Modes or Modal-sets are points or regions of space where the underlying data density is locally-maximal. They are relevant in problems such as clustering, outlier detection, or can simply serve to identify salient structures in high-dimensional data (e.g. point-cloud data from medical imaging, astronomy, etc).

In this talk we will argue that modal-sets, as general extremal surfaces, yield more stable clustering than usual modes (extremal points) of a density. For one, modal-sets can be consistently estimated, at non-trivial convergence rates, despite the added complexity of unknown surface-shape and dimension. Furthermore, modal-sets neatly dovetail into existing approaches that cluster data around point-modes, yielding competitive, yet more stable clustering on a range of real-world problems.