  Spectral clustering is a popular and versatile clustering method based on a
relaxation of the normalised graph cut objective. Despite its popularity,
however, there is no single agreed upon method for tuning the important scaling
parameter, nor for determining automatically the number of clusters to extract.
Popular heuristics exist, but corresponding theoretical results are scarce. In
this paper we investigate the asymptotic value of the normalised cut for an
increasing sample assumed to arise from an underlying probability distribution,
and based on this result provide recommendations for improving spectral
clustering methodology. A corresponding algorithm is proposed with strong
empirical performance.
