  The ever-growing sample of observed supernovae enhances our capacity for
comprehensive supernova population studies, providing a richer dataset for
understanding the diverse characteristics of Type Ia supernovae and possibly
that of their progenitors. Here, we present a data-driven analysis of observed
Type Ia supernova photometric light curves collected in the Open Supernova
Catalog. Where available, we add the environmental information from the host
galaxy. We focus on identifying sub-classes of Type Ia supernovae without
imposing the pre-defined sub-classes found in the literature to date. To do so,
we employ an implicit-rank minimizing autoencoder neural network for developing
low-dimensional data representations, providing a compact representation of the
supernova light curve diversity. When we analyze light curves alone, we find
that one of our resulting latent variables is strongly correlated with
redshift, allowing us to approximately ``de-redshift'' the other latent
variables describing each event. After doing so, we find that three of our
latent variables account for $\sim$95\% of the variance in our sample, and
provide a natural separation between 91T and 91bg thermonuclear supernovae. Of
note, the 02cx subclass is not unambiguously delineated from the 91bg sample in
our results, nor do either the over-luminous 91T or the under-luminous
91bg/02cx samples form a clearly distinct population from the broader sample of
``other'' SN Ia events. We identify the physical characteristics of supernova
light curves which best distinguish SNe 91T from SNe 91bg \& 02cx, and discuss
prospects for future refinements and applications to other classes of
supernovae as well as other transients.
