  We explore unsupervised machine learning for galaxy morphology analyses using
a combination of feature extraction with a vector-quantised variational
autoencoder (VQ-VAE) and hierarchical clustering (HC). We propose a new
methodology that includes: (1) consideration of the clustering performance
simultaneously when learning features from images; (2) allowing for various
distance thresholds within the HC algorithm; (3) using the galaxy orientation
to determine the number of clusters. This setup provides 27 clusters created
with this unsupervised learning which we show are well separated based on
galaxy shape and structure (e.g., S\'ersic index, concentration, asymmetry,
Gini coefficient). These resulting clusters also correlate well with physical
properties such as the colour-magnitude diagram, and span the range of
scaling-relations such as mass vs. size amongst the different machine-defined
clusters. When we merge these multiple clusters into two large preliminary
clusters to provide a binary classification, an accuracy of $\sim87\%$ is
reached using an imbalanced dataset, matching real galaxy distributions, which
includes 22.7\% early-type galaxies and 77.3\% late-type galaxies. Comparing
the given clusters with classic Hubble types (ellipticals, lenticulars, early
spirals, late spirals, and irregulars), we show that there is an intrinsic
vagueness in visual classification systems, in particular galaxies with
transitional features such as lenticulars and early spirals. Based on this, the
main result in this work is not how well our unsupervised method matches visual
classifications and physical properties, but that the method provides an
independent classification that may be more physically meaningful than any
visually based ones.
