Identifying clusters on a discrete periodic lattice via machine learning

Given the ubiquity of lattice models in physics, it is imperative for researchers to possess robust methods for quantifying clusters on the lattice — whether they be Ising spins or clumps of molecules. Inspired by biophysical studies, we present Python code for handling clusters on a 2D periodic lattice. Properties of individual clusters, such as their area, can be obtained with a few function calls. Our code invokes an unsupervised machine learning method called hierarchical clustering, which is simultaneously effective for the present problem and simple enough for non-experts to grasp qualitatively. Moreover, our code transparently merges clusters neighboring each other across periodic boundaries using breadth-first search (BFS), an algorithm well-documented in computer science pedagogy. The fact that our code is written in Python – instead of proprietary languages – further enhances its value for reproducible science.鉴于晶格模型在物理学中应用广泛，研究者亟需掌握稳健的晶格团簇量化方法——无论团簇对应伊辛自旋（Ising spins）还是分子聚集体。受生物物理学研究启发，我们开发了用于处理二维周期性晶格上团簇的Python代码。仅需数次函数调用，即可获取单个团簇的各项属性（如面积）。本代码调用了一种名为层次聚类（hierarchical clustering）的无监督机器学习方法，该方法既适用于当前研究场景，又足够简洁，可让非专业人员从定性层面理解其原理。此外，本代码借助广度优先搜索（breadth-first search, BFS）——一种在计算机科学教学中被广泛阐释的经典算法——透明地合并周期性边界两侧的相邻团簇。相较于专有编程语言，本代码采用Python编写，这进一步提升了其在可复现科学（reproducible science）领域的应用价值。