  We investigate the large-scale clustering of the final spectroscopic sample
of quasars from the recently completed extended Baryon Oscillation
Spectroscopic Survey (eBOSS). The sample contains $343708$ objects in the
redshift range $0.8<z<2.2$ and $72667$ objects with redshifts $2.2<z<3.5$,
covering an effective area of $4699~{\rm deg}^{2}$. We develop a neural
network-based approach to mitigate spurious fluctuations in the density field
caused by spatial variations in the quality of the imaging data used to select
targets for follow-up spectroscopy. Simulations are used with the same angular
and radial distributions as the real data to estimate covariance matrices,
perform error analyses, and assess residual systematic uncertainties. We
measure the mean density contrast and cross-correlations of the eBOSS quasars
against maps of potential sources of imaging systematics to address algorithm
effectiveness, finding that the neural network-based approach outperforms
standard linear regression. Stellar density is one of the most important
sources of spurious fluctuations, and a new template constructed using data
from the Gaia spacecraft provides the best match to the observed quasar
clustering. The end-product from this work is a new value-added quasar
catalogue with the improved weights to correct for nonlinear imaging systematic
effects, which will be made public. Our quasar catalogue is used to measure the
local-type primordial non-Gaussianity in our companion paper, Mueller et al. in
preparation.
