  In the near future, all-sky radio surveys are set to produce catalogues of
tens of millions of sources with limited multi-wavelength photometry.
Spectroscopic redshifts will only be possible for a small fraction of these
new-found sources. In this paper, we provide the first in-depth investigation
into the use of k-Nearest Neighbours Regression for the estimation of redshift
of these sources. We use the Australia Telescope Large Area Survey radio data,
combined with the Spitzer Wide-Area Infrared Extragalactic Survey infra-red,
the Dark Energy Survey optical and the Australian Dark Energy Survey
spectroscopic survey data. We then reduce the depth of photometry to match what
is expected from upcoming Evolutionary Map of the Universe survey, testing
against both data sets. To examine the generalisation of our methods, we test
one of the sub-fields of Australia Telescope Large Area Survey against the
other. We achieve an outlier rate of ~10% across all tests, showing that the
k-Nearest Neighbours regression algorithm is an acceptable method of estimating
redshift, and would perform better given a sample training set with uniform
redshift coverage.
