Published on Tue Jan 31 2017

Prototypal Analysis and Prototypal Regression

Chenyue Wu, Esteban G. Tabak

Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality. Prototypal regression is developed, a supervised procedure which allows the use of distributions as either features or labels.

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Abstract

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.

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