  Modern spectroscopic surveys of galaxies such as MaNGA consist of millions of
diverse spectra covering different regions of thousands of galaxies. We propose
and implement a deep unsupervised machine learning method to summarize the
entire diversity of MaNGA spectra onto a 15x15 map (DESOM-1), where
neighbouring points on the map represent similar spectra. We demonstrate our
method as an alternative to conventional full spectral fitting for deriving
physical quantities, as well as their full probability distributions, much more
efficiently than traditional resource-intensive Bayesian methods. Since spectra
are grouped by similarity, the distribution of spectra onto the map for a
single galaxy, i.e., its "fingerprint", reveals the presence of distinct
stellar populations within the galaxy indicating smoother or episodic
star-formation histories. We further map the diversity of galaxy fingerprints
onto a second map (DESOM-2). Using galaxy images and independent measures of
galaxy morphology, we confirm that galaxies with similar fingerprints have
similar morphologies and inclination angles. Since morphological information
was not used in the mapping algorithm, relating galaxy morphology to the
star-formation histories encoded in the fingerprints is one example of how the
DESOM maps can be used to make scientific inferences.
