Galaxy Morphological Classification with Zernike Moments and Machine Learning Approaches

Classifying galaxies is an essential step for studying their structures and dynamics. Using GalaxyZoo2 (GZ2) fractions thresholds, we collect 545 and 11,735 samples in non-galaxy and galaxy classes, respectively. We compute the Zernike moments (ZMs) for GZ2 images, extracting unique and independent characteristics of galaxies. The uniqueness due to the orthogonality and completeness of Zernike polynomials, reconstruction of the original images with minimum errors, invariances (rotation, translation, and scaling), different block structures, and discriminant decision boundaries of ZMs' probability density functions for different order numbers indicate the capability of ZMs in describing galaxy features. We classify the GZ2 samples, firstly into the galaxies and non-galaxies and secondly, galaxies into spiral, elliptical, and odd objects (e.g., ring, lens, disturbed, irregular, merger, and dust lane). The two models include the support vector machine (SVM) and one-dimensional convolutional neural network (1D-CNN), which use ZMs, compared with the other three classification models of 2D-CNN, ResNet50, and VGG16 that apply the features from original images. We find the true skill statistic (TSS) greater than 0.86 for the SVM and 1D-CNN with ZMs for the oversampled galaxy-non-galaxy classifier. The SVM with ZMs model has a high-performance classification for galaxy and non-galaxy datasets. We show that the SVM with ZMs, 1D-CNN with ZMs, and VGG16 with vision transformer are high-performance (accuracy larger than 0.90 and TSS greater than 0.86) models for classifying the galaxies into spiral, elliptical, and odd objects. We conclude that these machine-learning algorithms are helpful tools for classifying galaxy images.