Dark soliton detection using persistent homology

TL;DR

This paper demonstrates how persistent homology, a topological data analysis method, can efficiently identify dark solitons in atomic Bose-Einstein condensate images, simplifying feature extraction for machine learning.

Contribution

It introduces a topological approach for feature detection in experimental images, reducing reliance on extensive training data and computational resources.

Findings

Persistent homology accurately identifies dark solitons in BEC images.

Simple supervised models like logistic regression perform well with topological features.

The method offers a rapid, reliable alternative to traditional image classification techniques.

Abstract

Classifying images often requires manual identification of qualitative features. Machine learning approaches including convolutional neural networks can achieve accuracy comparable to human classifiers, but require extensive data and computational resources to train. We show how a topological data analysis technique, persistent homology, can be used to rapidly and reliably identify qualitative features in experimental image data. The identified features can be used as inputs to simple supervised machine learning models such as logistic regression models, which are easier to train. As an example we consider the identification of dark solitons using a dataset of 6257 labelled atomic Bose-Einstein condensate density images.