  We present a new method for the mitigation of observational systematic
effects in angular galaxy clustering via corrective random galaxy catalogues.
Real and synthetic galaxy data, from the Kilo Degree Survey's (KiDS)
4$^{\rm{th}}$ Data Release (KiDS-$1000$) and the Full-sky Lognormal
Astro-fields Simulation Kit (FLASK) package respectively, are used to train
self-organising maps (SOMs) to learn the multivariate relationships between
observed galaxy number density and up to six systematic-tracer variables,
including seeing, Galactic dust extinction, and Galactic stellar density. We
then create `organised' randoms, i.e. random galaxy catalogues with spatially
variable number densities, mimicking the learnt systematic density modes in the
data. Using realistically biased mock data, we show that these organised
randoms consistently subtract spurious density modes from the two-point angular
correlation function $w(\vartheta)$, correcting biases of up to $12\sigma$ in
the mean clustering amplitude to as low as $0.1\sigma$, over a high
signal-to-noise angular range of 7-100 arcmin. Their performance is also
validated for angular clustering cross-correlations in a bright, flux-limited
subset of KiDS-$1000$, comparing against an analogous sample constructed from
highly-complete spectroscopic redshift data. Each organised random catalogue
object is a `clone' carrying the properties of a real galaxy, and is
distributed throughout the survey footprint according to the parent galaxy's
position in systematics-space. Thus, sub-sample randoms are readily derived
from a single master random catalogue via the same selection as applied to the
real galaxies. Our method is expected to improve in performance with increased
survey area, galaxy number density, and systematic contamination, making
organised randoms extremely promising for current and future clustering
analyses of faint samples.
