  Galaxy morphology offers significant insights into the evolutionary pathways
and underlying physics of galaxies. As astronomical data grows with surveys
such as Euclid and Vera C. Rubin , there is a need for tools to classify and
analyze the vast numbers of galaxies that will be observed. In this work, we
introduce a novel classification technique blending unsupervised clustering
based on morphological metrics with the scalability of supervised Convolutional
Neural Networks. We delve into a comparative analysis between the well-known
CAS (Concentration, Asymmetry, and Smoothness) metrics and our newly proposed
EGG (Entropy, Gini, and Gradient Pattern Analysis). Our choice of the EGG
system stems from its separation-oriented metrics, maximizing morphological
class contrast. We leverage relationships between metrics and morphological
classes, leading to an internal agreement between unsupervised clustering and
supervised classification. Applying our methodology to the Sloan Digital Sky
Survey data, we obtain 95% of Overall Accuracy of purely unsupervised
classification and when we replicate T-Type and visually classified galaxy
catalogs with accuracy of 88% and 89% respectively, illustrating the method's
practicality. Furthermore, the application to Hubble Space Telescope data
heralds the potential for unsupervised exploration of a higher redshift range.
A notable achievement is our 95% accuracy in unsupervised classification, a
result that rivals when juxtaposed with Traditional Machine Learning and
closely trails when compared to Deep Learning benchmarks.
