3D-VoCC: 3D vortex correlation clustering on spatial data based on masked hough transform

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.