E(2)-Equivariant Features in Machine Learning for Morphological Classification of Radio Galaxies

TL;DR

This paper explores the use of E(2)-equivariant features like Minkowski functionals, Haralick features, and elliptical Fourier descriptors for classifying radio galaxies, achieving comparable accuracy to CNNs with significantly less computational cost.

Contribution

It introduces the use of directly extracted E(2)-equivariant features for radio galaxy classification, reducing computational costs compared to G-steerable CNNs.

Findings

MF features are most informative for classification.

E(2)-equivariant features require ~50 times less computation.

Combining features yields marginal accuracy improvements.

Abstract

With the growth of data from new radio telescope facilities, machine-learning approaches to the morphological classification of radio galaxies are increasingly being utilised. However, while widely employed deep-learning models using convolutional neural networks (CNNs) are equivariant to translations within images, neither CNNs nor most other machine-learning approaches are equivariant to additional isometries of the Euclidean plane, such as rotations and reflections. Recent work has attempted to address this by using G-steerable CNNs, designed to be equivariant to a specified subset of 2-dimensional Euclidean, E(2), transformations. Although this approach improved model performance, the computational costs were a recognised drawback. Here we consider the use of directly extracted E(2)-equivariant features for the classification of radio galaxies. Specifically, we investigate the use of Minkowski functionals (MFs), Haralick features (HFs) and elliptical Fourier descriptors (EFDs). We show that, while these features do not perform equivalently well to CNNs in terms of accuracy, they are able to inform the classification of radio galaxies, requiring ~50 times less computational runtime. We demonstrate that MFs are the most informative, EFDs the least informative, and show that combinations of all three result in only incrementally improved performance, which we suggest is due to information overlap between feature sets.