将DBSCAN算法扩展到周期性边界空间，高效处理具有循环对称性的数据聚类。
DBSCAN in domains with periodic boundary conditions
- 基于传统DBSCAN思想，在周期域内重构邻近关系计算机制
- 保持$O(N\log N)$时间复杂度，兼容现有优化实现
- 适用于流体气泡、晶体结构等具周期性特征的数据分析
许多科学问题涉及嵌入在周期边界条件空间中的数据，例如数据中存在固有的循环或旋转对称性，或空间上的周期性分布。针对此类数据的分析需要专门设计的方法以满足问题的周期边界特性。本文提出一种基于DBSCAN的聚类方法，适用于嵌入周期域的数据。该方法在内部利用传统DBSCAN算法处理开边界域的机制，从而保持与所有优化邻域搜索实现的兼容性，运行时间复杂度仍为$O(N\log N)$。通过一维、二维和三维的合成数据验证了方法的有效性，并应用于湍流中气泡聚类的真实案例。所提方法已实现为可直接使用的Python工具包并公开发布。
原文摘要 · Abstract (English)
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.
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