Modeling the Spectral Diversity of Quasars in the Sixteenth Data Release
  from the Sloan Digital Sky Survey
  We present a new approach to capturing the broad diversity of emission line
and continuum properties in quasar spectra. We identify populations of
spectrally similar quasars through pixel-level clustering on 12,968 high
signal-to-noise spectra from the Sloan Digital Sky Survey (SDSS) in the
redshift range of $1.57<z<2.4$. Our clustering analysis finds 396 quasar
spectra that are not assigned to any population, 15 misclassified spectra, and
six quasars with incorrect redshifts. We compress the quasar populations into a
library of 684 high signal-to-noise composite spectra, anchored in redshift
space by the Mg II emission line. Principal component analysis on the library
results in an eigenspectrum basis spanning 1067 to 4007 $\r{A}$. We model
independent samples of SDSS quasar spectra with the eigenbasis, allowing for a
free redshift parameter. Our models achieve a median reduced chi-squared on
non-BAL quasar spectra that is reduced by 8.5% relative to models using the
eigenspectra from the SDSS spectroscopic pipeline. A significant contribution
to the relative improvement is from the ability to reconstruct the range of
emission line variation. The redshift estimates from our model are consistent
with the Mg II emission line redshift with an average offset that displays
51.4% less redshift-dependent variation relative to the SDSS eigenspectra. Our
method for developing quasar spectra models can improve automated
classification and predict the intrinsic spectrum in regions affected by
intervening absorbers such as Ly$\alpha$, C IV, and Mg II, thus benefiting
studies of large-scale structure.
