into account.

Marine scientists investigate the movement of oceanic water particles with floating measurement devices released in the real ocean, as well as with virtual particles released in numerical model simulations. The detection, visualization, and evolution of clustered particles is key for gaining a comprehensive understanding of the underlying processes in the oceans. Thereby, vast amounts of mobility data (3D coordinates of these particles over time) need to be analyzed using mobility data science methods. In this paper, we describe the application of data science techniques to detect particle clusters and, more importantly, to track the evolution of these clusters over time in order to support the analysis of oceanic flows. In particular, we apply a well-known concept for tracking the cluster evolution from the data mining community that relies on pair-counting and, thus, is rather inefficient. In order to be applicable to large amounts of particles, we further elaborate two heuristic solutions to compute the cluster transitions based on spatial approximations. Experiments on real world data show a considerable speed-up while sacrificing marginal accuracy drops. Our prototype is used by domain experts for the analysis of the large-scale ocean by virtual particle release experiments in ocean simulations.