DBSCAN in domains with periodic boundary conditions
This work addresses the need for efficient clustering methods in scientific domains with periodic data, such as cyclic or rotational symmetries, though it is incremental as it builds on the existing DBSCAN algorithm.
The authors tackled the problem of clustering data in periodic domains by adapting the DBSCAN algorithm to handle periodic boundary conditions, achieving the same optimized runtime complexity of O(N log N) and demonstrating its application on synthetic and real-world turbulent flow data.
Many scientific problems involve data that is embedded in a space with periodic boundary conditions. This can for instance be related to an inherent cyclic or rotational symmetry in the data or a spatially extended periodicity. When analyzing such data, well-tailored methods are needed to obtain efficient approaches that obey the periodic boundary conditions of the problem. In this work, we present a method for applying a clustering algorithm to data embedded in a periodic domain based on the DBSCAN algorithm, a widely used unsupervised machine learning method that identifies clusters in data. The proposed method internally leverages the conventional DBSCAN algorithm for domains with open boundaries, such that it remains compatible with all optimized implementations for neighborhood searches in open domains. In this way, it retains the same optimized runtime complexity of $O(N\log N)$. We demonstrate the workings of the proposed method using synthetic data in one, two and three dimensions and also apply it to a real-world example involving the clustering of bubbles in a turbulent flow. The proposed approach is implemented in a ready-to-use Python package that we make publicly available.