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.
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