# Identifying Clusters on a Discrete Periodic Lattice via Machine Learning

## TL;DR

This paper introduces Python tools utilizing hierarchical clustering and BFS algorithms to identify and analyze clusters on 2D periodic lattices, facilitating physics research with accessible, reproducible code.

## Contribution

The paper presents an open-source Python implementation combining hierarchical clustering and BFS for cluster detection on periodic lattices, enhancing accessibility and reproducibility.

## Key findings

- Effective clustering of lattice sites using hierarchical methods.
- Transparent merging of clusters across boundaries with BFS.
- Code is accessible and suitable for non-experts.

## Abstract

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.