  Kernel Additive Modelling (KAM) is a framework for source separation aiming
to explicitly model inherent properties of sound sources to help with their
identification and separation. KAM separates a given source by applying robust
statistics on the selection of time-frequency bins obtained through a
source-specific kernel, typically the k-NN function. Even though the parameter
k appears to be key for a successful separation, little discussion on its
influence or optimisation can be found in the literature. Here we propose a
novel method, based on graph theory statistics, to automatically optimise $k$
in a vocal separation task. We introduce the k-NN hubness as an indicator to
find a tailored k at a low computational cost. Subsequently, we evaluate our
method in comparison to the common approach to choose k. We further discuss the
influence and importance of this parameter with illuminating results.
