  Searches for continuous gravitational waves target nearly monochromatic
gravitational wave emission from e.g. non-axysmmetric fast-spinning neutron
stars. Broad surveys often require to explicitly search for a very large number
of different waveforms, easily exceeding $\sim10^{17}$ templates. In such
cases, for practical reasons, only the top, say $\sim10^{10}$, results are
saved and followed-up through a hierarchy of stages. Most of these candidates
are not completely independent of neighbouring ones, but arise due to some
common cause: a fluctuation, a signal or a disturbance. By judiciously
clustering together candidates stemming from the same root cause, the
subsequent follow-ups become more effective. A number of clustering algorithms
have been employed in past searches based on iteratively finding symmetric and
compact over-densities around candidates with high detection statistic values.
The new clustering method presented in this paper is a significant improvement
over previous methods: it is agnostic about the shape of the over-densities, is
very efficient and it is effective: at a very high detection efficiency, it has
a noise rejection of $99.99\%$ , is capable of clustering two orders of
magnitude more candidates than attainable before and, at fixed sensitivity it
enables more than a factor of 30 faster follow-ups. We also demonstrate how to
optimally choose the clustering parameters.
