Dark soliton detection using persistent homology.

Area of Science:

• Physics
• Data Science
• Machine Learning

Background:

• Image classification typically relies on manual feature identification.
• Machine learning models like convolutional neural networks offer high accuracy but demand substantial data and computational power for training.

Purpose of the Study:

• To demonstrate the utility of persistent homology for rapid and reliable identification of qualitative features in experimental image data.
• To enable the use of these features as inputs for simpler, more easily trained supervised machine learning models.

Main Methods:

• Application of persistent homology, a topological data analysis technique, to experimental image datasets.
• Utilizing identified topological features as inputs for logistic regression models, a type of simple supervised learning model.

Main Results:

• Persistent homology effectively identifies qualitative image features.
• The identified features facilitate the training of simpler machine learning models.
• Successful application demonstrated in classifying dark solitons within atomic Bose-Einstein condensate density images.

Conclusions:

• Persistent homology provides an efficient alternative to traditional feature extraction methods in image classification.
• This technique reduces the data and computational requirements for training machine learning models.
• The method shows promise for analyzing complex experimental image data, such as in quantum physics.