  Prototypal analysis is introduced to overcome two shortcomings of archetypal
analysis: its sensitivity to outliers and its non-locality, which reduces its
applicability as a learning tool. Same as archetypal analysis, prototypal
analysis finds prototypes through convex combination of the data points and
approximates the data through convex combination of the archetypes, but it adds
a penalty for using prototypes distant from the data points for their
reconstruction. Prototypal analysis can be extended---via kernel embedding---to
probability distributions, since the convexity of the prototypes makes them
interpretable as mixtures. Finally, prototypal regression is developed, a
robust supervised procedure which allows the use of distributions as either
features or labels.
